id	sid	tid	token	lemma	pos
cord-326631-7gd3hjc3	1	1	key	key	NN
cord-326631-7gd3hjc3	1	2	:	:	:
cord-326631-7gd3hjc3	2	1	cord-326631	cord-326631	NNP
cord-326631-7gd3hjc3	2	2	-	-	HYPH
cord-326631-7gd3hjc3	2	3	7gd3hjc3	7gd3hjc3	CD
cord-326631-7gd3hjc3	2	4	authors	author	NNS
cord-326631-7gd3hjc3	2	5	:	:	:
cord-326631-7gd3hjc3	2	6	Ma	Ma	NNP
cord-326631-7gd3hjc3	2	7	,	,	,
cord-326631-7gd3hjc3	2	8	Junling	Junling	NNP
cord-326631-7gd3hjc3	2	9	;	;	:
cord-326631-7gd3hjc3	2	10	Earn	earn	VB
cord-326631-7gd3hjc3	2	11	,	,	,
cord-326631-7gd3hjc3	2	12	David	David	NNP
cord-326631-7gd3hjc3	2	13	J.	J.	NNP
cord-326631-7gd3hjc3	2	14	D.	D.	NNP
cord-326631-7gd3hjc3	2	15	title	title	NN
cord-326631-7gd3hjc3	2	16	:	:	:
cord-326631-7gd3hjc3	3	1	Generality	generality	NN
cord-326631-7gd3hjc3	3	2	of	of	IN
cord-326631-7gd3hjc3	3	3	the	the	DT
cord-326631-7gd3hjc3	3	4	Final	Final	NNP
cord-326631-7gd3hjc3	3	5	Size	Size	NNP
cord-326631-7gd3hjc3	3	6	Formula	Formula	NNP
cord-326631-7gd3hjc3	3	7	for	for	IN
cord-326631-7gd3hjc3	3	8	an	an	DT
cord-326631-7gd3hjc3	3	9	Epidemic	epidemic	NN
cord-326631-7gd3hjc3	3	10	of	of	IN
cord-326631-7gd3hjc3	3	11	a	a	DT
cord-326631-7gd3hjc3	3	12	Newly	newly	RB
cord-326631-7gd3hjc3	3	13	Invading	invade	VBG
cord-326631-7gd3hjc3	3	14	Infectious	Infectious	NNP
cord-326631-7gd3hjc3	3	15	Disease	Disease	NNP
cord-326631-7gd3hjc3	3	16	date	date	NN
cord-326631-7gd3hjc3	3	17	:	:	:
cord-326631-7gd3hjc3	3	18	2006	2006	CD
cord-326631-7gd3hjc3	3	19	-	-	HYPH
cord-326631-7gd3hjc3	3	20	04	04	CD
cord-326631-7gd3hjc3	3	21	-	-	HYPH
cord-326631-7gd3hjc3	3	22	08	08	CD
cord-326631-7gd3hjc3	3	23	journal	journal	NN
cord-326631-7gd3hjc3	3	24	:	:	:
cord-326631-7gd3hjc3	4	1	Bull	Bull	NNP
cord-326631-7gd3hjc3	4	2	Math	Math	NNP
cord-326631-7gd3hjc3	4	3	Biol	Biol	NNP
cord-326631-7gd3hjc3	4	4	DOI	DOI	NNP
cord-326631-7gd3hjc3	4	5	:	:	:
cord-326631-7gd3hjc3	4	6	10.1007	10.1007	CD
cord-326631-7gd3hjc3	4	7	/	/	SYM
cord-326631-7gd3hjc3	4	8	s11538	s11538	NNP
cord-326631-7gd3hjc3	4	9	-	-	HYPH
cord-326631-7gd3hjc3	4	10	005	005	CD
cord-326631-7gd3hjc3	4	11	-	-	HYPH
cord-326631-7gd3hjc3	4	12	9047	9047	CD
cord-326631-7gd3hjc3	4	13	-	-	SYM
cord-326631-7gd3hjc3	4	14	7	7	CD
cord-326631-7gd3hjc3	4	15	sha	sha	NN
cord-326631-7gd3hjc3	4	16	:	:	:
cord-326631-7gd3hjc3	4	17	e4dc4fb77ff0a8a10cf07bf0cceb5ad06e722d0c	e4dc4fb77ff0a8a10cf07bf0cceb5ad06e722d0c	NNP
cord-326631-7gd3hjc3	4	18	doc_id	doc_id	CD
cord-326631-7gd3hjc3	4	19	:	:	:
cord-326631-7gd3hjc3	4	20	326631	326631	CD
cord-326631-7gd3hjc3	4	21	cord_uid	cord_uid	NNS
cord-326631-7gd3hjc3	4	22	:	:	:
cord-326631-7gd3hjc3	4	23	7gd3hjc3	7gd3hjc3	CD
cord-326631-7gd3hjc3	5	1	The	the	DT
cord-326631-7gd3hjc3	5	2	well	well	RB
cord-326631-7gd3hjc3	5	3	-	-	HYPH
cord-326631-7gd3hjc3	5	4	known	know	VBN
cord-326631-7gd3hjc3	5	5	formula	formula	NN
cord-326631-7gd3hjc3	5	6	for	for	IN
cord-326631-7gd3hjc3	5	7	the	the	DT
cord-326631-7gd3hjc3	5	8	final	final	JJ
cord-326631-7gd3hjc3	5	9	size	size	NN
cord-326631-7gd3hjc3	5	10	of	of	IN
cord-326631-7gd3hjc3	5	11	an	an	DT
cord-326631-7gd3hjc3	5	12	epidemic	epidemic	NN
cord-326631-7gd3hjc3	5	13	was	be	VBD
cord-326631-7gd3hjc3	5	14	published	publish	VBN
cord-326631-7gd3hjc3	5	15	by	by	IN
cord-326631-7gd3hjc3	5	16	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	5	17	and	and	CC
cord-326631-7gd3hjc3	5	18	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	5	19	in	in	IN
cord-326631-7gd3hjc3	5	20	1927	1927	CD
cord-326631-7gd3hjc3	5	21	.	.	.
cord-326631-7gd3hjc3	6	1	Their	-PRON-	PRP$
cord-326631-7gd3hjc3	6	2	analysis	analysis	NN
cord-326631-7gd3hjc3	6	3	was	be	VBD
cord-326631-7gd3hjc3	6	4	based	base	VBN
cord-326631-7gd3hjc3	6	5	on	on	IN
cord-326631-7gd3hjc3	6	6	a	a	DT
cord-326631-7gd3hjc3	6	7	simple	simple	JJ
cord-326631-7gd3hjc3	6	8	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	6	9	-	-	HYPH
cord-326631-7gd3hjc3	6	10	infected	infected	JJ
cord-326631-7gd3hjc3	6	11	-	-	HYPH
cord-326631-7gd3hjc3	6	12	recovered	recovered	JJ
cord-326631-7gd3hjc3	6	13	(	(	-LRB-
cord-326631-7gd3hjc3	6	14	SIR	SIR	NNP
cord-326631-7gd3hjc3	6	15	)	)	-RRB-
cord-326631-7gd3hjc3	6	16	model	model	NN
cord-326631-7gd3hjc3	6	17	that	that	WDT
cord-326631-7gd3hjc3	6	18	assumes	assume	VBZ
cord-326631-7gd3hjc3	6	19	exponentially	exponentially	RB
cord-326631-7gd3hjc3	6	20	distributed	distribute	VBN
cord-326631-7gd3hjc3	6	21	infectious	infectious	JJ
cord-326631-7gd3hjc3	6	22	periods	period	NNS
cord-326631-7gd3hjc3	6	23	.	.	.
cord-326631-7gd3hjc3	7	1	More	More	JJR
cord-326631-7gd3hjc3	7	2	recent	recent	JJ
cord-326631-7gd3hjc3	7	3	analyses	analysis	NNS
cord-326631-7gd3hjc3	7	4	have	have	VBP
cord-326631-7gd3hjc3	7	5	established	establish	VBN
cord-326631-7gd3hjc3	7	6	that	that	IN
cord-326631-7gd3hjc3	7	7	the	the	DT
cord-326631-7gd3hjc3	7	8	standard	standard	JJ
cord-326631-7gd3hjc3	7	9	final	final	JJ
cord-326631-7gd3hjc3	7	10	size	size	NN
cord-326631-7gd3hjc3	7	11	formula	formula	NN
cord-326631-7gd3hjc3	7	12	is	be	VBZ
cord-326631-7gd3hjc3	7	13	valid	valid	JJ
cord-326631-7gd3hjc3	7	14	regardless	regardless	RB
cord-326631-7gd3hjc3	7	15	of	of	IN
cord-326631-7gd3hjc3	7	16	the	the	DT
cord-326631-7gd3hjc3	7	17	distribution	distribution	NN
cord-326631-7gd3hjc3	7	18	of	of	IN
cord-326631-7gd3hjc3	7	19	infectious	infectious	JJ
cord-326631-7gd3hjc3	7	20	periods	period	NNS
cord-326631-7gd3hjc3	7	21	,	,	,
cord-326631-7gd3hjc3	7	22	but	but	CC
cord-326631-7gd3hjc3	7	23	that	that	IN
cord-326631-7gd3hjc3	7	24	it	-PRON-	PRP
cord-326631-7gd3hjc3	7	25	fails	fail	VBZ
cord-326631-7gd3hjc3	7	26	to	to	TO
cord-326631-7gd3hjc3	7	27	be	be	VB
cord-326631-7gd3hjc3	7	28	correct	correct	JJ
cord-326631-7gd3hjc3	7	29	in	in	IN
cord-326631-7gd3hjc3	7	30	the	the	DT
cord-326631-7gd3hjc3	7	31	presence	presence	NN
cord-326631-7gd3hjc3	7	32	of	of	IN
cord-326631-7gd3hjc3	7	33	certain	certain	JJ
cord-326631-7gd3hjc3	7	34	kinds	kind	NNS
cord-326631-7gd3hjc3	7	35	of	of	IN
cord-326631-7gd3hjc3	7	36	heterogeneous	heterogeneous	JJ
cord-326631-7gd3hjc3	7	37	mixing	mixing	NN
cord-326631-7gd3hjc3	7	38	(	(	-LRB-
cord-326631-7gd3hjc3	7	39	e.g.	e.g.	RB
cord-326631-7gd3hjc3	7	40	,	,	,
cord-326631-7gd3hjc3	7	41	if	if	IN
cord-326631-7gd3hjc3	7	42	there	there	EX
cord-326631-7gd3hjc3	7	43	is	be	VBZ
cord-326631-7gd3hjc3	7	44	a	a	DT
cord-326631-7gd3hjc3	7	45	core	core	NN
cord-326631-7gd3hjc3	7	46	group	group	NN
cord-326631-7gd3hjc3	7	47	,	,	,
cord-326631-7gd3hjc3	7	48	as	as	IN
cord-326631-7gd3hjc3	7	49	for	for	IN
cord-326631-7gd3hjc3	7	50	sexually	sexually	RB
cord-326631-7gd3hjc3	7	51	transmitted	transmit	VBN
cord-326631-7gd3hjc3	7	52	diseases	disease	NNS
cord-326631-7gd3hjc3	7	53	)	)	-RRB-
cord-326631-7gd3hjc3	7	54	.	.	.
cord-326631-7gd3hjc3	8	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	8	2	review	review	VBP
cord-326631-7gd3hjc3	8	3	previous	previous	JJ
cord-326631-7gd3hjc3	8	4	work	work	NN
cord-326631-7gd3hjc3	8	5	and	and	CC
cord-326631-7gd3hjc3	8	6	establish	establish	VB
cord-326631-7gd3hjc3	8	7	more	more	JJR
cord-326631-7gd3hjc3	8	8	general	general	JJ
cord-326631-7gd3hjc3	8	9	conditions	condition	NNS
cord-326631-7gd3hjc3	8	10	under	under	IN
cord-326631-7gd3hjc3	8	11	which	which	WDT
cord-326631-7gd3hjc3	8	12	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	8	13	and	and	CC
cord-326631-7gd3hjc3	8	14	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	8	15	's	's	POS
cord-326631-7gd3hjc3	8	16	formula	formula	NN
cord-326631-7gd3hjc3	8	17	is	be	VBZ
cord-326631-7gd3hjc3	8	18	valid	valid	JJ
cord-326631-7gd3hjc3	8	19	.	.	.
cord-326631-7gd3hjc3	9	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	9	2	show	show	VBP
cord-326631-7gd3hjc3	9	3	that	that	IN
cord-326631-7gd3hjc3	9	4	the	the	DT
cord-326631-7gd3hjc3	9	5	final	final	JJ
cord-326631-7gd3hjc3	9	6	size	size	NN
cord-326631-7gd3hjc3	9	7	formula	formula	NN
cord-326631-7gd3hjc3	9	8	is	be	VBZ
cord-326631-7gd3hjc3	9	9	unchanged	unchanged	JJ
cord-326631-7gd3hjc3	9	10	if	if	IN
cord-326631-7gd3hjc3	9	11	there	there	EX
cord-326631-7gd3hjc3	9	12	is	be	VBZ
cord-326631-7gd3hjc3	9	13	a	a	DT
cord-326631-7gd3hjc3	9	14	latent	latent	JJ
cord-326631-7gd3hjc3	9	15	stage	stage	NN
cord-326631-7gd3hjc3	9	16	,	,	,
cord-326631-7gd3hjc3	9	17	any	any	DT
cord-326631-7gd3hjc3	9	18	number	number	NN
cord-326631-7gd3hjc3	9	19	of	of	IN
cord-326631-7gd3hjc3	9	20	distinct	distinct	JJ
cord-326631-7gd3hjc3	9	21	infectious	infectious	JJ
cord-326631-7gd3hjc3	9	22	stages	stage	NNS
cord-326631-7gd3hjc3	9	23	and/or	and/or	CC
cord-326631-7gd3hjc3	9	24	a	a	DT
cord-326631-7gd3hjc3	9	25	stage	stage	NN
cord-326631-7gd3hjc3	9	26	during	during	IN
cord-326631-7gd3hjc3	9	27	which	which	WDT
cord-326631-7gd3hjc3	9	28	infectives	infective	NNS
cord-326631-7gd3hjc3	9	29	are	be	VBP
cord-326631-7gd3hjc3	9	30	isolated	isolate	VBN
cord-326631-7gd3hjc3	9	31	(	(	-LRB-
cord-326631-7gd3hjc3	9	32	the	the	DT
cord-326631-7gd3hjc3	9	33	durations	duration	NNS
cord-326631-7gd3hjc3	9	34	of	of	IN
cord-326631-7gd3hjc3	9	35	each	each	DT
cord-326631-7gd3hjc3	9	36	stage	stage	NN
cord-326631-7gd3hjc3	9	37	can	can	MD
cord-326631-7gd3hjc3	9	38	be	be	VB
cord-326631-7gd3hjc3	9	39	drawn	draw	VBN
cord-326631-7gd3hjc3	9	40	from	from	IN
cord-326631-7gd3hjc3	9	41	any	any	DT
cord-326631-7gd3hjc3	9	42	integrable	integrable	JJ
cord-326631-7gd3hjc3	9	43	distribution	distribution	NN
cord-326631-7gd3hjc3	9	44	)	)	-RRB-
cord-326631-7gd3hjc3	9	45	.	.	.
cord-326631-7gd3hjc3	10	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	10	2	also	also	RB
cord-326631-7gd3hjc3	10	3	consider	consider	VBP
cord-326631-7gd3hjc3	10	4	the	the	DT
cord-326631-7gd3hjc3	10	5	possibility	possibility	NN
cord-326631-7gd3hjc3	10	6	that	that	IN
cord-326631-7gd3hjc3	10	7	the	the	DT
cord-326631-7gd3hjc3	10	8	transmission	transmission	NN
cord-326631-7gd3hjc3	10	9	rates	rate	NNS
cord-326631-7gd3hjc3	10	10	of	of	IN
cord-326631-7gd3hjc3	10	11	infectious	infectious	JJ
cord-326631-7gd3hjc3	10	12	individuals	individual	NNS
cord-326631-7gd3hjc3	10	13	are	be	VBP
cord-326631-7gd3hjc3	10	14	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	10	15	distributed	distribute	VBN
cord-326631-7gd3hjc3	10	16	—	—	:
cord-326631-7gd3hjc3	10	17	allowing	allow	VBG
cord-326631-7gd3hjc3	10	18	,	,	,
cord-326631-7gd3hjc3	10	19	in	in	IN
cord-326631-7gd3hjc3	10	20	particular	particular	JJ
cord-326631-7gd3hjc3	10	21	,	,	,
cord-326631-7gd3hjc3	10	22	for	for	IN
cord-326631-7gd3hjc3	10	23	the	the	DT
cord-326631-7gd3hjc3	10	24	existence	existence	NN
cord-326631-7gd3hjc3	10	25	of	of	IN
cord-326631-7gd3hjc3	10	26	super	super	JJ
cord-326631-7gd3hjc3	10	27	-	-	NNS
cord-326631-7gd3hjc3	10	28	spreaders	spreader	NNS
cord-326631-7gd3hjc3	10	29	—	—	:
cord-326631-7gd3hjc3	10	30	and	and	CC
cord-326631-7gd3hjc3	10	31	prove	prove	VBP
cord-326631-7gd3hjc3	10	32	that	that	IN
cord-326631-7gd3hjc3	10	33	this	this	DT
cord-326631-7gd3hjc3	10	34	potential	potential	JJ
cord-326631-7gd3hjc3	10	35	complexity	complexity	NN
cord-326631-7gd3hjc3	10	36	has	have	VBZ
cord-326631-7gd3hjc3	10	37	no	no	DT
cord-326631-7gd3hjc3	10	38	impact	impact	NN
cord-326631-7gd3hjc3	10	39	on	on	IN
cord-326631-7gd3hjc3	10	40	the	the	DT
cord-326631-7gd3hjc3	10	41	final	final	JJ
cord-326631-7gd3hjc3	10	42	size	size	NN
cord-326631-7gd3hjc3	10	43	formula	formula	NN
cord-326631-7gd3hjc3	10	44	.	.	.
cord-326631-7gd3hjc3	11	1	Finally	finally	RB
cord-326631-7gd3hjc3	11	2	,	,	,
cord-326631-7gd3hjc3	11	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	11	4	show	show	VBP
cord-326631-7gd3hjc3	11	5	that	that	IN
cord-326631-7gd3hjc3	11	6	the	the	DT
cord-326631-7gd3hjc3	11	7	final	final	JJ
cord-326631-7gd3hjc3	11	8	size	size	NN
cord-326631-7gd3hjc3	11	9	formula	formula	NN
cord-326631-7gd3hjc3	11	10	is	be	VBZ
cord-326631-7gd3hjc3	11	11	unchanged	unchanged	JJ
cord-326631-7gd3hjc3	11	12	even	even	RB
cord-326631-7gd3hjc3	11	13	for	for	IN
cord-326631-7gd3hjc3	11	14	a	a	DT
cord-326631-7gd3hjc3	11	15	general	general	JJ
cord-326631-7gd3hjc3	11	16	class	class	NN
cord-326631-7gd3hjc3	11	17	of	of	IN
cord-326631-7gd3hjc3	11	18	spatial	spatial	JJ
cord-326631-7gd3hjc3	11	19	contact	contact	NN
cord-326631-7gd3hjc3	11	20	structures	structure	NNS
cord-326631-7gd3hjc3	11	21	.	.	.
cord-326631-7gd3hjc3	12	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	12	2	conclude	conclude	VBP
cord-326631-7gd3hjc3	12	3	that	that	IN
cord-326631-7gd3hjc3	12	4	whenever	whenever	WRB
cord-326631-7gd3hjc3	12	5	a	a	DT
cord-326631-7gd3hjc3	12	6	new	new	JJ
cord-326631-7gd3hjc3	12	7	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	12	8	pathogen	pathogen	NN
cord-326631-7gd3hjc3	12	9	emerges	emerge	VBZ
cord-326631-7gd3hjc3	12	10	,	,	,
cord-326631-7gd3hjc3	12	11	an	an	DT
cord-326631-7gd3hjc3	12	12	estimate	estimate	NN
cord-326631-7gd3hjc3	12	13	of	of	IN
cord-326631-7gd3hjc3	12	14	the	the	DT
cord-326631-7gd3hjc3	12	15	expected	expect	VBN
cord-326631-7gd3hjc3	12	16	magnitude	magnitude	NN
cord-326631-7gd3hjc3	12	17	of	of	IN
cord-326631-7gd3hjc3	12	18	the	the	DT
cord-326631-7gd3hjc3	12	19	epidemic	epidemic	NN
cord-326631-7gd3hjc3	12	20	can	can	MD
cord-326631-7gd3hjc3	12	21	be	be	VB
cord-326631-7gd3hjc3	12	22	made	make	VBN
cord-326631-7gd3hjc3	12	23	as	as	RB
cord-326631-7gd3hjc3	12	24	soon	soon	RB
cord-326631-7gd3hjc3	12	25	the	the	DT
cord-326631-7gd3hjc3	12	26	basic	basic	JJ
cord-326631-7gd3hjc3	12	27	reproduction	reproduction	NN
cord-326631-7gd3hjc3	12	28	number	number	NN
cord-326631-7gd3hjc3	12	29	ℝ(0	ℝ(0	CD
cord-326631-7gd3hjc3	12	30	)	)	-RRB-
cord-326631-7gd3hjc3	12	31	can	can	MD
cord-326631-7gd3hjc3	12	32	be	be	VB
cord-326631-7gd3hjc3	12	33	approximated	approximate	VBN
cord-326631-7gd3hjc3	12	34	,	,	,
cord-326631-7gd3hjc3	12	35	and	and	CC
cord-326631-7gd3hjc3	12	36	this	this	DT
cord-326631-7gd3hjc3	12	37	estimate	estimate	NN
cord-326631-7gd3hjc3	12	38	is	be	VBZ
cord-326631-7gd3hjc3	12	39	likely	likely	JJ
cord-326631-7gd3hjc3	12	40	to	to	TO
cord-326631-7gd3hjc3	12	41	be	be	VB
cord-326631-7gd3hjc3	12	42	improved	improve	VBN
cord-326631-7gd3hjc3	12	43	only	only	RB
cord-326631-7gd3hjc3	12	44	by	by	IN
cord-326631-7gd3hjc3	12	45	more	more	RBR
cord-326631-7gd3hjc3	12	46	accurate	accurate	JJ
cord-326631-7gd3hjc3	12	47	estimates	estimate	NNS
cord-326631-7gd3hjc3	12	48	of	of	IN
cord-326631-7gd3hjc3	12	49	ℝ(0	ℝ(0	CD
cord-326631-7gd3hjc3	12	50	)	)	-RRB-
cord-326631-7gd3hjc3	12	51	,	,	,
cord-326631-7gd3hjc3	12	52	not	not	RB
cord-326631-7gd3hjc3	12	53	by	by	IN
cord-326631-7gd3hjc3	12	54	knowledge	knowledge	NN
cord-326631-7gd3hjc3	12	55	of	of	IN
cord-326631-7gd3hjc3	12	56	any	any	DT
cord-326631-7gd3hjc3	12	57	other	other	JJ
cord-326631-7gd3hjc3	12	58	epidemiological	epidemiological	JJ
cord-326631-7gd3hjc3	12	59	details	detail	NNS
cord-326631-7gd3hjc3	12	60	.	.	.
cord-326631-7gd3hjc3	13	1	Whenever	whenever	WRB
cord-326631-7gd3hjc3	13	2	a	a	DT
cord-326631-7gd3hjc3	13	3	serious	serious	JJ
cord-326631-7gd3hjc3	13	4	infectious	infectious	JJ
cord-326631-7gd3hjc3	13	5	disease	disease	NN
cord-326631-7gd3hjc3	13	6	emerges	emerge	VBZ
cord-326631-7gd3hjc3	13	7	or	or	CC
cord-326631-7gd3hjc3	13	8	re	re	NN
cord-326631-7gd3hjc3	13	9	-	-	NN
cord-326631-7gd3hjc3	13	10	emerges	emerge	VBZ
cord-326631-7gd3hjc3	13	11	in	in	IN
cord-326631-7gd3hjc3	13	12	a	a	DT
cord-326631-7gd3hjc3	13	13	human	human	JJ
cord-326631-7gd3hjc3	13	14	population	population	NN
cord-326631-7gd3hjc3	13	15	,	,	,
cord-326631-7gd3hjc3	13	16	a	a	DT
cord-326631-7gd3hjc3	13	17	matter	matter	NN
cord-326631-7gd3hjc3	13	18	of	of	IN
cord-326631-7gd3hjc3	13	19	immediate	immediate	JJ
cord-326631-7gd3hjc3	13	20	interest	interest	NN
cord-326631-7gd3hjc3	13	21	is	be	VBZ
cord-326631-7gd3hjc3	13	22	the	the	DT
cord-326631-7gd3hjc3	13	23	likely	likely	JJ
cord-326631-7gd3hjc3	13	24	magnitude	magnitude	NN
cord-326631-7gd3hjc3	13	25	of	of	IN
cord-326631-7gd3hjc3	13	26	the	the	DT
cord-326631-7gd3hjc3	13	27	outbreak	outbreak	NN
cord-326631-7gd3hjc3	13	28	.	.	.
cord-326631-7gd3hjc3	14	1	This	this	DT
cord-326631-7gd3hjc3	14	2	is	be	VBZ
cord-326631-7gd3hjc3	14	3	often	often	RB
cord-326631-7gd3hjc3	14	4	called	call	VBN
cord-326631-7gd3hjc3	14	5	the	the	DT
cord-326631-7gd3hjc3	14	6	expected	expect	VBN
cord-326631-7gd3hjc3	14	7	final	final	JJ
cord-326631-7gd3hjc3	14	8	size	size	NN
cord-326631-7gd3hjc3	14	9	of	of	IN
cord-326631-7gd3hjc3	14	10	the	the	DT
cord-326631-7gd3hjc3	14	11	epidemic	epidemic	NN
cord-326631-7gd3hjc3	14	12	(	(	-LRB-
cord-326631-7gd3hjc3	14	13	Bailey	Bailey	NNP
cord-326631-7gd3hjc3	14	14	,	,	,
cord-326631-7gd3hjc3	14	15	1975	1975	CD
cord-326631-7gd3hjc3	14	16	;	;	:
cord-326631-7gd3hjc3	14	17	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	14	18	and	and	CC
cord-326631-7gd3hjc3	14	19	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	14	20	,	,	,
cord-326631-7gd3hjc3	14	21	1980	1980	CD
cord-326631-7gd3hjc3	14	22	;	;	:
cord-326631-7gd3hjc3	14	23	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	14	24	and	and	CC
cord-326631-7gd3hjc3	14	25	May	May	NNP
cord-326631-7gd3hjc3	14	26	,	,	,
cord-326631-7gd3hjc3	14	27	1991	1991	CD
cord-326631-7gd3hjc3	14	28	;	;	:
cord-326631-7gd3hjc3	14	29	Andersson	Andersson	NNP
cord-326631-7gd3hjc3	14	30	and	and	CC
cord-326631-7gd3hjc3	14	31	Britton	Britton	NNP
cord-326631-7gd3hjc3	14	32	,	,	,
cord-326631-7gd3hjc3	14	33	2000	2000	CD
cord-326631-7gd3hjc3	14	34	;	;	:
cord-326631-7gd3hjc3	14	35	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	14	36	and	and	CC
cord-326631-7gd3hjc3	14	37	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	14	38	,	,	,
cord-326631-7gd3hjc3	14	39	2000	2000	CD
cord-326631-7gd3hjc3	14	40	)	)	-RRB-
cord-326631-7gd3hjc3	14	41	,	,	,
cord-326631-7gd3hjc3	14	42	which	which	WDT
cord-326631-7gd3hjc3	14	43	we	-PRON-	PRP
cord-326631-7gd3hjc3	14	44	denote	denote	VBP
cord-326631-7gd3hjc3	14	45	Z.	Z.	NNP
cord-326631-7gd3hjc3	15	1	Of	of	RB
cord-326631-7gd3hjc3	15	2	course	course	RB
cord-326631-7gd3hjc3	15	3	,	,	,
cord-326631-7gd3hjc3	15	4	if	if	IN
cord-326631-7gd3hjc3	15	5	the	the	DT
cord-326631-7gd3hjc3	15	6	emergent	emergent	JJ
cord-326631-7gd3hjc3	15	7	pathogen	pathogen	NN
cord-326631-7gd3hjc3	15	8	becomes	become	VBZ
cord-326631-7gd3hjc3	15	9	endemic	endemic	JJ
cord-326631-7gd3hjc3	15	10	in	in	IN
cord-326631-7gd3hjc3	15	11	the	the	DT
cord-326631-7gd3hjc3	15	12	population	population	NN
cord-326631-7gd3hjc3	15	13	then	then	RB
cord-326631-7gd3hjc3	15	14	there	there	EX
cord-326631-7gd3hjc3	15	15	will	will	MD
cord-326631-7gd3hjc3	15	16	never	never	RB
cord-326631-7gd3hjc3	15	17	really	really	RB
cord-326631-7gd3hjc3	15	18	be	be	VB
cord-326631-7gd3hjc3	15	19	a	a	DT
cord-326631-7gd3hjc3	15	20	"	"	``
cord-326631-7gd3hjc3	15	21	final	final	JJ
cord-326631-7gd3hjc3	15	22	"	"	''
cord-326631-7gd3hjc3	15	23	size	size	NN
cord-326631-7gd3hjc3	15	24	,	,	,
cord-326631-7gd3hjc3	15	25	but	but	CC
cord-326631-7gd3hjc3	15	26	in	in	IN
cord-326631-7gd3hjc3	15	27	that	that	DT
cord-326631-7gd3hjc3	15	28	case	case	NN
cord-326631-7gd3hjc3	15	29	the	the	DT
cord-326631-7gd3hjc3	15	30	matter	matter	NN
cord-326631-7gd3hjc3	15	31	at	at	IN
cord-326631-7gd3hjc3	15	32	issue	issue	NN
cord-326631-7gd3hjc3	15	33	is	be	VBZ
cord-326631-7gd3hjc3	15	34	the	the	DT
cord-326631-7gd3hjc3	15	35	likely	likely	JJ
cord-326631-7gd3hjc3	15	36	magnitude	magnitude	NN
cord-326631-7gd3hjc3	15	37	of	of	IN
cord-326631-7gd3hjc3	15	38	the	the	DT
cord-326631-7gd3hjc3	15	39	first	first	JJ
cord-326631-7gd3hjc3	15	40	major	major	JJ
cord-326631-7gd3hjc3	15	41	wave	wave	NN
cord-326631-7gd3hjc3	15	42	of	of	IN
cord-326631-7gd3hjc3	15	43	cases	case	NNS
cord-326631-7gd3hjc3	15	44	.	.	.
cord-326631-7gd3hjc3	16	1	To	to	IN
cord-326631-7gd3hjc3	16	2	our	-PRON-	PRP$
cord-326631-7gd3hjc3	16	3	knowledge	knowledge	NN
cord-326631-7gd3hjc3	16	4	,	,	,
cord-326631-7gd3hjc3	16	5	a	a	DT
cord-326631-7gd3hjc3	16	6	formal	formal	JJ
cord-326631-7gd3hjc3	16	7	,	,	,
cord-326631-7gd3hjc3	16	8	mathematical	mathematical	JJ
cord-326631-7gd3hjc3	16	9	argument	argument	NN
cord-326631-7gd3hjc3	16	10	leading	lead	VBG
cord-326631-7gd3hjc3	16	11	to	to	IN
cord-326631-7gd3hjc3	16	12	an	an	DT
cord-326631-7gd3hjc3	16	13	estimate	estimate	NN
cord-326631-7gd3hjc3	16	14	of	of	IN
cord-326631-7gd3hjc3	16	15	an	an	DT
cord-326631-7gd3hjc3	16	16	epidemic	epidemic	NN
cord-326631-7gd3hjc3	16	17	's	's	POS
cord-326631-7gd3hjc3	16	18	expected	expect	VBN
cord-326631-7gd3hjc3	16	19	final	final	JJ
cord-326631-7gd3hjc3	16	20	size	size	NN
cord-326631-7gd3hjc3	16	21	Z	Z	NNP
cord-326631-7gd3hjc3	16	22	was	be	VBD
cord-326631-7gd3hjc3	16	23	first	first	RB
cord-326631-7gd3hjc3	16	24	published	publish	VBN
cord-326631-7gd3hjc3	16	25	in	in	IN
cord-326631-7gd3hjc3	16	26	the	the	DT
cord-326631-7gd3hjc3	16	27	landmark	landmark	JJ
cord-326631-7gd3hjc3	16	28	1927	1927	CD
cord-326631-7gd3hjc3	16	29	paper	paper	NN
cord-326631-7gd3hjc3	16	30	by	by	IN
cord-326631-7gd3hjc3	16	31	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	16	32	and	and	CC
cord-326631-7gd3hjc3	16	33	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	16	34	(	(	-LRB-
cord-326631-7gd3hjc3	16	35	1927	1927	CD
cord-326631-7gd3hjc3	16	36	)	)	-RRB-
cord-326631-7gd3hjc3	16	37	.	.	.
cord-326631-7gd3hjc3	17	1	The	the	DT
cord-326631-7gd3hjc3	17	2	formula	formula	NN
cord-326631-7gd3hjc3	17	3	for	for	IN
cord-326631-7gd3hjc3	17	4	Z	Z	NNP
cord-326631-7gd3hjc3	17	5	that	that	WDT
cord-326631-7gd3hjc3	17	6	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	17	7	and	and	CC
cord-326631-7gd3hjc3	17	8	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	17	9	obtained	obtain	VBD
cord-326631-7gd3hjc3	17	10	[	[	-LRB-
cord-326631-7gd3hjc3	17	11	Eq	Eq	NNP
cord-326631-7gd3hjc3	17	12	.	.	.
cord-326631-7gd3hjc3	18	1	(	(	-LRB-
cord-326631-7gd3hjc3	18	2	5	5	LS
cord-326631-7gd3hjc3	18	3	)	)	-RRB-
cord-326631-7gd3hjc3	18	4	below	below	IN
cord-326631-7gd3hjc3	18	5	]	]	-RRB-
cord-326631-7gd3hjc3	18	6	depends	depend	VBZ
cord-326631-7gd3hjc3	18	7	only	only	RB
cord-326631-7gd3hjc3	18	8	on	on	IN
cord-326631-7gd3hjc3	18	9	the	the	DT
cord-326631-7gd3hjc3	18	10	basic	basic	JJ
cord-326631-7gd3hjc3	18	11	reproduction	reproduction	NN
cord-326631-7gd3hjc3	18	12	number	number	NN
cord-326631-7gd3hjc3	18	13	,	,	,
cord-326631-7gd3hjc3	18	14	R	r	NN
cord-326631-7gd3hjc3	18	15	0	0	NFP
cord-326631-7gd3hjc3	18	16	(	(	-LRB-
cord-326631-7gd3hjc3	18	17	the	the	DT
cord-326631-7gd3hjc3	18	18	expected	expect	VBN
cord-326631-7gd3hjc3	18	19	number	number	NN
cord-326631-7gd3hjc3	18	20	of	of	IN
cord-326631-7gd3hjc3	18	21	secondary	secondary	JJ
cord-326631-7gd3hjc3	18	22	cases	case	NNS
cord-326631-7gd3hjc3	18	23	caused	cause	VBN
cord-326631-7gd3hjc3	18	24	by	by	IN
cord-326631-7gd3hjc3	18	25	a	a	DT
cord-326631-7gd3hjc3	18	26	typical	typical	JJ
cord-326631-7gd3hjc3	18	27	primary	primary	JJ
cord-326631-7gd3hjc3	18	28	case	case	NN
cord-326631-7gd3hjc3	18	29	in	in	IN
cord-326631-7gd3hjc3	18	30	a	a	DT
cord-326631-7gd3hjc3	18	31	fully	fully	RB
cord-326631-7gd3hjc3	18	32	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	18	33	population	population	NN
cord-326631-7gd3hjc3	18	34	)	)	-RRB-
cord-326631-7gd3hjc3	18	35	.	.	.
cord-326631-7gd3hjc3	19	1	However	however	RB
cord-326631-7gd3hjc3	19	2	,	,	,
cord-326631-7gd3hjc3	19	3	without	without	IN
cord-326631-7gd3hjc3	19	4	further	further	JJ
cord-326631-7gd3hjc3	19	5	analysis	analysis	NN
cord-326631-7gd3hjc3	19	6	,	,	,
cord-326631-7gd3hjc3	19	7	it	-PRON-	PRP
cord-326631-7gd3hjc3	19	8	is	be	VBZ
cord-326631-7gd3hjc3	19	9	unclear	unclear	JJ
cord-326631-7gd3hjc3	19	10	to	to	TO
cord-326631-7gd3hjc3	19	11	what	what	WDT
cord-326631-7gd3hjc3	19	12	extent	extent	NN
cord-326631-7gd3hjc3	19	13	this	this	DT
cord-326631-7gd3hjc3	19	14	formula	formula	NN
cord-326631-7gd3hjc3	19	15	depends	depend	VBZ
cord-326631-7gd3hjc3	19	16	on	on	IN
cord-326631-7gd3hjc3	19	17	the	the	DT
cord-326631-7gd3hjc3	19	18	particular	particular	JJ
cord-326631-7gd3hjc3	19	19	assumptions	assumption	NNS
cord-326631-7gd3hjc3	19	20	that	that	WDT
cord-326631-7gd3hjc3	19	21	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	19	22	and	and	CC
cord-326631-7gd3hjc3	19	23	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	19	24	made	make	VBD
cord-326631-7gd3hjc3	19	25	in	in	IN
cord-326631-7gd3hjc3	19	26	constructing	construct	VBG
cord-326631-7gd3hjc3	19	27	their	-PRON-	PRP$
cord-326631-7gd3hjc3	19	28	model	model	NN
cord-326631-7gd3hjc3	19	29	,	,	,
cord-326631-7gd3hjc3	19	30	and	and	CC
cord-326631-7gd3hjc3	19	31	hence	hence	RB
cord-326631-7gd3hjc3	19	32	whether	whether	IN
cord-326631-7gd3hjc3	19	33	it	-PRON-	PRP
cord-326631-7gd3hjc3	19	34	bears	bear	VBZ
cord-326631-7gd3hjc3	19	35	a	a	DT
cord-326631-7gd3hjc3	19	36	strong	strong	JJ
cord-326631-7gd3hjc3	19	37	relationship	relationship	NN
cord-326631-7gd3hjc3	19	38	to	to	IN
cord-326631-7gd3hjc3	19	39	the	the	DT
cord-326631-7gd3hjc3	19	40	final	final	JJ
cord-326631-7gd3hjc3	19	41	size	size	NN
cord-326631-7gd3hjc3	19	42	in	in	IN
cord-326631-7gd3hjc3	19	43	realistic	realistic	JJ
cord-326631-7gd3hjc3	19	44	situations	situation	NNS
cord-326631-7gd3hjc3	19	45	.	.	.
cord-326631-7gd3hjc3	20	1	One	one	CD
cord-326631-7gd3hjc3	20	2	implicit	implicit	JJ
cord-326631-7gd3hjc3	20	3	assumption	assumption	NN
cord-326631-7gd3hjc3	20	4	of	of	IN
cord-326631-7gd3hjc3	20	5	the	the	DT
cord-326631-7gd3hjc3	20	6	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	20	7	and	and	CC
cord-326631-7gd3hjc3	20	8	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	20	9	(	(	-LRB-
cord-326631-7gd3hjc3	20	10	1927	1927	CD
cord-326631-7gd3hjc3	20	11	)	)	-RRB-
cord-326631-7gd3hjc3	20	12	analysis	analysis	NN
cord-326631-7gd3hjc3	20	13	is	be	VBZ
cord-326631-7gd3hjc3	20	14	that	that	IN
cord-326631-7gd3hjc3	20	15	infectious	infectious	JJ
cord-326631-7gd3hjc3	20	16	periods	period	NNS
cord-326631-7gd3hjc3	20	17	are	be	VBP
cord-326631-7gd3hjc3	20	18	exponentially	exponentially	RB
cord-326631-7gd3hjc3	20	19	distributed	distribute	VBN
cord-326631-7gd3hjc3	20	20	.	.	.
cord-326631-7gd3hjc3	21	1	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	21	2	and	and	CC
cord-326631-7gd3hjc3	21	3	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	21	4	(	(	-LRB-
cord-326631-7gd3hjc3	21	5	1980	1980	CD
cord-326631-7gd3hjc3	21	6	)	)	-RRB-
cord-326631-7gd3hjc3	21	7	showed	show	VBD
cord-326631-7gd3hjc3	21	8	that	that	IN
cord-326631-7gd3hjc3	21	9	the	the	DT
cord-326631-7gd3hjc3	21	10	final	final	JJ
cord-326631-7gd3hjc3	21	11	size	size	NN
cord-326631-7gd3hjc3	21	12	formula	formula	NN
cord-326631-7gd3hjc3	21	13	remains	remain	VBZ
cord-326631-7gd3hjc3	21	14	valid	valid	JJ
cord-326631-7gd3hjc3	21	15	if	if	IN
cord-326631-7gd3hjc3	21	16	infectious	infectious	JJ
cord-326631-7gd3hjc3	21	17	periods	period	NNS
cord-326631-7gd3hjc3	21	18	follow	follow	VBP
cord-326631-7gd3hjc3	21	19	a	a	DT
cord-326631-7gd3hjc3	21	20	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	21	21	distribution	distribution	NN
cord-326631-7gd3hjc3	21	22	.	.	.
cord-326631-7gd3hjc3	22	1	In	in	IN
cord-326631-7gd3hjc3	22	2	Section	section	NN
cord-326631-7gd3hjc3	22	3	1.3	1.3	CD
cord-326631-7gd3hjc3	22	4	of	of	IN
cord-326631-7gd3hjc3	22	5	their	-PRON-	PRP$
cord-326631-7gd3hjc3	22	6	book	book	NN
cord-326631-7gd3hjc3	22	7	,	,	,
cord-326631-7gd3hjc3	22	8	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	22	9	and	and	CC
cord-326631-7gd3hjc3	22	10	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	22	11	(	(	-LRB-
cord-326631-7gd3hjc3	22	12	2000	2000	CD
cord-326631-7gd3hjc3	22	13	)	)	-RRB-
cord-326631-7gd3hjc3	22	14	generalized	generalize	VBD
cord-326631-7gd3hjc3	22	15	this	this	DT
cord-326631-7gd3hjc3	22	16	statement	statement	NN
cord-326631-7gd3hjc3	22	17	to	to	TO
cord-326631-7gd3hjc3	22	18	cover	cover	VB
cord-326631-7gd3hjc3	22	19	an	an	DT
cord-326631-7gd3hjc3	22	20	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	22	21	distribution	distribution	NN
cord-326631-7gd3hjc3	22	22	of	of	IN
cord-326631-7gd3hjc3	22	23	infectious	infectious	JJ
cord-326631-7gd3hjc3	22	24	periods	period	NNS
cord-326631-7gd3hjc3	22	25	.	.	.
cord-326631-7gd3hjc3	23	1	Another	another	DT
cord-326631-7gd3hjc3	23	2	key	key	JJ
cord-326631-7gd3hjc3	23	3	assumption	assumption	NN
cord-326631-7gd3hjc3	23	4	of	of	IN
cord-326631-7gd3hjc3	23	5	the	the	DT
cord-326631-7gd3hjc3	23	6	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	23	7	and	and	CC
cord-326631-7gd3hjc3	23	8	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	23	9	(	(	-LRB-
cord-326631-7gd3hjc3	23	10	1927	1927	CD
cord-326631-7gd3hjc3	23	11	)	)	-RRB-
cord-326631-7gd3hjc3	23	12	analysis	analysis	NN
cord-326631-7gd3hjc3	23	13	is	be	VBZ
cord-326631-7gd3hjc3	23	14	that	that	IN
cord-326631-7gd3hjc3	23	15	the	the	DT
cord-326631-7gd3hjc3	23	16	host	host	NN
cord-326631-7gd3hjc3	23	17	population	population	NN
cord-326631-7gd3hjc3	23	18	is	be	VBZ
cord-326631-7gd3hjc3	23	19	homogeneously	homogeneously	RB
cord-326631-7gd3hjc3	23	20	mixed	mixed	JJ
cord-326631-7gd3hjc3	23	21	.	.	.
cord-326631-7gd3hjc3	24	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	24	2	is	be	VBZ
cord-326631-7gd3hjc3	24	3	well	well	RB
cord-326631-7gd3hjc3	24	4	known	know	VBN
cord-326631-7gd3hjc3	24	5	that	that	IN
cord-326631-7gd3hjc3	24	6	if	if	IN
cord-326631-7gd3hjc3	24	7	this	this	DT
cord-326631-7gd3hjc3	24	8	assumption	assumption	NN
cord-326631-7gd3hjc3	24	9	is	be	VBZ
cord-326631-7gd3hjc3	24	10	dropped	drop	VBN
cord-326631-7gd3hjc3	24	11	then	then	RB
cord-326631-7gd3hjc3	24	12	the	the	DT
cord-326631-7gd3hjc3	24	13	final	final	JJ
cord-326631-7gd3hjc3	24	14	size	size	NN
cord-326631-7gd3hjc3	24	15	will	will	MD
cord-326631-7gd3hjc3	24	16	not	not	RB
cord-326631-7gd3hjc3	24	17	necessarily	necessarily	RB
cord-326631-7gd3hjc3	24	18	be	be	VB
cord-326631-7gd3hjc3	24	19	given	give	VBN
cord-326631-7gd3hjc3	24	20	by	by	IN
cord-326631-7gd3hjc3	24	21	the	the	DT
cord-326631-7gd3hjc3	24	22	standard	standard	JJ
cord-326631-7gd3hjc3	24	23	formula	formula	NN
cord-326631-7gd3hjc3	24	24	.	.	.
cord-326631-7gd3hjc3	25	1	In	in	IN
cord-326631-7gd3hjc3	25	2	particular	particular	JJ
cord-326631-7gd3hjc3	25	3	,	,	,
cord-326631-7gd3hjc3	25	4	the	the	DT
cord-326631-7gd3hjc3	25	5	existence	existence	NN
cord-326631-7gd3hjc3	25	6	of	of	IN
cord-326631-7gd3hjc3	25	7	a	a	DT
cord-326631-7gd3hjc3	25	8	core	core	NN
cord-326631-7gd3hjc3	25	9	group	group	NN
cord-326631-7gd3hjc3	25	10	,	,	,
cord-326631-7gd3hjc3	25	11	as	as	IN
cord-326631-7gd3hjc3	25	12	for	for	IN
cord-326631-7gd3hjc3	25	13	sexually	sexually	RB
cord-326631-7gd3hjc3	25	14	transmitted	transmit	VBN
cord-326631-7gd3hjc3	25	15	diseases	disease	NNS
cord-326631-7gd3hjc3	25	16	,	,	,
cord-326631-7gd3hjc3	25	17	gives	give	VBZ
cord-326631-7gd3hjc3	25	18	rise	rise	NN
cord-326631-7gd3hjc3	25	19	to	to	IN
cord-326631-7gd3hjc3	25	20	a	a	DT
cord-326631-7gd3hjc3	25	21	different	different	JJ
cord-326631-7gd3hjc3	25	22	formula	formula	NN
cord-326631-7gd3hjc3	25	23	for	for	IN
cord-326631-7gd3hjc3	25	24	the	the	DT
cord-326631-7gd3hjc3	25	25	final	final	JJ
cord-326631-7gd3hjc3	25	26	size	size	NN
cord-326631-7gd3hjc3	25	27	(	(	-LRB-
cord-326631-7gd3hjc3	25	28	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	25	29	and	and	CC
cord-326631-7gd3hjc3	25	30	May	May	NNP
cord-326631-7gd3hjc3	25	31	,	,	,
cord-326631-7gd3hjc3	25	32	1991	1991	CD
cord-326631-7gd3hjc3	25	33	;	;	:
cord-326631-7gd3hjc3	25	34	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	25	35	and	and	CC
cord-326631-7gd3hjc3	25	36	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	25	37	,	,	,
cord-326631-7gd3hjc3	25	38	2000	2000	CD
cord-326631-7gd3hjc3	25	39	)	)	-RRB-
cord-326631-7gd3hjc3	25	40	.	.	.
cord-326631-7gd3hjc3	26	1	In	in	IN
cord-326631-7gd3hjc3	26	2	this	this	DT
cord-326631-7gd3hjc3	26	3	paper	paper	NN
cord-326631-7gd3hjc3	26	4	,	,	,
cord-326631-7gd3hjc3	26	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	26	6	explore	explore	VBP
cord-326631-7gd3hjc3	26	7	the	the	DT
cord-326631-7gd3hjc3	26	8	generality	generality	NN
cord-326631-7gd3hjc3	26	9	of	of	IN
cord-326631-7gd3hjc3	26	10	the	the	DT
cord-326631-7gd3hjc3	26	11	standard	standard	JJ
cord-326631-7gd3hjc3	26	12	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	26	13	-	-	HYPH
cord-326631-7gd3hjc3	26	14	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	26	15	final	final	JJ
cord-326631-7gd3hjc3	26	16	size	size	NN
cord-326631-7gd3hjc3	26	17	formula	formula	NN
cord-326631-7gd3hjc3	26	18	(	(	-LRB-
cord-326631-7gd3hjc3	26	19	5	5	CD
cord-326631-7gd3hjc3	26	20	)	)	-RRB-
cord-326631-7gd3hjc3	26	21	.	.	.
cord-326631-7gd3hjc3	27	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	27	2	begin	begin	VBP
cord-326631-7gd3hjc3	27	3	with	with	IN
cord-326631-7gd3hjc3	27	4	a	a	DT
cord-326631-7gd3hjc3	27	5	pedagogical	pedagogical	JJ
cord-326631-7gd3hjc3	27	6	review	review	NN
cord-326631-7gd3hjc3	27	7	of	of	IN
cord-326631-7gd3hjc3	27	8	the	the	DT
cord-326631-7gd3hjc3	27	9	main	main	JJ
cord-326631-7gd3hjc3	27	10	results	result	NNS
cord-326631-7gd3hjc3	27	11	that	that	WDT
cord-326631-7gd3hjc3	27	12	have	have	VBP
cord-326631-7gd3hjc3	27	13	been	be	VBN
cord-326631-7gd3hjc3	27	14	obtained	obtain	VBN
cord-326631-7gd3hjc3	27	15	previously	previously	RB
cord-326631-7gd3hjc3	27	16	,	,	,
cord-326631-7gd3hjc3	27	17	adding	add	VBG
cord-326631-7gd3hjc3	27	18	model	model	NN
cord-326631-7gd3hjc3	27	19	structure	structure	NN
cord-326631-7gd3hjc3	27	20	in	in	IN
cord-326631-7gd3hjc3	27	21	steps	step	NNS
cord-326631-7gd3hjc3	27	22	.	.	.
cord-326631-7gd3hjc3	28	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	28	2	then	then	RB
cord-326631-7gd3hjc3	28	3	proceed	proceed	VBP
cord-326631-7gd3hjc3	28	4	to	to	TO
cord-326631-7gd3hjc3	28	5	generalize	generalize	VB
cord-326631-7gd3hjc3	28	6	these	these	DT
cord-326631-7gd3hjc3	28	7	results	result	NNS
cord-326631-7gd3hjc3	28	8	in	in	IN
cord-326631-7gd3hjc3	28	9	three	three	CD
cord-326631-7gd3hjc3	28	10	new	new	JJ
cord-326631-7gd3hjc3	28	11	directions	direction	NNS
cord-326631-7gd3hjc3	28	12	,	,	,
cord-326631-7gd3hjc3	28	13	showing	show	VBG
cord-326631-7gd3hjc3	28	14	that	that	IN
cord-326631-7gd3hjc3	28	15	the	the	DT
cord-326631-7gd3hjc3	28	16	standard	standard	JJ
cord-326631-7gd3hjc3	28	17	formula	formula	NN
cord-326631-7gd3hjc3	28	18	remains	remain	VBZ
cord-326631-7gd3hjc3	28	19	valid	valid	JJ
cord-326631-7gd3hjc3	29	1	(	(	-LRB-
cord-326631-7gd3hjc3	29	2	i	i	NN
cord-326631-7gd3hjc3	29	3	)	)	-RRB-
cord-326631-7gd3hjc3	30	1	regardless	regardless	RB
cord-326631-7gd3hjc3	30	2	of	of	IN
cord-326631-7gd3hjc3	30	3	the	the	DT
cord-326631-7gd3hjc3	30	4	number	number	NN
cord-326631-7gd3hjc3	30	5	of	of	IN
cord-326631-7gd3hjc3	30	6	distinct	distinct	JJ
cord-326631-7gd3hjc3	30	7	infectious	infectious	JJ
cord-326631-7gd3hjc3	30	8	stages	stage	NNS
cord-326631-7gd3hjc3	30	9	,	,	,
cord-326631-7gd3hjc3	30	10	(	(	-LRB-
cord-326631-7gd3hjc3	30	11	ii	ii	LS
cord-326631-7gd3hjc3	30	12	)	)	-RRB-
cord-326631-7gd3hjc3	30	13	if	if	IN
cord-326631-7gd3hjc3	30	14	the	the	DT
cord-326631-7gd3hjc3	30	15	mean	mean	JJ
cord-326631-7gd3hjc3	30	16	contact	contact	NN
cord-326631-7gd3hjc3	30	17	rate	rate	NN
cord-326631-7gd3hjc3	30	18	is	be	VBZ
cord-326631-7gd3hjc3	30	19	itself	-PRON-	PRP
cord-326631-7gd3hjc3	30	20	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	30	21	distributed	distribute	VBN
cord-326631-7gd3hjc3	30	22	and	and	CC
cord-326631-7gd3hjc3	30	23	(	(	-LRB-
cord-326631-7gd3hjc3	30	24	iii	iii	NN
cord-326631-7gd3hjc3	30	25	)	)	-RRB-
cord-326631-7gd3hjc3	30	26	for	for	IN
cord-326631-7gd3hjc3	30	27	a	a	DT
cord-326631-7gd3hjc3	30	28	large	large	JJ
cord-326631-7gd3hjc3	30	29	class	class	NN
cord-326631-7gd3hjc3	30	30	of	of	IN
cord-326631-7gd3hjc3	30	31	spatially	spatially	RB
cord-326631-7gd3hjc3	30	32	heterogeneous	heterogeneous	JJ
cord-326631-7gd3hjc3	30	33	contact	contact	NN
cord-326631-7gd3hjc3	30	34	structures	structure	NNS
cord-326631-7gd3hjc3	30	35	.	.	.
cord-326631-7gd3hjc3	31	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	31	2	conclude	conclude	VBP
cord-326631-7gd3hjc3	31	3	that	that	IN
cord-326631-7gd3hjc3	31	4	the	the	DT
cord-326631-7gd3hjc3	31	5	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	31	6	-	-	HYPH
cord-326631-7gd3hjc3	31	7	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	31	8	formula	formula	NN
cord-326631-7gd3hjc3	31	9	(	(	-LRB-
cord-326631-7gd3hjc3	31	10	5	5	LS
cord-326631-7gd3hjc3	31	11	)	)	-RRB-
cord-326631-7gd3hjc3	31	12	applies	apply	VBZ
cord-326631-7gd3hjc3	31	13	in	in	IN
cord-326631-7gd3hjc3	31	14	great	great	JJ
cord-326631-7gd3hjc3	31	15	generality	generality	NN
cord-326631-7gd3hjc3	31	16	,	,	,
cord-326631-7gd3hjc3	31	17	making	make	VBG
cord-326631-7gd3hjc3	31	18	it	-PRON-	PRP
cord-326631-7gd3hjc3	31	19	an	an	DT
cord-326631-7gd3hjc3	31	20	extremely	extremely	RB
cord-326631-7gd3hjc3	31	21	useful	useful	JJ
cord-326631-7gd3hjc3	31	22	relationship	relationship	NN
cord-326631-7gd3hjc3	31	23	in	in	IN
cord-326631-7gd3hjc3	31	24	practice	practice	NN
cord-326631-7gd3hjc3	31	25	.	.	.
cord-326631-7gd3hjc3	32	1	The	the	DT
cord-326631-7gd3hjc3	32	2	standard	standard	JJ
cord-326631-7gd3hjc3	32	3	SIR	SIR	NNP
cord-326631-7gd3hjc3	32	4	model	model	NN
cord-326631-7gd3hjc3	32	5	(	(	-LRB-
cord-326631-7gd3hjc3	32	6	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	32	7	and	and	CC
cord-326631-7gd3hjc3	32	8	May	May	NNP
cord-326631-7gd3hjc3	32	9	,	,	,
cord-326631-7gd3hjc3	32	10	1991	1991	CD
cord-326631-7gd3hjc3	32	11	;	;	:
cord-326631-7gd3hjc3	32	12	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	32	13	and	and	CC
cord-326631-7gd3hjc3	32	14	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	32	15	,	,	,
cord-326631-7gd3hjc3	32	16	2000	2000	CD
cord-326631-7gd3hjc3	32	17	;	;	:
cord-326631-7gd3hjc3	32	18	Brauer	Brauer	NNP
cord-326631-7gd3hjc3	32	19	and	and	CC
cord-326631-7gd3hjc3	32	20	Castillo	Castillo	NNP
cord-326631-7gd3hjc3	32	21	-	-	HYPH
cord-326631-7gd3hjc3	32	22	Chavez	Chavez	NNP
cord-326631-7gd3hjc3	32	23	,	,	,
cord-326631-7gd3hjc3	32	24	2001	2001	CD
cord-326631-7gd3hjc3	32	25	)	)	-RRB-
cord-326631-7gd3hjc3	32	26	is	be	VBZ
cord-326631-7gd3hjc3	32	27	represented	represent	VBN
cord-326631-7gd3hjc3	32	28	by	by	IN
cord-326631-7gd3hjc3	32	29	a	a	DT
cord-326631-7gd3hjc3	32	30	system	system	NN
cord-326631-7gd3hjc3	32	31	of	of	IN
cord-326631-7gd3hjc3	32	32	three	three	CD
cord-326631-7gd3hjc3	32	33	ordinary	ordinary	JJ
cord-326631-7gd3hjc3	32	34	differential	differential	JJ
cord-326631-7gd3hjc3	32	35	equations	equation	NNS
cord-326631-7gd3hjc3	32	36	,	,	,
cord-326631-7gd3hjc3	32	37	Here	here	RB
cord-326631-7gd3hjc3	32	38	,	,	,
cord-326631-7gd3hjc3	32	39	S	S	NNP
cord-326631-7gd3hjc3	32	40	,	,	,
cord-326631-7gd3hjc3	32	41	I	-PRON-	PRP
cord-326631-7gd3hjc3	32	42	,	,	,
cord-326631-7gd3hjc3	32	43	and	and	CC
cord-326631-7gd3hjc3	32	44	R	r	NN
cord-326631-7gd3hjc3	32	45	denote	denote	VBP
cord-326631-7gd3hjc3	32	46	the	the	DT
cord-326631-7gd3hjc3	32	47	proportions	proportion	NNS
cord-326631-7gd3hjc3	32	48	of	of	IN
cord-326631-7gd3hjc3	32	49	the	the	DT
cord-326631-7gd3hjc3	32	50	population	population	NN
cord-326631-7gd3hjc3	32	51	that	that	WDT
cord-326631-7gd3hjc3	32	52	are	be	VBP
cord-326631-7gd3hjc3	32	53	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	32	54	,	,	,
cord-326631-7gd3hjc3	32	55	infectious	infectious	JJ
cord-326631-7gd3hjc3	32	56	and	and	CC
cord-326631-7gd3hjc3	32	57	recovered	recovered	JJ
cord-326631-7gd3hjc3	32	58	,	,	,
cord-326631-7gd3hjc3	32	59	respectively	respectively	RB
cord-326631-7gd3hjc3	32	60	.	.	.
cord-326631-7gd3hjc3	33	1	Recovered	recover	VBN
cord-326631-7gd3hjc3	33	2	individuals	individual	NNS
cord-326631-7gd3hjc3	33	3	are	be	VBP
cord-326631-7gd3hjc3	33	4	assumed	assume	VBN
cord-326631-7gd3hjc3	33	5	to	to	TO
cord-326631-7gd3hjc3	33	6	be	be	VB
cord-326631-7gd3hjc3	33	7	immune	immune	JJ
cord-326631-7gd3hjc3	33	8	to	to	IN
cord-326631-7gd3hjc3	33	9	reinfection	reinfection	NN
cord-326631-7gd3hjc3	33	10	.	.	.
cord-326631-7gd3hjc3	34	1	Since	since	IN
cord-326631-7gd3hjc3	34	2	S	S	NNP
cord-326631-7gd3hjc3	34	3	+	+	CC
cord-326631-7gd3hjc3	34	4	I	i	NN
cord-326631-7gd3hjc3	34	5	+	+	CC
cord-326631-7gd3hjc3	34	6	R	r	NN
cord-326631-7gd3hjc3	34	7	=	=	SYM
cord-326631-7gd3hjc3	34	8	1	1	CD
cord-326631-7gd3hjc3	34	9	,	,	,
cord-326631-7gd3hjc3	34	10	one	one	CD
cord-326631-7gd3hjc3	34	11	of	of	IN
cord-326631-7gd3hjc3	34	12	the	the	DT
cord-326631-7gd3hjc3	34	13	three	three	CD
cord-326631-7gd3hjc3	34	14	equations	equation	NNS
cord-326631-7gd3hjc3	34	15	is	be	VBZ
cord-326631-7gd3hjc3	34	16	redundant	redundant	JJ
cord-326631-7gd3hjc3	34	17	.	.	.
cord-326631-7gd3hjc3	35	1	The	the	DT
cord-326631-7gd3hjc3	35	2	two	two	CD
cord-326631-7gd3hjc3	35	3	parameters	parameter	NNS
cord-326631-7gd3hjc3	35	4	in	in	IN
cord-326631-7gd3hjc3	35	5	the	the	DT
cord-326631-7gd3hjc3	35	6	model	model	NN
cord-326631-7gd3hjc3	35	7	are	be	VBP
cord-326631-7gd3hjc3	35	8	the	the	DT
cord-326631-7gd3hjc3	35	9	transmission	transmission	NN
cord-326631-7gd3hjc3	35	10	rate	rate	NN
cord-326631-7gd3hjc3	35	11	(	(	-LRB-
cord-326631-7gd3hjc3	35	12	β	β	NN
cord-326631-7gd3hjc3	35	13	)	)	-RRB-
cord-326631-7gd3hjc3	35	14	and	and	CC
cord-326631-7gd3hjc3	35	15	the	the	DT
cord-326631-7gd3hjc3	35	16	recovery	recovery	NN
cord-326631-7gd3hjc3	35	17	rate	rate	NN
cord-326631-7gd3hjc3	35	18	(	(	-LRB-
cord-326631-7gd3hjc3	35	19	γ	γ	NN
cord-326631-7gd3hjc3	35	20	)	)	-RRB-
cord-326631-7gd3hjc3	35	21	.	.	.
cord-326631-7gd3hjc3	36	1	The	the	DT
cord-326631-7gd3hjc3	36	2	mean	mean	JJ
cord-326631-7gd3hjc3	36	3	infectious	infectious	JJ
cord-326631-7gd3hjc3	36	4	period	period	NN
cord-326631-7gd3hjc3	36	5	is	be	VBZ
cord-326631-7gd3hjc3	36	6	T	T	NNP
cord-326631-7gd3hjc3	36	7	=	=	SYM
cord-326631-7gd3hjc3	36	8	1	1	CD
cord-326631-7gd3hjc3	36	9	/	/	SYM
cord-326631-7gd3hjc3	36	10	γ	γ	NN
cord-326631-7gd3hjc3	36	11	.	.	.
cord-326631-7gd3hjc3	37	1	The	the	DT
cord-326631-7gd3hjc3	37	2	basic	basic	JJ
cord-326631-7gd3hjc3	37	3	reproduction	reproduction	NN
cord-326631-7gd3hjc3	37	4	number	number	NN
cord-326631-7gd3hjc3	37	5	is	be	VBZ
cord-326631-7gd3hjc3	37	6	R	r	NN
cord-326631-7gd3hjc3	37	7	0	0	CD
cord-326631-7gd3hjc3	37	8	=	=	NFP
cord-326631-7gd3hjc3	38	1	βT.	βT.	NNP
cord-326631-7gd3hjc3	39	1	The	the	DT
cord-326631-7gd3hjc3	39	2	proportion	proportion	NN
cord-326631-7gd3hjc3	39	3	of	of	IN
cord-326631-7gd3hjc3	39	4	the	the	DT
cord-326631-7gd3hjc3	39	5	population	population	NN
cord-326631-7gd3hjc3	39	6	that	that	WDT
cord-326631-7gd3hjc3	39	7	is	be	VBZ
cord-326631-7gd3hjc3	39	8	infected	infect	VBN
cord-326631-7gd3hjc3	39	9	can	can	MD
cord-326631-7gd3hjc3	39	10	increase	increase	VB
cord-326631-7gd3hjc3	39	11	,	,	,
cord-326631-7gd3hjc3	39	12	and	and	CC
cord-326631-7gd3hjc3	39	13	hence	hence	RB
cord-326631-7gd3hjc3	39	14	an	an	DT
cord-326631-7gd3hjc3	39	15	epidemic	epidemic	NN
cord-326631-7gd3hjc3	39	16	can	can	MD
cord-326631-7gd3hjc3	39	17	occur	occur	VB
cord-326631-7gd3hjc3	39	18	,	,	,
cord-326631-7gd3hjc3	39	19	if	if	IN
cord-326631-7gd3hjc3	39	20	and	and	CC
cord-326631-7gd3hjc3	39	21	only	only	RB
cord-326631-7gd3hjc3	39	22	if	if	IN
cord-326631-7gd3hjc3	39	23	R	r	NN
cord-326631-7gd3hjc3	39	24	0	0	CD
cord-326631-7gd3hjc3	39	25	>	>	SYM
cord-326631-7gd3hjc3	39	26	1	1	CD
cord-326631-7gd3hjc3	39	27	.	.	.
cord-326631-7gd3hjc3	40	1	In	in	IN
cord-326631-7gd3hjc3	40	2	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	40	3	.	.	.
cord-326631-7gd3hjc3	41	1	(	(	-LRB-
cord-326631-7gd3hjc3	41	2	1	1	LS
cord-326631-7gd3hjc3	41	3	)	)	-RRB-
cord-326631-7gd3hjc3	41	4	,	,	,
cord-326631-7gd3hjc3	41	5	recruitment	recruitment	NN
cord-326631-7gd3hjc3	41	6	of	of	IN
cord-326631-7gd3hjc3	41	7	new	new	JJ
cord-326631-7gd3hjc3	41	8	susceptibles	susceptible	NNS
cord-326631-7gd3hjc3	41	9	through	through	IN
cord-326631-7gd3hjc3	41	10	birth	birth	NN
cord-326631-7gd3hjc3	41	11	or	or	CC
cord-326631-7gd3hjc3	41	12	immigration	immigration	NN
cord-326631-7gd3hjc3	41	13	is	be	VBZ
cord-326631-7gd3hjc3	41	14	ignored	ignore	VBN
cord-326631-7gd3hjc3	41	15	,	,	,
cord-326631-7gd3hjc3	41	16	as	as	IN
cord-326631-7gd3hjc3	41	17	is	be	VBZ
cord-326631-7gd3hjc3	41	18	loss	loss	NN
cord-326631-7gd3hjc3	41	19	of	of	IN
cord-326631-7gd3hjc3	41	20	individuals	individual	NNS
cord-326631-7gd3hjc3	41	21	through	through	IN
cord-326631-7gd3hjc3	41	22	mortality	mortality	NN
cord-326631-7gd3hjc3	41	23	or	or	CC
cord-326631-7gd3hjc3	41	24	emmigration	emmigration	NN
cord-326631-7gd3hjc3	41	25	.	.	.
cord-326631-7gd3hjc3	42	1	This	this	DT
cord-326631-7gd3hjc3	42	2	approximation	approximation	NN
cord-326631-7gd3hjc3	42	3	is	be	VBZ
cord-326631-7gd3hjc3	42	4	reasonable	reasonable	JJ
cord-326631-7gd3hjc3	42	5	provided	provide	VBN
cord-326631-7gd3hjc3	42	6	the	the	DT
cord-326631-7gd3hjc3	42	7	timescale	timescale	NN
cord-326631-7gd3hjc3	42	8	of	of	IN
cord-326631-7gd3hjc3	42	9	the	the	DT
cord-326631-7gd3hjc3	42	10	epidemic	epidemic	NN
cord-326631-7gd3hjc3	42	11	is	be	VBZ
cord-326631-7gd3hjc3	42	12	much	much	RB
cord-326631-7gd3hjc3	42	13	shorter	short	JJR
cord-326631-7gd3hjc3	42	14	than	than	IN
cord-326631-7gd3hjc3	42	15	the	the	DT
cord-326631-7gd3hjc3	42	16	timescale	timescale	NN
cord-326631-7gd3hjc3	42	17	over	over	IN
cord-326631-7gd3hjc3	42	18	which	which	WDT
cord-326631-7gd3hjc3	42	19	demographic	demographic	JJ
cord-326631-7gd3hjc3	42	20	turnover	turnover	NN
cord-326631-7gd3hjc3	42	21	occurs	occur	VBZ
cord-326631-7gd3hjc3	42	22	.	.	.
cord-326631-7gd3hjc3	43	1	No	no	DT
cord-326631-7gd3hjc3	43	2	recruitment	recruitment	NN
cord-326631-7gd3hjc3	43	3	ensures	ensure	VBZ
cord-326631-7gd3hjc3	43	4	that	that	IN
cord-326631-7gd3hjc3	43	5	the	the	DT
cord-326631-7gd3hjc3	43	6	disease	disease	NN
cord-326631-7gd3hjc3	43	7	will	will	MD
cord-326631-7gd3hjc3	43	8	eventually	eventually	RB
cord-326631-7gd3hjc3	43	9	burn	burn	VB
cord-326631-7gd3hjc3	43	10	out	out	RP
cord-326631-7gd3hjc3	43	11	,	,	,
cord-326631-7gd3hjc3	43	12	i.e.	i.e.	FW
cord-326631-7gd3hjc3	43	13	,	,	,
cord-326631-7gd3hjc3	43	14	I(∞	I(∞	NNP
cord-326631-7gd3hjc3	43	15	)	)	-RRB-
cord-326631-7gd3hjc3	43	16	=	=	SYM
cord-326631-7gd3hjc3	43	17	0	0	CD
cord-326631-7gd3hjc3	43	18	.	.	.
cord-326631-7gd3hjc3	44	1	To	to	TO
cord-326631-7gd3hjc3	44	2	see	see	VB
cord-326631-7gd3hjc3	44	3	formally	formally	RB
cord-326631-7gd3hjc3	44	4	that	that	IN
cord-326631-7gd3hjc3	44	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	44	6	must	must	MD
cord-326631-7gd3hjc3	44	7	have	have	VB
cord-326631-7gd3hjc3	44	8	I(∞	I(∞	NNP
cord-326631-7gd3hjc3	44	9	)	)	-RRB-
cord-326631-7gd3hjc3	44	10	=	=	SYM
cord-326631-7gd3hjc3	44	11	0	0	CD
cord-326631-7gd3hjc3	44	12	,	,	,
cord-326631-7gd3hjc3	44	13	note	note	VB
cord-326631-7gd3hjc3	44	14	that	that	IN
cord-326631-7gd3hjc3	44	15	the	the	DT
cord-326631-7gd3hjc3	44	16	positive	positive	JJ
cord-326631-7gd3hjc3	44	17	orthant	orthant	NN
cord-326631-7gd3hjc3	44	18	is	be	VBZ
cord-326631-7gd3hjc3	44	19	invariant	invariant	JJ
cord-326631-7gd3hjc3	44	20	so	so	IN
cord-326631-7gd3hjc3	44	21	all	all	DT
cord-326631-7gd3hjc3	44	22	solutions	solution	NNS
cord-326631-7gd3hjc3	44	23	of	of	IN
cord-326631-7gd3hjc3	44	24	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	44	25	.	.	.
cord-326631-7gd3hjc3	45	1	(	(	-LRB-
cord-326631-7gd3hjc3	45	2	1	1	LS
cord-326631-7gd3hjc3	45	3	)	)	-RRB-
cord-326631-7gd3hjc3	45	4	lie	lie	VB
cord-326631-7gd3hjc3	45	5	in	in	IN
cord-326631-7gd3hjc3	45	6	the	the	DT
cord-326631-7gd3hjc3	45	7	non	non	JJ
cord-326631-7gd3hjc3	45	8	-	-	JJ
cord-326631-7gd3hjc3	45	9	negative	negative	JJ
cord-326631-7gd3hjc3	45	10	,	,	,
cord-326631-7gd3hjc3	45	11	bounded	bound	VBN
cord-326631-7gd3hjc3	45	12	set	set	NN
cord-326631-7gd3hjc3	45	13	defined	define	VBN
cord-326631-7gd3hjc3	45	14	by	by	IN
cord-326631-7gd3hjc3	45	15	S	S	NNP
cord-326631-7gd3hjc3	45	16	,	,	,
cord-326631-7gd3hjc3	45	17	I	-PRON-	PRP
cord-326631-7gd3hjc3	45	18	,	,	,
cord-326631-7gd3hjc3	45	19	R	r	NN
cord-326631-7gd3hjc3	45	20	≥	≥	CD
cord-326631-7gd3hjc3	45	21	0	0	NFP
cord-326631-7gd3hjc3	45	22	and	and	CC
cord-326631-7gd3hjc3	45	23	S	S	NNP
cord-326631-7gd3hjc3	46	1	+	+	CC
cord-326631-7gd3hjc3	47	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	47	2	+	+	CC
cord-326631-7gd3hjc3	47	3	R	r	NN
cord-326631-7gd3hjc3	47	4	=	=	SYM
cord-326631-7gd3hjc3	47	5	1	1	CD
cord-326631-7gd3hjc3	47	6	.	.	.
cord-326631-7gd3hjc3	48	1	Observing	observe	VBG
cord-326631-7gd3hjc3	48	2	that	that	IN
cord-326631-7gd3hjc3	48	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	48	4	see	see	VBP
cord-326631-7gd3hjc3	48	5	that	that	DT
cord-326631-7gd3hjc3	48	6	S	s	NN
cord-326631-7gd3hjc3	49	1	+	+	CC
cord-326631-7gd3hjc3	50	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	50	2	is	be	VBZ
cord-326631-7gd3hjc3	50	3	decreasing	decrease	VBG
cord-326631-7gd3hjc3	50	4	whenever	whenever	WRB
cord-326631-7gd3hjc3	50	5	I	-PRON-	PRP
cord-326631-7gd3hjc3	50	6	>	>	XX
cord-326631-7gd3hjc3	50	7	0	0	NFP
cord-326631-7gd3hjc3	50	8	.	.	.
cord-326631-7gd3hjc3	51	1	However	however	RB
cord-326631-7gd3hjc3	51	2	,	,	,
cord-326631-7gd3hjc3	51	3	S	S	NNP
cord-326631-7gd3hjc3	51	4	+	+	CC
cord-326631-7gd3hjc3	52	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	52	2	is	be	VBZ
cord-326631-7gd3hjc3	52	3	bounded	bound	VBN
cord-326631-7gd3hjc3	52	4	below	below	IN
cord-326631-7gd3hjc3	52	5	by	by	IN
cord-326631-7gd3hjc3	52	6	0	0	CD
cord-326631-7gd3hjc3	52	7	;	;	:
cord-326631-7gd3hjc3	52	8	hence	hence	RB
cord-326631-7gd3hjc3	52	9	it	-PRON-	PRP
cord-326631-7gd3hjc3	52	10	has	have	VBZ
cord-326631-7gd3hjc3	52	11	a	a	DT
cord-326631-7gd3hjc3	52	12	limit	limit	NN
cord-326631-7gd3hjc3	52	13	.	.	.
cord-326631-7gd3hjc3	53	1	Moreover	moreover	RB
cord-326631-7gd3hjc3	53	2	,	,	,
cord-326631-7gd3hjc3	53	3	Eq	Eq	NNP
cord-326631-7gd3hjc3	53	4	.	.	.
cord-326631-7gd3hjc3	54	1	(	(	-LRB-
cord-326631-7gd3hjc3	54	2	2	2	LS
cord-326631-7gd3hjc3	54	3	)	)	-RRB-
cord-326631-7gd3hjc3	54	4	implies	imply	VBZ
cord-326631-7gd3hjc3	54	5	that	that	IN
cord-326631-7gd3hjc3	54	6	d	d	NNP
cord-326631-7gd3hjc3	54	7	dt	dt	NNP
cord-326631-7gd3hjc3	54	8	(	(	-LRB-
cord-326631-7gd3hjc3	54	9	S	s	NN
cord-326631-7gd3hjc3	54	10	+	+	CC
cord-326631-7gd3hjc3	54	11	I	i	NN
cord-326631-7gd3hjc3	54	12	)	)	-RRB-
cord-326631-7gd3hjc3	54	13	is	be	VBZ
cord-326631-7gd3hjc3	54	14	bounded	bound	VBN
cord-326631-7gd3hjc3	54	15	because	because	IN
cord-326631-7gd3hjc3	54	16	I	-PRON-	PRP
cord-326631-7gd3hjc3	54	17	is	be	VBZ
cord-326631-7gd3hjc3	54	18	bounded	bound	VBN
cord-326631-7gd3hjc3	54	19	.	.	.
cord-326631-7gd3hjc3	55	1	Hence	hence	RB
cord-326631-7gd3hjc3	55	2	lim	lim	NNP
cord-326631-7gd3hjc3	55	3	t→∞	t→∞	NNP
cord-326631-7gd3hjc3	55	4	d	d	NNP
cord-326631-7gd3hjc3	55	5	dt	dt	NNP
cord-326631-7gd3hjc3	55	6	(	(	-LRB-
cord-326631-7gd3hjc3	55	7	S	s	NN
cord-326631-7gd3hjc3	55	8	+	+	CC
cord-326631-7gd3hjc3	55	9	I	i	NN
cord-326631-7gd3hjc3	55	10	)	)	-RRB-
cord-326631-7gd3hjc3	55	11	=	=	SYM
cord-326631-7gd3hjc3	55	12	0	0	NFP
cord-326631-7gd3hjc3	55	13	,	,	,
cord-326631-7gd3hjc3	55	14	so	so	RB
cord-326631-7gd3hjc3	55	15	Eq	Eq	NNP
cord-326631-7gd3hjc3	55	16	.	.	.
cord-326631-7gd3hjc3	56	1	(	(	-LRB-
cord-326631-7gd3hjc3	56	2	2	2	LS
cord-326631-7gd3hjc3	56	3	)	)	-RRB-
cord-326631-7gd3hjc3	56	4	yields	yield	NNS
cord-326631-7gd3hjc3	56	5	I(∞	I(∞	NNP
cord-326631-7gd3hjc3	56	6	)	)	-RRB-
cord-326631-7gd3hjc3	56	7	=	=	SYM
cord-326631-7gd3hjc3	56	8	0	0	CD
cord-326631-7gd3hjc3	56	9	.	.	.
cord-326631-7gd3hjc3	57	1	This	this	DT
cord-326631-7gd3hjc3	57	2	model	model	NN
cord-326631-7gd3hjc3	57	3	(	(	-LRB-
cord-326631-7gd3hjc3	57	4	1	1	CD
cord-326631-7gd3hjc3	57	5	)	)	-RRB-
cord-326631-7gd3hjc3	57	6	is	be	VBZ
cord-326631-7gd3hjc3	57	7	sufficiently	sufficiently	RB
cord-326631-7gd3hjc3	57	8	simple	simple	JJ
cord-326631-7gd3hjc3	57	9	that	that	IN
cord-326631-7gd3hjc3	57	10	an	an	DT
cord-326631-7gd3hjc3	57	11	exact	exact	JJ
cord-326631-7gd3hjc3	57	12	solution	solution	NN
cord-326631-7gd3hjc3	57	13	can	can	MD
cord-326631-7gd3hjc3	57	14	be	be	VB
cord-326631-7gd3hjc3	57	15	obtained	obtain	VBN
cord-326631-7gd3hjc3	57	16	for	for	IN
cord-326631-7gd3hjc3	57	17	the	the	DT
cord-326631-7gd3hjc3	57	18	phase	phase	NN
cord-326631-7gd3hjc3	57	19	portrait	portrait	NN
cord-326631-7gd3hjc3	57	20	.	.	.
cord-326631-7gd3hjc3	58	1	Forming	form	VBG
cord-326631-7gd3hjc3	58	2	dI	dI	NNP
cord-326631-7gd3hjc3	58	3	/	/	SYM
cord-326631-7gd3hjc3	58	4	dS	ds	NN
cord-326631-7gd3hjc3	58	5	and	and	CC
cord-326631-7gd3hjc3	58	6	integrating	integrate	VBG
cord-326631-7gd3hjc3	58	7	yields	yield	NNS
cord-326631-7gd3hjc3	58	8	An	an	DT
cord-326631-7gd3hjc3	58	9	epidemic	epidemic	NN
cord-326631-7gd3hjc3	58	10	ends	end	VBZ
cord-326631-7gd3hjc3	58	11	when	when	WRB
cord-326631-7gd3hjc3	58	12	no	no	DT
cord-326631-7gd3hjc3	58	13	infectives	infective	NNS
cord-326631-7gd3hjc3	58	14	remain	remain	VBP
cord-326631-7gd3hjc3	58	15	.	.	.
cord-326631-7gd3hjc3	59	1	Consequently	consequently	RB
cord-326631-7gd3hjc3	59	2	,	,	,
cord-326631-7gd3hjc3	59	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	59	4	can	can	MD
cord-326631-7gd3hjc3	59	5	find	find	VB
cord-326631-7gd3hjc3	59	6	the	the	DT
cord-326631-7gd3hjc3	59	7	final	final	JJ
cord-326631-7gd3hjc3	59	8	size	size	NN
cord-326631-7gd3hjc3	59	9	Z	z	NN
cord-326631-7gd3hjc3	59	10	by	by	IN
cord-326631-7gd3hjc3	59	11	setting	set	VBG
cord-326631-7gd3hjc3	59	12	I	-PRON-	PRP
cord-326631-7gd3hjc3	59	13	=	=	VBZ
cord-326631-7gd3hjc3	59	14	0	0	NFP
cord-326631-7gd3hjc3	60	1	in	in	IN
cord-326631-7gd3hjc3	60	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	60	3	.	.	.
cord-326631-7gd3hjc3	61	1	(	(	-LRB-
cord-326631-7gd3hjc3	61	2	3	3	LS
cord-326631-7gd3hjc3	61	3	)	)	-RRB-
cord-326631-7gd3hjc3	61	4	and	and	CC
cord-326631-7gd3hjc3	61	5	solving	solve	VBG
cord-326631-7gd3hjc3	61	6	for	for	IN
cord-326631-7gd3hjc3	61	7	Z	z	NN
cord-326631-7gd3hjc3	61	8	=	=	NN
cord-326631-7gd3hjc3	61	9	S(0	s(0	NN
cord-326631-7gd3hjc3	61	10	)	)	-RRB-
cord-326631-7gd3hjc3	62	1	−	−	NNP
cord-326631-7gd3hjc3	62	2	S.	S.	NNP
cord-326631-7gd3hjc3	63	1	This	this	DT
cord-326631-7gd3hjc3	63	2	yields	yield	VBZ
cord-326631-7gd3hjc3	63	3	the	the	DT
cord-326631-7gd3hjc3	63	4	implicit	implicit	JJ
cord-326631-7gd3hjc3	63	5	relation	relation	NN
cord-326631-7gd3hjc3	63	6	(	(	-LRB-
cord-326631-7gd3hjc3	63	7	an	an	DT
cord-326631-7gd3hjc3	63	8	explicit	explicit	JJ
cord-326631-7gd3hjc3	63	9	form	form	NN
cord-326631-7gd3hjc3	63	10	is	be	VBZ
cord-326631-7gd3hjc3	63	11	given	give	VBN
cord-326631-7gd3hjc3	63	12	in	in	IN
cord-326631-7gd3hjc3	63	13	Appendix	Appendix	NNP
cord-326631-7gd3hjc3	63	14	A	A	NNP
cord-326631-7gd3hjc3	63	15	)	)	-RRB-
cord-326631-7gd3hjc3	63	16	.	.	.
cord-326631-7gd3hjc3	64	1	The	the	DT
cord-326631-7gd3hjc3	64	2	general	general	JJ
cord-326631-7gd3hjc3	64	3	formula	formula	NN
cord-326631-7gd3hjc3	64	4	(	(	-LRB-
cord-326631-7gd3hjc3	64	5	4	4	LS
cord-326631-7gd3hjc3	64	6	)	)	-RRB-
cord-326631-7gd3hjc3	64	7	applies	apply	VBZ
cord-326631-7gd3hjc3	64	8	regardless	regardless	RB
cord-326631-7gd3hjc3	64	9	of	of	IN
cord-326631-7gd3hjc3	64	10	the	the	DT
cord-326631-7gd3hjc3	64	11	proportions	proportion	NNS
cord-326631-7gd3hjc3	64	12	of	of	IN
cord-326631-7gd3hjc3	64	13	the	the	DT
cord-326631-7gd3hjc3	64	14	population	population	NN
cord-326631-7gd3hjc3	64	15	that	that	WDT
cord-326631-7gd3hjc3	64	16	are	be	VBP
cord-326631-7gd3hjc3	64	17	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	64	18	and	and	CC
cord-326631-7gd3hjc3	64	19	infective	infective	JJ
cord-326631-7gd3hjc3	64	20	initially	initially	RB
cord-326631-7gd3hjc3	64	21	.	.	.
cord-326631-7gd3hjc3	65	1	A	a	DT
cord-326631-7gd3hjc3	65	2	less	less	JJR
cord-326631-7gd3hjc3	65	3	than	than	IN
cord-326631-7gd3hjc3	65	4	fully	fully	RB
cord-326631-7gd3hjc3	65	5	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	65	6	population	population	NN
cord-326631-7gd3hjc3	65	7	must	must	MD
cord-326631-7gd3hjc3	65	8	be	be	VB
cord-326631-7gd3hjc3	65	9	taken	take	VBN
cord-326631-7gd3hjc3	65	10	into	into	IN
cord-326631-7gd3hjc3	65	11	account	account	NN
cord-326631-7gd3hjc3	65	12	if	if	IN
cord-326631-7gd3hjc3	65	13	some	some	DT
cord-326631-7gd3hjc3	65	14	individuals	individual	NNS
cord-326631-7gd3hjc3	65	15	have	have	VBP
cord-326631-7gd3hjc3	65	16	been	be	VBN
cord-326631-7gd3hjc3	65	17	vaccinated	vaccinate	VBN
cord-326631-7gd3hjc3	65	18	or	or	CC
cord-326631-7gd3hjc3	65	19	retain	retain	VB
cord-326631-7gd3hjc3	65	20	immunity	immunity	NN
cord-326631-7gd3hjc3	65	21	from	from	IN
cord-326631-7gd3hjc3	65	22	previous	previous	JJ
cord-326631-7gd3hjc3	65	23	exposures	exposure	NNS
cord-326631-7gd3hjc3	65	24	.	.	.
cord-326631-7gd3hjc3	66	1	However	however	RB
cord-326631-7gd3hjc3	66	2	,	,	,
cord-326631-7gd3hjc3	66	3	in	in	IN
cord-326631-7gd3hjc3	66	4	the	the	DT
cord-326631-7gd3hjc3	66	5	important	important	JJ
cord-326631-7gd3hjc3	66	6	special	special	JJ
cord-326631-7gd3hjc3	66	7	case	case	NN
cord-326631-7gd3hjc3	66	8	where	where	WRB
cord-326631-7gd3hjc3	66	9	a	a	DT
cord-326631-7gd3hjc3	66	10	new	new	JJ
cord-326631-7gd3hjc3	66	11	pathogen	pathogen	NN
cord-326631-7gd3hjc3	66	12	enters	enter	VBZ
cord-326631-7gd3hjc3	66	13	a	a	DT
cord-326631-7gd3hjc3	66	14	fully	fully	RB
cord-326631-7gd3hjc3	66	15	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	66	16	population	population	NN
cord-326631-7gd3hjc3	66	17	,	,	,
cord-326631-7gd3hjc3	66	18	we	-PRON-	PRP
cord-326631-7gd3hjc3	66	19	have	have	VBP
cord-326631-7gd3hjc3	66	20	both	both	DT
cord-326631-7gd3hjc3	67	1	I(0	I(0	NNP
cord-326631-7gd3hjc3	67	2	)	)	-RRB-
cord-326631-7gd3hjc3	67	3	1	1	CD
cord-326631-7gd3hjc3	67	4	and	and	CC
cord-326631-7gd3hjc3	67	5	S(0	S(0	NNP
cord-326631-7gd3hjc3	67	6	)	)	-RRB-
cord-326631-7gd3hjc3	67	7	∼	∼	NNP
cord-326631-7gd3hjc3	67	8	1	1	CD
cord-326631-7gd3hjc3	67	9	.	.	.
cord-326631-7gd3hjc3	68	1	In	in	IN
cord-326631-7gd3hjc3	68	2	the	the	DT
cord-326631-7gd3hjc3	68	3	limit	limit	NN
cord-326631-7gd3hjc3	68	4	I(0	I(0	NNP
cord-326631-7gd3hjc3	68	5	)	)	-RRB-
cord-326631-7gd3hjc3	68	6	→	→	SYM
cord-326631-7gd3hjc3	68	7	0	0	CD
cord-326631-7gd3hjc3	68	8	,	,	,
cord-326631-7gd3hjc3	68	9	S(0	S(0	NNP
cord-326631-7gd3hjc3	68	10	)	)	-RRB-
cord-326631-7gd3hjc3	68	11	→	→	SYM
cord-326631-7gd3hjc3	68	12	1	1	CD
cord-326631-7gd3hjc3	68	13	,	,	,
cord-326631-7gd3hjc3	68	14	which	which	WDT
cord-326631-7gd3hjc3	68	15	is	be	VBZ
cord-326631-7gd3hjc3	68	16	the	the	DT
cord-326631-7gd3hjc3	68	17	usual	usual	JJ
cord-326631-7gd3hjc3	68	18	final	final	JJ
cord-326631-7gd3hjc3	68	19	size	size	NN
cord-326631-7gd3hjc3	68	20	formula	formula	NN
cord-326631-7gd3hjc3	68	21	.	.	.
cord-326631-7gd3hjc3	69	1	The	the	DT
cord-326631-7gd3hjc3	69	2	practical	practical	JJ
cord-326631-7gd3hjc3	69	3	utility	utility	NN
cord-326631-7gd3hjc3	69	4	of	of	IN
cord-326631-7gd3hjc3	69	5	the	the	DT
cord-326631-7gd3hjc3	69	6	final	final	JJ
cord-326631-7gd3hjc3	69	7	size	size	NN
cord-326631-7gd3hjc3	69	8	formula	formula	NN
cord-326631-7gd3hjc3	69	9	would	would	MD
cord-326631-7gd3hjc3	69	10	appear	appear	VB
cord-326631-7gd3hjc3	69	11	to	to	TO
cord-326631-7gd3hjc3	69	12	be	be	VB
cord-326631-7gd3hjc3	69	13	limited	limit	VBN
cord-326631-7gd3hjc3	69	14	by	by	IN
cord-326631-7gd3hjc3	69	15	the	the	DT
cord-326631-7gd3hjc3	69	16	fact	fact	NN
cord-326631-7gd3hjc3	69	17	that	that	IN
cord-326631-7gd3hjc3	69	18	it	-PRON-	PRP
cord-326631-7gd3hjc3	69	19	is	be	VBZ
cord-326631-7gd3hjc3	69	20	derived	derive	VBN
cord-326631-7gd3hjc3	69	21	from	from	IN
cord-326631-7gd3hjc3	69	22	the	the	DT
cord-326631-7gd3hjc3	69	23	overly	overly	RB
cord-326631-7gd3hjc3	69	24	simplistic	simplistic	JJ
cord-326631-7gd3hjc3	69	25	standard	standard	JJ
cord-326631-7gd3hjc3	69	26	SIR	SIR	NNP
cord-326631-7gd3hjc3	69	27	model	model	NN
cord-326631-7gd3hjc3	69	28	.	.	.
cord-326631-7gd3hjc3	70	1	In	in	IN
cord-326631-7gd3hjc3	70	2	the	the	DT
cord-326631-7gd3hjc3	70	3	remainder	remainder	NN
cord-326631-7gd3hjc3	70	4	of	of	IN
cord-326631-7gd3hjc3	70	5	this	this	DT
cord-326631-7gd3hjc3	70	6	paper	paper	NN
cord-326631-7gd3hjc3	70	7	we	-PRON-	PRP
cord-326631-7gd3hjc3	70	8	show	show	VBP
cord-326631-7gd3hjc3	70	9	that	that	IN
cord-326631-7gd3hjc3	70	10	,	,	,
cord-326631-7gd3hjc3	70	11	in	in	IN
cord-326631-7gd3hjc3	70	12	fact	fact	NN
cord-326631-7gd3hjc3	70	13	,	,	,
cord-326631-7gd3hjc3	70	14	the	the	DT
cord-326631-7gd3hjc3	70	15	formula	formula	NN
cord-326631-7gd3hjc3	70	16	is	be	VBZ
cord-326631-7gd3hjc3	70	17	valid	valid	JJ
cord-326631-7gd3hjc3	70	18	under	under	IN
cord-326631-7gd3hjc3	70	19	very	very	RB
cord-326631-7gd3hjc3	70	20	general	general	JJ
cord-326631-7gd3hjc3	70	21	circumstances	circumstance	NNS
cord-326631-7gd3hjc3	70	22	.	.	.
cord-326631-7gd3hjc3	71	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	71	2	generalize	generalize	VBP
cord-326631-7gd3hjc3	71	3	the	the	DT
cord-326631-7gd3hjc3	71	4	model	model	NN
cord-326631-7gd3hjc3	71	5	in	in	IN
cord-326631-7gd3hjc3	71	6	several	several	JJ
cord-326631-7gd3hjc3	71	7	steps	step	NNS
cord-326631-7gd3hjc3	71	8	,	,	,
cord-326631-7gd3hjc3	71	9	in	in	IN
cord-326631-7gd3hjc3	71	10	order	order	NN
cord-326631-7gd3hjc3	71	11	to	to	TO
cord-326631-7gd3hjc3	71	12	explain	explain	VB
cord-326631-7gd3hjc3	71	13	the	the	DT
cord-326631-7gd3hjc3	71	14	ideas	idea	NNS
cord-326631-7gd3hjc3	71	15	clearly	clearly	RB
cord-326631-7gd3hjc3	71	16	and	and	CC
cord-326631-7gd3hjc3	71	17	to	to	TO
cord-326631-7gd3hjc3	71	18	avoid	avoid	VB
cord-326631-7gd3hjc3	71	19	exposing	expose	VBG
cord-326631-7gd3hjc3	71	20	the	the	DT
cord-326631-7gd3hjc3	71	21	reader	reader	NN
cord-326631-7gd3hjc3	71	22	to	to	IN
cord-326631-7gd3hjc3	71	23	a	a	DT
cord-326631-7gd3hjc3	71	24	notational	notational	JJ
cord-326631-7gd3hjc3	71	25	burden	burden	NN
cord-326631-7gd3hjc3	71	26	at	at	IN
cord-326631-7gd3hjc3	71	27	the	the	DT
cord-326631-7gd3hjc3	71	28	outset	outset	NN
cord-326631-7gd3hjc3	71	29	.	.	.
cord-326631-7gd3hjc3	72	1	The	the	DT
cord-326631-7gd3hjc3	72	2	standard	standard	JJ
cord-326631-7gd3hjc3	72	3	SIR	SIR	NNP
cord-326631-7gd3hjc3	72	4	model	model	NN
cord-326631-7gd3hjc3	72	5	ignores	ignore	VBZ
cord-326631-7gd3hjc3	72	6	any	any	DT
cord-326631-7gd3hjc3	72	7	delay	delay	NN
cord-326631-7gd3hjc3	72	8	between	between	IN
cord-326631-7gd3hjc3	72	9	the	the	DT
cord-326631-7gd3hjc3	72	10	time	time	NN
cord-326631-7gd3hjc3	72	11	an	an	DT
cord-326631-7gd3hjc3	72	12	individual	individual	NN
cord-326631-7gd3hjc3	72	13	is	be	VBZ
cord-326631-7gd3hjc3	72	14	infected	infect	VBN
cord-326631-7gd3hjc3	72	15	and	and	CC
cord-326631-7gd3hjc3	72	16	the	the	DT
cord-326631-7gd3hjc3	72	17	onset	onset	NN
cord-326631-7gd3hjc3	72	18	of	of	IN
cord-326631-7gd3hjc3	72	19	infectiousness	infectiousness	NN
cord-326631-7gd3hjc3	72	20	.	.	.
cord-326631-7gd3hjc3	73	1	This	this	DT
cord-326631-7gd3hjc3	73	2	latent	latent	JJ
cord-326631-7gd3hjc3	73	3	period	period	NN
cord-326631-7gd3hjc3	73	4	is	be	VBZ
cord-326631-7gd3hjc3	73	5	often	often	RB
cord-326631-7gd3hjc3	73	6	substantial	substantial	JJ
cord-326631-7gd3hjc3	73	7	compared	compare	VBN
cord-326631-7gd3hjc3	73	8	with	with	IN
cord-326631-7gd3hjc3	73	9	the	the	DT
cord-326631-7gd3hjc3	73	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	73	11	period	period	NN
cord-326631-7gd3hjc3	73	12	(	(	-LRB-
cord-326631-7gd3hjc3	73	13	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	73	14	and	and	CC
cord-326631-7gd3hjc3	73	15	May	May	NNP
cord-326631-7gd3hjc3	73	16	,	,	,
cord-326631-7gd3hjc3	73	17	1991	1991	CD
cord-326631-7gd3hjc3	73	18	)	)	-RRB-
cord-326631-7gd3hjc3	73	19	.	.	.
cord-326631-7gd3hjc3	74	1	In	in	IN
cord-326631-7gd3hjc3	74	2	addition	addition	NN
cord-326631-7gd3hjc3	74	3	,	,	,
cord-326631-7gd3hjc3	74	4	some	some	DT
cord-326631-7gd3hjc3	74	5	pathogens	pathogen	NNS
cord-326631-7gd3hjc3	74	6	(	(	-LRB-
cord-326631-7gd3hjc3	74	7	notably	notably	RB
cord-326631-7gd3hjc3	74	8	HIV	HIV	NNP
cord-326631-7gd3hjc3	74	9	)	)	-RRB-
cord-326631-7gd3hjc3	74	10	give	give	VBP
cord-326631-7gd3hjc3	74	11	rise	rise	NN
cord-326631-7gd3hjc3	74	12	to	to	IN
cord-326631-7gd3hjc3	74	13	a	a	DT
cord-326631-7gd3hjc3	74	14	sequence	sequence	NN
cord-326631-7gd3hjc3	74	15	of	of	IN
cord-326631-7gd3hjc3	74	16	distinct	distinct	JJ
cord-326631-7gd3hjc3	74	17	stages	stage	NNS
cord-326631-7gd3hjc3	74	18	of	of	IN
cord-326631-7gd3hjc3	74	19	infection	infection	NN
cord-326631-7gd3hjc3	74	20	,	,	,
cord-326631-7gd3hjc3	74	21	each	each	DT
cord-326631-7gd3hjc3	74	22	yielding	yield	VBG
cord-326631-7gd3hjc3	74	23	a	a	DT
cord-326631-7gd3hjc3	74	24	different	different	JJ
cord-326631-7gd3hjc3	74	25	transmission	transmission	NN
cord-326631-7gd3hjc3	74	26	rate	rate	NN
cord-326631-7gd3hjc3	74	27	(	(	-LRB-
cord-326631-7gd3hjc3	74	28	Redfield	Redfield	NNP
cord-326631-7gd3hjc3	74	29	et	et	NNP
cord-326631-7gd3hjc3	74	30	al	al	NNP
cord-326631-7gd3hjc3	74	31	.	.	NNP
cord-326631-7gd3hjc3	74	32	,	,	,
cord-326631-7gd3hjc3	74	33	1986	1986	CD
cord-326631-7gd3hjc3	74	34	;	;	.
cord-326631-7gd3hjc3	75	1	Seligmann	Seligmann	NNP
cord-326631-7gd3hjc3	75	2	et	et	NNP
cord-326631-7gd3hjc3	75	3	al	al	NNP
cord-326631-7gd3hjc3	75	4	.	.	NNP
cord-326631-7gd3hjc3	75	5	,	,	,
cord-326631-7gd3hjc3	75	6	1987	1987	CD
cord-326631-7gd3hjc3	75	7	)	)	-RRB-
cord-326631-7gd3hjc3	75	8	.	.	.
cord-326631-7gd3hjc3	76	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	76	2	is	be	VBZ
cord-326631-7gd3hjc3	76	3	common	common	JJ
cord-326631-7gd3hjc3	76	4	to	to	TO
cord-326631-7gd3hjc3	76	5	incorporate	incorporate	VB
cord-326631-7gd3hjc3	76	6	latency	latency	NN
cord-326631-7gd3hjc3	76	7	by	by	IN
cord-326631-7gd3hjc3	76	8	including	include	VBG
cord-326631-7gd3hjc3	76	9	an	an	DT
cord-326631-7gd3hjc3	76	10	"	"	``
cord-326631-7gd3hjc3	76	11	exposed	expose	VBN
cord-326631-7gd3hjc3	76	12	"	"	''
cord-326631-7gd3hjc3	76	13	class	class	NN
cord-326631-7gd3hjc3	76	14	(	(	-LRB-
cord-326631-7gd3hjc3	76	15	E	E	NNP
cord-326631-7gd3hjc3	76	16	)	)	-RRB-
cord-326631-7gd3hjc3	76	17	,	,	,
cord-326631-7gd3hjc3	76	18	yielding	yield	VBG
cord-326631-7gd3hjc3	76	19	an	an	DT
cord-326631-7gd3hjc3	76	20	SEIR	seir	NN
cord-326631-7gd3hjc3	76	21	model	model	NN
cord-326631-7gd3hjc3	76	22	(	(	-LRB-
cord-326631-7gd3hjc3	76	23	Schwartz	Schwartz	NNP
cord-326631-7gd3hjc3	76	24	and	and	CC
cord-326631-7gd3hjc3	76	25	Smith	Smith	NNP
cord-326631-7gd3hjc3	76	26	,	,	,
cord-326631-7gd3hjc3	76	27	1983	1983	CD
cord-326631-7gd3hjc3	76	28	;	;	:
cord-326631-7gd3hjc3	77	1	Earn	earn	VB
cord-326631-7gd3hjc3	77	2	et	et	FW
cord-326631-7gd3hjc3	77	3	al	al	NNP
cord-326631-7gd3hjc3	77	4	.	.	NNP
cord-326631-7gd3hjc3	77	5	,	,	,
cord-326631-7gd3hjc3	77	6	2000a	2000a	CD
cord-326631-7gd3hjc3	77	7	)	)	-RRB-
cord-326631-7gd3hjc3	77	8	.	.	.
cord-326631-7gd3hjc3	78	1	However	however	RB
cord-326631-7gd3hjc3	78	2	,	,	,
cord-326631-7gd3hjc3	78	3	noting	note	VBG
cord-326631-7gd3hjc3	78	4	that	that	IN
cord-326631-7gd3hjc3	78	5	the	the	DT
cord-326631-7gd3hjc3	78	6	exposed	expose	VBN
cord-326631-7gd3hjc3	78	7	stage	stage	NN
cord-326631-7gd3hjc3	78	8	can	can	MD
cord-326631-7gd3hjc3	78	9	be	be	VB
cord-326631-7gd3hjc3	78	10	regarded	regard	VBN
cord-326631-7gd3hjc3	78	11	as	as	IN
cord-326631-7gd3hjc3	78	12	an	an	DT
cord-326631-7gd3hjc3	78	13	infectious	infectious	JJ
cord-326631-7gd3hjc3	78	14	stage	stage	NN
cord-326631-7gd3hjc3	78	15	during	during	IN
cord-326631-7gd3hjc3	78	16	which	which	WDT
cord-326631-7gd3hjc3	78	17	the	the	DT
cord-326631-7gd3hjc3	78	18	transmission	transmission	NN
cord-326631-7gd3hjc3	78	19	rate	rate	NN
cord-326631-7gd3hjc3	78	20	happens	happen	VBZ
cord-326631-7gd3hjc3	78	21	to	to	TO
cord-326631-7gd3hjc3	78	22	be	be	VB
cord-326631-7gd3hjc3	78	23	zero	zero	CD
cord-326631-7gd3hjc3	78	24	,	,	,
cord-326631-7gd3hjc3	78	25	we	-PRON-	PRP
cord-326631-7gd3hjc3	78	26	lose	lose	VBP
cord-326631-7gd3hjc3	78	27	no	no	DT
cord-326631-7gd3hjc3	78	28	generality	generality	NN
cord-326631-7gd3hjc3	78	29	by	by	IN
cord-326631-7gd3hjc3	78	30	restricting	restrict	VBG
cord-326631-7gd3hjc3	78	31	attention	attention	NN
cord-326631-7gd3hjc3	78	32	to	to	IN
cord-326631-7gd3hjc3	78	33	multiple	multiple	JJ
cord-326631-7gd3hjc3	78	34	infectious	infectious	JJ
cord-326631-7gd3hjc3	78	35	stage	stage	NN
cord-326631-7gd3hjc3	78	36	models	model	NNS
cord-326631-7gd3hjc3	78	37	,	,	,
cord-326631-7gd3hjc3	78	38	which	which	WDT
cord-326631-7gd3hjc3	78	39	we	-PRON-	PRP
cord-326631-7gd3hjc3	78	40	refer	refer	VBP
cord-326631-7gd3hjc3	78	41	to	to	IN
cord-326631-7gd3hjc3	78	42	as	as	IN
cord-326631-7gd3hjc3	78	43	SI	SI	NNP
cord-326631-7gd3hjc3	78	44	n	n	NN
cord-326631-7gd3hjc3	78	45	R	r	NN
cord-326631-7gd3hjc3	78	46	models	model	NNS
cord-326631-7gd3hjc3	78	47	if	if	IN
cord-326631-7gd3hjc3	78	48	there	there	EX
cord-326631-7gd3hjc3	78	49	are	be	VBP
cord-326631-7gd3hjc3	78	50	n	n	NN
cord-326631-7gd3hjc3	78	51	infectious	infectious	JJ
cord-326631-7gd3hjc3	78	52	stages	stage	NNS
cord-326631-7gd3hjc3	78	53	.	.	.
cord-326631-7gd3hjc3	79	1	Generalizing	generalize	VBG
cord-326631-7gd3hjc3	79	2	the	the	DT
cord-326631-7gd3hjc3	79	3	SIR	SIR	NNP
cord-326631-7gd3hjc3	79	4	model	model	NN
cord-326631-7gd3hjc3	79	5	(	(	-LRB-
cord-326631-7gd3hjc3	79	6	1	1	CD
cord-326631-7gd3hjc3	79	7	)	)	-RRB-
cord-326631-7gd3hjc3	79	8	to	to	TO
cord-326631-7gd3hjc3	79	9	include	include	VB
cord-326631-7gd3hjc3	79	10	multiple	multiple	JJ
cord-326631-7gd3hjc3	79	11	infectious	infectious	JJ
cord-326631-7gd3hjc3	79	12	stages	stage	NNS
cord-326631-7gd3hjc3	79	13	,	,	,
cord-326631-7gd3hjc3	79	14	the	the	DT
cord-326631-7gd3hjc3	79	15	equations	equation	NNS
cord-326631-7gd3hjc3	79	16	for	for	IN
cord-326631-7gd3hjc3	79	17	an	an	DT
cord-326631-7gd3hjc3	79	18	SI	SI	NNP
cord-326631-7gd3hjc3	79	19	n	n	NN
cord-326631-7gd3hjc3	79	20	R	r	NN
cord-326631-7gd3hjc3	79	21	arė	arė	JJ
cord-326631-7gd3hjc3	79	22	where	where	WRB
cord-326631-7gd3hjc3	79	23	I	-PRON-	PRP
cord-326631-7gd3hjc3	79	24	i	i	PRP
cord-326631-7gd3hjc3	79	25	is	be	VBZ
cord-326631-7gd3hjc3	79	26	the	the	DT
cord-326631-7gd3hjc3	79	27	density	density	NN
cord-326631-7gd3hjc3	79	28	of	of	IN
cord-326631-7gd3hjc3	79	29	individuals	individual	NNS
cord-326631-7gd3hjc3	79	30	in	in	IN
cord-326631-7gd3hjc3	79	31	the	the	DT
cord-326631-7gd3hjc3	79	32	ith	ith	JJ
cord-326631-7gd3hjc3	79	33	infectious	infectious	JJ
cord-326631-7gd3hjc3	79	34	stage	stage	NN
cord-326631-7gd3hjc3	79	35	,	,	,
cord-326631-7gd3hjc3	79	36	β	β	NN
cord-326631-7gd3hjc3	79	37	i	i	PRP
cord-326631-7gd3hjc3	79	38	is	be	VBZ
cord-326631-7gd3hjc3	79	39	the	the	DT
cord-326631-7gd3hjc3	79	40	transmission	transmission	NN
cord-326631-7gd3hjc3	79	41	rate	rate	NN
cord-326631-7gd3hjc3	79	42	for	for	IN
cord-326631-7gd3hjc3	79	43	contact	contact	NN
cord-326631-7gd3hjc3	79	44	with	with	IN
cord-326631-7gd3hjc3	79	45	individuals	individual	NNS
cord-326631-7gd3hjc3	79	46	in	in	IN
cord-326631-7gd3hjc3	79	47	this	this	DT
cord-326631-7gd3hjc3	79	48	stage	stage	NN
cord-326631-7gd3hjc3	79	49	,	,	,
cord-326631-7gd3hjc3	79	50	and	and	CC
cord-326631-7gd3hjc3	79	51	1	1	CD
cord-326631-7gd3hjc3	79	52	γi	γi	NN
cord-326631-7gd3hjc3	79	53	is	be	VBZ
cord-326631-7gd3hjc3	79	54	the	the	DT
cord-326631-7gd3hjc3	79	55	mean	mean	JJ
cord-326631-7gd3hjc3	79	56	duration	duration	NN
cord-326631-7gd3hjc3	79	57	of	of	IN
cord-326631-7gd3hjc3	79	58	this	this	DT
cord-326631-7gd3hjc3	79	59	stage	stage	NN
cord-326631-7gd3hjc3	79	60	.	.	.
cord-326631-7gd3hjc3	80	1	The	the	DT
cord-326631-7gd3hjc3	80	2	sum	sum	NN
cord-326631-7gd3hjc3	80	3	of	of	IN
cord-326631-7gd3hjc3	80	4	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	80	5	.	.	.
cord-326631-7gd3hjc3	81	1	(	(	-LRB-
cord-326631-7gd3hjc3	81	2	6	6	LS
cord-326631-7gd3hjc3	81	3	)	)	-RRB-
cord-326631-7gd3hjc3	81	4	is	be	VBZ
cord-326631-7gd3hjc3	81	5	zero	zero	CD
cord-326631-7gd3hjc3	81	6	,	,	,
cord-326631-7gd3hjc3	81	7	implying	imply	VBG
cord-326631-7gd3hjc3	81	8	that	that	IN
cord-326631-7gd3hjc3	81	9	S	S	NNP
cord-326631-7gd3hjc3	81	10	+	+	CC
cord-326631-7gd3hjc3	81	11	n	n	CD
cord-326631-7gd3hjc3	81	12	i=1	i=1	NNS
cord-326631-7gd3hjc3	82	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	83	1	i	i	PRP
cord-326631-7gd3hjc3	83	2	+	+	CC
cord-326631-7gd3hjc3	83	3	R	r	NN
cord-326631-7gd3hjc3	83	4	is	be	VBZ
cord-326631-7gd3hjc3	83	5	invariant	invariant	JJ
cord-326631-7gd3hjc3	83	6	(	(	-LRB-
cord-326631-7gd3hjc3	83	7	and	and	CC
cord-326631-7gd3hjc3	84	1	hence	hence	RB
cord-326631-7gd3hjc3	84	2	that	that	IN
cord-326631-7gd3hjc3	84	3	Eq	Eq	NNP
cord-326631-7gd3hjc3	84	4	.	.	.
cord-326631-7gd3hjc3	85	1	(	(	-LRB-
cord-326631-7gd3hjc3	85	2	6d	6d	NNP
cord-326631-7gd3hjc3	85	3	)	)	-RRB-
cord-326631-7gd3hjc3	85	4	is	be	VBZ
cord-326631-7gd3hjc3	85	5	superfluous	superfluous	JJ
cord-326631-7gd3hjc3	85	6	,	,	,
cord-326631-7gd3hjc3	85	7	as	as	IN
cord-326631-7gd3hjc3	85	8	in	in	IN
cord-326631-7gd3hjc3	85	9	the	the	DT
cord-326631-7gd3hjc3	85	10	basic	basic	JJ
cord-326631-7gd3hjc3	85	11	SIR	SIR	NNP
cord-326631-7gd3hjc3	85	12	model	model	NN
cord-326631-7gd3hjc3	85	13	)	)	-RRB-
cord-326631-7gd3hjc3	85	14	.	.	.
cord-326631-7gd3hjc3	86	1	To	to	TO
cord-326631-7gd3hjc3	86	2	see	see	VB
cord-326631-7gd3hjc3	86	3	that	that	IN
cord-326631-7gd3hjc3	86	4	the	the	DT
cord-326631-7gd3hjc3	86	5	final	final	JJ
cord-326631-7gd3hjc3	86	6	size	size	NN
cord-326631-7gd3hjc3	86	7	is	be	VBZ
cord-326631-7gd3hjc3	86	8	well	well	RB
cord-326631-7gd3hjc3	86	9	-	-	HYPH
cord-326631-7gd3hjc3	86	10	defined	define	VBN
cord-326631-7gd3hjc3	86	11	in	in	IN
cord-326631-7gd3hjc3	86	12	this	this	DT
cord-326631-7gd3hjc3	86	13	model	model	NN
cord-326631-7gd3hjc3	86	14	,	,	,
cord-326631-7gd3hjc3	86	15	we	-PRON-	PRP
cord-326631-7gd3hjc3	86	16	generalize	generalize	VBP
cord-326631-7gd3hjc3	86	17	the	the	DT
cord-326631-7gd3hjc3	86	18	argument	argument	NN
cord-326631-7gd3hjc3	86	19	given	give	VBN
cord-326631-7gd3hjc3	86	20	for	for	IN
cord-326631-7gd3hjc3	86	21	the	the	DT
cord-326631-7gd3hjc3	86	22	simple	simple	JJ
cord-326631-7gd3hjc3	86	23	SIR	SIR	NNP
cord-326631-7gd3hjc3	86	24	model	model	NN
cord-326631-7gd3hjc3	86	25	in	in	IN
cord-326631-7gd3hjc3	86	26	Section	section	NN
cord-326631-7gd3hjc3	86	27	2	2	CD
cord-326631-7gd3hjc3	86	28	.	.	.
cord-326631-7gd3hjc3	87	1	Let	let	VB
cord-326631-7gd3hjc3	87	2	J	J	NNP
cord-326631-7gd3hjc3	87	3	k	k	XX
cord-326631-7gd3hjc3	87	4	=	=	SYM
cord-326631-7gd3hjc3	87	5	S	s	NN
cord-326631-7gd3hjc3	88	1	+	+	CC
cord-326631-7gd3hjc3	89	1	k	k	NNP
cord-326631-7gd3hjc3	89	2	i=1	i=1	NNP
cord-326631-7gd3hjc3	90	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	91	1	i	i	PRP
cord-326631-7gd3hjc3	91	2	.	.	.
cord-326631-7gd3hjc3	92	1	Then	then	RB
cord-326631-7gd3hjc3	92	2	d	d	XX
cord-326631-7gd3hjc3	92	3	dt	dt	NN
cord-326631-7gd3hjc3	93	1	J	J	NNP
cord-326631-7gd3hjc3	93	2	k	k	NNP
cord-326631-7gd3hjc3	94	1	=	=	NFP
cord-326631-7gd3hjc3	94	2	−γ	−γ	VBN
cord-326631-7gd3hjc3	95	1	k	k	NNP
cord-326631-7gd3hjc3	96	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	96	2	k	k	XX
cord-326631-7gd3hjc3	97	1	,	,	,
cord-326631-7gd3hjc3	97	2	so	so	RB
cord-326631-7gd3hjc3	97	3	I	-PRON-	PRP
cord-326631-7gd3hjc3	97	4	k	k	XX
cord-326631-7gd3hjc3	97	5	>	>	XX
cord-326631-7gd3hjc3	97	6	0	0	NFP
cord-326631-7gd3hjc3	97	7	implies	imply	VBZ
cord-326631-7gd3hjc3	97	8	J	J	NNP
cord-326631-7gd3hjc3	97	9	k	k	NNP
cord-326631-7gd3hjc3	97	10	is	be	VBZ
cord-326631-7gd3hjc3	97	11	decreasing	decrease	VBG
cord-326631-7gd3hjc3	97	12	and	and	CC
cord-326631-7gd3hjc3	98	1	lim	lim	NNP
cord-326631-7gd3hjc3	98	2	t→∞	t→∞	NNP
cord-326631-7gd3hjc3	98	3	d	d	NNP
cord-326631-7gd3hjc3	98	4	dt	dt	NNP
cord-326631-7gd3hjc3	98	5	J	J	NNP
cord-326631-7gd3hjc3	98	6	k	k	NN
cord-326631-7gd3hjc3	98	7	=	=	SYM
cord-326631-7gd3hjc3	98	8	0	0	CD
cord-326631-7gd3hjc3	98	9	.	.	.
cord-326631-7gd3hjc3	99	1	Hence	hence	RB
cord-326631-7gd3hjc3	99	2	I	-PRON-	PRP
cord-326631-7gd3hjc3	99	3	k	k	XX
cord-326631-7gd3hjc3	99	4	(	(	-LRB-
cord-326631-7gd3hjc3	99	5	∞	∞	NNP
cord-326631-7gd3hjc3	99	6	)	)	-RRB-
cord-326631-7gd3hjc3	100	1	=	=	LS
cord-326631-7gd3hjc3	100	2	0	0	NFP
cord-326631-7gd3hjc3	101	1	for	for	IN
cord-326631-7gd3hjc3	101	2	all	all	DT
cord-326631-7gd3hjc3	101	3	k.	k.	NNP
cord-326631-7gd3hjc3	101	4	Before	before	IN
cord-326631-7gd3hjc3	101	5	a	a	DT
cord-326631-7gd3hjc3	101	6	new	new	JJ
cord-326631-7gd3hjc3	101	7	disease	disease	NN
cord-326631-7gd3hjc3	101	8	is	be	VBZ
cord-326631-7gd3hjc3	101	9	introduced	introduce	VBN
cord-326631-7gd3hjc3	101	10	into	into	IN
cord-326631-7gd3hjc3	101	11	a	a	DT
cord-326631-7gd3hjc3	101	12	population	population	NN
cord-326631-7gd3hjc3	101	13	,	,	,
cord-326631-7gd3hjc3	101	14	everyone	everyone	NN
cord-326631-7gd3hjc3	101	15	is	be	VBZ
cord-326631-7gd3hjc3	101	16	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	101	17	,	,	,
cord-326631-7gd3hjc3	101	18	i.e.	i.e.	FW
cord-326631-7gd3hjc3	101	19	,	,	,
cord-326631-7gd3hjc3	101	20	S	s	NN
cord-326631-7gd3hjc3	101	21	=	=	SYM
cord-326631-7gd3hjc3	101	22	1	1	CD
cord-326631-7gd3hjc3	101	23	,	,	,
cord-326631-7gd3hjc3	101	24	I	-PRON-	PRP
cord-326631-7gd3hjc3	101	25	1	1	CD
cord-326631-7gd3hjc3	101	26	=	=	SYM
cord-326631-7gd3hjc3	101	27	·	·	NFP
cord-326631-7gd3hjc3	101	28	·	·	NFP
cord-326631-7gd3hjc3	102	1	·	·	NFP
cord-326631-7gd3hjc3	102	2	=	=	NFP
cord-326631-7gd3hjc3	103	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	103	2	n	n	CC
cord-326631-7gd3hjc3	103	3	=	=	SYM
cord-326631-7gd3hjc3	103	4	0	0	NFP
cord-326631-7gd3hjc3	103	5	and	and	CC
cord-326631-7gd3hjc3	103	6	R	r	NN
cord-326631-7gd3hjc3	103	7	=	=	SYM
cord-326631-7gd3hjc3	103	8	0	0	CD
cord-326631-7gd3hjc3	103	9	,	,	,
cord-326631-7gd3hjc3	103	10	which	which	WDT
cord-326631-7gd3hjc3	103	11	is	be	VBZ
cord-326631-7gd3hjc3	103	12	known	know	VBN
cord-326631-7gd3hjc3	103	13	as	as	IN
cord-326631-7gd3hjc3	103	14	the	the	DT
cord-326631-7gd3hjc3	103	15	disease	disease	NN
cord-326631-7gd3hjc3	103	16	free	free	JJ
cord-326631-7gd3hjc3	103	17	equilibrium	equilibrium	NN
cord-326631-7gd3hjc3	103	18	(	(	-LRB-
cord-326631-7gd3hjc3	103	19	DFE	DFE	NNP
cord-326631-7gd3hjc3	103	20	)	)	-RRB-
cord-326631-7gd3hjc3	103	21	.	.	.
cord-326631-7gd3hjc3	104	1	The	the	DT
cord-326631-7gd3hjc3	104	2	stability	stability	NN
cord-326631-7gd3hjc3	104	3	of	of	IN
cord-326631-7gd3hjc3	104	4	the	the	DT
cord-326631-7gd3hjc3	104	5	DFE	DFE	NNP
cord-326631-7gd3hjc3	104	6	determines	determine	VBZ
cord-326631-7gd3hjc3	104	7	whether	whether	IN
cord-326631-7gd3hjc3	104	8	the	the	DT
cord-326631-7gd3hjc3	104	9	new	new	JJ
cord-326631-7gd3hjc3	104	10	disease	disease	NN
cord-326631-7gd3hjc3	104	11	can	can	MD
cord-326631-7gd3hjc3	104	12	cause	cause	VB
cord-326631-7gd3hjc3	104	13	an	an	DT
cord-326631-7gd3hjc3	104	14	epidemic	epidemic	NN
cord-326631-7gd3hjc3	104	15	.	.	.
cord-326631-7gd3hjc3	105	1	Hyman	Hyman	NNP
cord-326631-7gd3hjc3	105	2	et	et	NNP
cord-326631-7gd3hjc3	105	3	al	al	NNP
cord-326631-7gd3hjc3	105	4	.	.	.
cord-326631-7gd3hjc3	106	1	(	(	-LRB-
cord-326631-7gd3hjc3	106	2	1999	1999	CD
cord-326631-7gd3hjc3	106	3	)	)	-RRB-
cord-326631-7gd3hjc3	106	4	proved	prove	VBD
cord-326631-7gd3hjc3	106	5	that	that	IN
cord-326631-7gd3hjc3	106	6	the	the	DT
cord-326631-7gd3hjc3	106	7	quantity	quantity	NN
cord-326631-7gd3hjc3	106	8	determines	determine	VBZ
cord-326631-7gd3hjc3	106	9	the	the	DT
cord-326631-7gd3hjc3	106	10	stability	stability	NN
cord-326631-7gd3hjc3	106	11	of	of	IN
cord-326631-7gd3hjc3	106	12	the	the	DT
cord-326631-7gd3hjc3	106	13	DFE	DFE	NNP
cord-326631-7gd3hjc3	106	14	,	,	,
cord-326631-7gd3hjc3	106	15	i.e.	i.e.	FW
cord-326631-7gd3hjc3	106	16	,	,	,
cord-326631-7gd3hjc3	106	17	the	the	DT
cord-326631-7gd3hjc3	106	18	DFE	DFE	NNP
cord-326631-7gd3hjc3	106	19	is	be	VBZ
cord-326631-7gd3hjc3	106	20	locally	locally	RB
cord-326631-7gd3hjc3	106	21	stable	stable	JJ
cord-326631-7gd3hjc3	106	22	if	if	IN
cord-326631-7gd3hjc3	106	23	R	r	NN
cord-326631-7gd3hjc3	106	24	0	0	CD
cord-326631-7gd3hjc3	106	25	<	<	XX
cord-326631-7gd3hjc3	106	26	1	1	CD
cord-326631-7gd3hjc3	106	27	and	and	CC
cord-326631-7gd3hjc3	106	28	unstable	unstable	JJ
cord-326631-7gd3hjc3	107	1	if	if	IN
cord-326631-7gd3hjc3	107	2	R	r	NN
cord-326631-7gd3hjc3	107	3	0	0	CD
cord-326631-7gd3hjc3	107	4	>	>	SYM
cord-326631-7gd3hjc3	107	5	1	1	CD
cord-326631-7gd3hjc3	107	6	.	.	.
cord-326631-7gd3hjc3	108	1	Note	note	VB
cord-326631-7gd3hjc3	108	2	R	r	NN
cord-326631-7gd3hjc3	108	3	0	0	CD
cord-326631-7gd3hjc3	108	4	as	as	IN
cord-326631-7gd3hjc3	108	5	defined	define	VBN
cord-326631-7gd3hjc3	108	6	by	by	IN
cord-326631-7gd3hjc3	108	7	(	(	-LRB-
cord-326631-7gd3hjc3	108	8	7	7	CD
cord-326631-7gd3hjc3	108	9	)	)	-RRB-
cord-326631-7gd3hjc3	108	10	is	be	VBZ
cord-326631-7gd3hjc3	108	11	the	the	DT
cord-326631-7gd3hjc3	108	12	sum	sum	NN
cord-326631-7gd3hjc3	108	13	of	of	IN
cord-326631-7gd3hjc3	108	14	the	the	DT
cord-326631-7gd3hjc3	108	15	products	product	NNS
cord-326631-7gd3hjc3	108	16	of	of	IN
cord-326631-7gd3hjc3	108	17	the	the	DT
cord-326631-7gd3hjc3	108	18	transmission	transmission	NN
cord-326631-7gd3hjc3	108	19	rate	rate	NN
cord-326631-7gd3hjc3	108	20	and	and	CC
cord-326631-7gd3hjc3	108	21	mean	mean	JJ
cord-326631-7gd3hjc3	108	22	duration	duration	NN
cord-326631-7gd3hjc3	108	23	in	in	IN
cord-326631-7gd3hjc3	108	24	each	each	DT
cord-326631-7gd3hjc3	108	25	infectious	infectious	JJ
cord-326631-7gd3hjc3	108	26	stage	stage	NN
cord-326631-7gd3hjc3	108	27	,	,	,
cord-326631-7gd3hjc3	108	28	i.e.	i.e.	FW
cord-326631-7gd3hjc3	108	29	,	,	,
cord-326631-7gd3hjc3	108	30	it	-PRON-	PRP
cord-326631-7gd3hjc3	108	31	is	be	VBZ
cord-326631-7gd3hjc3	108	32	the	the	DT
cord-326631-7gd3hjc3	108	33	basic	basic	JJ
cord-326631-7gd3hjc3	108	34	reproduction	reproduction	NN
cord-326631-7gd3hjc3	108	35	number	number	NN
cord-326631-7gd3hjc3	108	36	for	for	IN
cord-326631-7gd3hjc3	108	37	this	this	DT
cord-326631-7gd3hjc3	108	38	model	model	NN
cord-326631-7gd3hjc3	108	39	.	.	.
cord-326631-7gd3hjc3	109	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	109	2	now	now	RB
cord-326631-7gd3hjc3	109	3	proceed	proceed	VBP
cord-326631-7gd3hjc3	109	4	to	to	TO
cord-326631-7gd3hjc3	109	5	show	show	VB
cord-326631-7gd3hjc3	109	6	that	that	IN
cord-326631-7gd3hjc3	109	7	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	109	8	.	.	.
cord-326631-7gd3hjc3	110	1	(	(	-LRB-
cord-326631-7gd3hjc3	110	2	6	6	LS
cord-326631-7gd3hjc3	110	3	)	)	-RRB-
cord-326631-7gd3hjc3	110	4	yield	yield	VB
cord-326631-7gd3hjc3	110	5	the	the	DT
cord-326631-7gd3hjc3	110	6	same	same	JJ
cord-326631-7gd3hjc3	110	7	final	final	JJ
cord-326631-7gd3hjc3	110	8	size	size	NN
cord-326631-7gd3hjc3	110	9	formula	formula	NN
cord-326631-7gd3hjc3	110	10	as	as	IN
cord-326631-7gd3hjc3	110	11	(	(	-LRB-
cord-326631-7gd3hjc3	110	12	5	5	CD
cord-326631-7gd3hjc3	110	13	)	)	-RRB-
cord-326631-7gd3hjc3	110	14	.	.	.
cord-326631-7gd3hjc3	111	1	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	111	2	and	and	CC
cord-326631-7gd3hjc3	111	3	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	111	4	(	(	-LRB-
cord-326631-7gd3hjc3	111	5	1980	1980	CD
cord-326631-7gd3hjc3	111	6	)	)	-RRB-
cord-326631-7gd3hjc3	111	7	established	establish	VBD
cord-326631-7gd3hjc3	111	8	this	this	DT
cord-326631-7gd3hjc3	111	9	for	for	IN
cord-326631-7gd3hjc3	111	10	the	the	DT
cord-326631-7gd3hjc3	111	11	special	special	JJ
cord-326631-7gd3hjc3	111	12	case	case	NN
cord-326631-7gd3hjc3	111	13	in	in	IN
cord-326631-7gd3hjc3	111	14	which	which	WDT
cord-326631-7gd3hjc3	111	15	each	each	DT
cord-326631-7gd3hjc3	111	16	stage	stage	NN
cord-326631-7gd3hjc3	111	17	has	have	VBZ
cord-326631-7gd3hjc3	111	18	the	the	DT
cord-326631-7gd3hjc3	111	19	same	same	JJ
cord-326631-7gd3hjc3	111	20	transmission	transmission	NN
cord-326631-7gd3hjc3	111	21	rate	rate	NN
cord-326631-7gd3hjc3	111	22	and	and	CC
cord-326631-7gd3hjc3	111	23	duration	duration	NN
cord-326631-7gd3hjc3	112	1	(	(	-LRB-
cord-326631-7gd3hjc3	112	2	β	β	NN
cord-326631-7gd3hjc3	112	3	i	i	NN
cord-326631-7gd3hjc3	112	4	=	=	SYM
cord-326631-7gd3hjc3	112	5	β	β	NN
cord-326631-7gd3hjc3	112	6	and	and	CC
cord-326631-7gd3hjc3	112	7	γ	γ	NNP
cord-326631-7gd3hjc3	112	8	i	i	NN
cord-326631-7gd3hjc3	112	9	=	=	SYM
cord-326631-7gd3hjc3	112	10	γ	γ	NN
cord-326631-7gd3hjc3	112	11	for	for	IN
cord-326631-7gd3hjc3	112	12	all	all	DT
cord-326631-7gd3hjc3	112	13	i	i	NN
cord-326631-7gd3hjc3	112	14	)	)	-RRB-
cord-326631-7gd3hjc3	112	15	.	.	.
cord-326631-7gd3hjc3	113	1	Their	-PRON-	PRP$
cord-326631-7gd3hjc3	113	2	method	method	NN
cord-326631-7gd3hjc3	113	3	can	can	MD
cord-326631-7gd3hjc3	113	4	easily	easily	RB
cord-326631-7gd3hjc3	113	5	be	be	VB
cord-326631-7gd3hjc3	113	6	generalized	generalize	VBN
cord-326631-7gd3hjc3	113	7	to	to	IN
cord-326631-7gd3hjc3	113	8	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	113	9	β	β	XX
cord-326631-7gd3hjc3	113	10	i	i	NN
cord-326631-7gd3hjc3	113	11	and	and	CC
cord-326631-7gd3hjc3	113	12	γ	γ	NNP
cord-326631-7gd3hjc3	113	13	i	i	PRP
cord-326631-7gd3hjc3	113	14	as	as	IN
cord-326631-7gd3hjc3	113	15	follows	follow	VBZ
cord-326631-7gd3hjc3	113	16	:	:	:
cord-326631-7gd3hjc3	113	17	Let	let	VB
cord-326631-7gd3hjc3	113	18	G	g	NN
cord-326631-7gd3hjc3	113	19	k	k	NN
cord-326631-7gd3hjc3	113	20	=	=	NN
cord-326631-7gd3hjc3	113	21	n	n	NN
cord-326631-7gd3hjc3	114	1	i	i	PRP
cord-326631-7gd3hjc3	115	1	=	=	NFP
cord-326631-7gd3hjc3	115	2	k+1	k+1	NNP
cord-326631-7gd3hjc3	116	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	117	1	i	i	PRP
cord-326631-7gd3hjc3	117	2	+	+	CC
cord-326631-7gd3hjc3	117	3	R	r	NN
cord-326631-7gd3hjc3	117	4	,	,	,
cord-326631-7gd3hjc3	117	5	k	k	NN
cord-326631-7gd3hjc3	117	6	=	=	SYM
cord-326631-7gd3hjc3	117	7	1	1	CD
cord-326631-7gd3hjc3	117	8	,	,	,
cord-326631-7gd3hjc3	117	9	.	.	.
cord-326631-7gd3hjc3	117	10	.	.	.
cord-326631-7gd3hjc3	117	11	.	.	.
cord-326631-7gd3hjc3	118	1	,	,	,
cord-326631-7gd3hjc3	118	2	n	n	CC
cord-326631-7gd3hjc3	118	3	−	−	NNP
cord-326631-7gd3hjc3	118	4	1	1	CD
cord-326631-7gd3hjc3	118	5	and	and	CC
cord-326631-7gd3hjc3	118	6	G	g	NN
cord-326631-7gd3hjc3	118	7	n	n	NN
cord-326631-7gd3hjc3	119	1	=	=	SYM
cord-326631-7gd3hjc3	119	2	R.	R.	NNP
cord-326631-7gd3hjc3	119	3	Then	then	RB
cord-326631-7gd3hjc3	119	4	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	119	5	.	.	.
cord-326631-7gd3hjc3	120	1	(	(	-LRB-
cord-326631-7gd3hjc3	120	2	6c	6c	NNP
cord-326631-7gd3hjc3	120	3	)	)	-RRB-
cord-326631-7gd3hjc3	120	4	and	and	CC
cord-326631-7gd3hjc3	120	5	(	(	-LRB-
cord-326631-7gd3hjc3	120	6	6d	6d	NNP
cord-326631-7gd3hjc3	120	7	)	)	-RRB-
cord-326631-7gd3hjc3	120	8	imply	imply	VBP
cord-326631-7gd3hjc3	120	9	d	d	NNP
cord-326631-7gd3hjc3	121	1	dt	dt	NNP
cord-326631-7gd3hjc3	121	2	G	G	NNP
cord-326631-7gd3hjc3	121	3	k	k	NN
cord-326631-7gd3hjc3	121	4	=	=	NN
cord-326631-7gd3hjc3	121	5	γ	γ	NN
cord-326631-7gd3hjc3	122	1	k	k	NNP
cord-326631-7gd3hjc3	122	2	I	-PRON-	PRP
cord-326631-7gd3hjc3	122	3	k	k	NNP
cord-326631-7gd3hjc3	122	4	for	for	IN
cord-326631-7gd3hjc3	122	5	each	each	DT
cord-326631-7gd3hjc3	122	6	k	k	XX
cord-326631-7gd3hjc3	122	7	=	=	SYM
cord-326631-7gd3hjc3	122	8	1	1	CD
cord-326631-7gd3hjc3	122	9	,	,	,
cord-326631-7gd3hjc3	122	10	.	.	.
cord-326631-7gd3hjc3	122	11	.	.	.
cord-326631-7gd3hjc3	122	12	.	.	.
cord-326631-7gd3hjc3	123	1	,	,	,
cord-326631-7gd3hjc3	123	2	n.	n.	NNP
cord-326631-7gd3hjc3	124	1	Consequently	consequently	RB
cord-326631-7gd3hjc3	124	2	,	,	,
cord-326631-7gd3hjc3	124	3	Eq	Eq	NNP
cord-326631-7gd3hjc3	124	4	.	.	.
cord-326631-7gd3hjc3	125	1	(	(	-LRB-
cord-326631-7gd3hjc3	125	2	6a	6a	LS
cord-326631-7gd3hjc3	125	3	)	)	-RRB-
cord-326631-7gd3hjc3	125	4	implies	imply	VBZ
cord-326631-7gd3hjc3	125	5	that	that	IN
cord-326631-7gd3hjc3	125	6	the	the	DT
cord-326631-7gd3hjc3	125	7	function	function	NN
cord-326631-7gd3hjc3	125	8	is	be	VBZ
cord-326631-7gd3hjc3	125	9	a	a	DT
cord-326631-7gd3hjc3	125	10	constant	constant	NN
cord-326631-7gd3hjc3	125	11	of	of	IN
cord-326631-7gd3hjc3	125	12	the	the	DT
cord-326631-7gd3hjc3	125	13	motion	motion	NN
cord-326631-7gd3hjc3	125	14	.	.	.
cord-326631-7gd3hjc3	126	1	For	for	IN
cord-326631-7gd3hjc3	126	2	a	a	DT
cord-326631-7gd3hjc3	126	3	newly	newly	RB
cord-326631-7gd3hjc3	126	4	invading	invade	VBG
cord-326631-7gd3hjc3	126	5	disease	disease	NN
cord-326631-7gd3hjc3	126	6	,	,	,
cord-326631-7gd3hjc3	126	7	S(0	S(0	NNP
cord-326631-7gd3hjc3	126	8	)	)	-RRB-
cord-326631-7gd3hjc3	127	1	→	→	IN
cord-326631-7gd3hjc3	127	2	1	1	CD
cord-326631-7gd3hjc3	127	3	,	,	,
cord-326631-7gd3hjc3	127	4	I	I	NNP
cord-326631-7gd3hjc3	127	5	k	k	NN
cord-326631-7gd3hjc3	127	6	(	(	-LRB-
cord-326631-7gd3hjc3	127	7	0	0	NFP
cord-326631-7gd3hjc3	127	8	)	)	-RRB-
cord-326631-7gd3hjc3	127	9	→	→	SYM
cord-326631-7gd3hjc3	127	10	0	0	CD
cord-326631-7gd3hjc3	127	11	and	and	CC
cord-326631-7gd3hjc3	127	12	Recalling	recall	VBG
cord-326631-7gd3hjc3	127	13	that	that	DT
cord-326631-7gd3hjc3	127	14	Z	z	NN
cord-326631-7gd3hjc3	127	15	=	=	NN
cord-326631-7gd3hjc3	127	16	R(∞	r(∞	NN
cord-326631-7gd3hjc3	127	17	)	)	-RRB-
cord-326631-7gd3hjc3	127	18	=	=	SYM
cord-326631-7gd3hjc3	127	19	1	1	CD
cord-326631-7gd3hjc3	127	20	−	−	NNP
cord-326631-7gd3hjc3	127	21	S(∞	S(∞	NNP
cord-326631-7gd3hjc3	127	22	)	)	-RRB-
cord-326631-7gd3hjc3	127	23	,	,	,
cord-326631-7gd3hjc3	127	24	and	and	CC
cord-326631-7gd3hjc3	127	25	Eq	Eq	NNP
cord-326631-7gd3hjc3	127	26	.	.	.
cord-326631-7gd3hjc3	128	1	(	(	-LRB-
cord-326631-7gd3hjc3	128	2	7	7	CD
cord-326631-7gd3hjc3	128	3	)	)	-RRB-
cord-326631-7gd3hjc3	128	4	,	,	,
cord-326631-7gd3hjc3	128	5	the	the	DT
cord-326631-7gd3hjc3	128	6	final	final	JJ
cord-326631-7gd3hjc3	128	7	size	size	NN
cord-326631-7gd3hjc3	128	8	formula	formula	NN
cord-326631-7gd3hjc3	128	9	Eq	Eq	NNP
cord-326631-7gd3hjc3	128	10	.	.	.
cord-326631-7gd3hjc3	129	1	(	(	-LRB-
cord-326631-7gd3hjc3	129	2	5	5	LS
cord-326631-7gd3hjc3	129	3	)	)	-RRB-
cord-326631-7gd3hjc3	129	4	immediately	immediately	RB
cord-326631-7gd3hjc3	129	5	follows	follow	VBZ
cord-326631-7gd3hjc3	129	6	.	.	.
cord-326631-7gd3hjc3	130	1	Consideration	consideration	NN
cord-326631-7gd3hjc3	130	2	of	of	IN
cord-326631-7gd3hjc3	130	3	a	a	DT
cord-326631-7gd3hjc3	130	4	special	special	JJ
cord-326631-7gd3hjc3	130	5	case	case	NN
cord-326631-7gd3hjc3	130	6	of	of	IN
cord-326631-7gd3hjc3	130	7	the	the	DT
cord-326631-7gd3hjc3	130	8	model	model	NN
cord-326631-7gd3hjc3	130	9	in	in	IN
cord-326631-7gd3hjc3	130	10	the	the	DT
cord-326631-7gd3hjc3	130	11	previous	previous	JJ
cord-326631-7gd3hjc3	130	12	section	section	NN
cord-326631-7gd3hjc3	130	13	allows	allow	VBZ
cord-326631-7gd3hjc3	130	14	us	-PRON-	PRP
cord-326631-7gd3hjc3	130	15	to	to	TO
cord-326631-7gd3hjc3	130	16	infer	infer	VB
cord-326631-7gd3hjc3	130	17	that	that	IN
cord-326631-7gd3hjc3	130	18	the	the	DT
cord-326631-7gd3hjc3	130	19	distribution	distribution	NN
cord-326631-7gd3hjc3	130	20	of	of	IN
cord-326631-7gd3hjc3	130	21	stage	stage	NN
cord-326631-7gd3hjc3	130	22	durations	duration	NNS
cord-326631-7gd3hjc3	130	23	in	in	IN
cord-326631-7gd3hjc3	130	24	any	any	DT
cord-326631-7gd3hjc3	130	25	infectious	infectious	JJ
cord-326631-7gd3hjc3	130	26	stage	stage	NN
cord-326631-7gd3hjc3	130	27	need	nee	MD
cord-326631-7gd3hjc3	130	28	not	not	RB
cord-326631-7gd3hjc3	130	29	be	be	VB
cord-326631-7gd3hjc3	130	30	exponentially	exponentially	RB
cord-326631-7gd3hjc3	130	31	distributed	distribute	VBN
cord-326631-7gd3hjc3	130	32	.	.	.
cord-326631-7gd3hjc3	131	1	The	the	DT
cord-326631-7gd3hjc3	131	2	final	final	JJ
cord-326631-7gd3hjc3	131	3	size	size	NN
cord-326631-7gd3hjc3	131	4	formula	formula	NN
cord-326631-7gd3hjc3	131	5	(	(	-LRB-
cord-326631-7gd3hjc3	131	6	5	5	LS
cord-326631-7gd3hjc3	131	7	)	)	-RRB-
cord-326631-7gd3hjc3	131	8	holds	hold	VBZ
cord-326631-7gd3hjc3	131	9	true	true	JJ
cord-326631-7gd3hjc3	131	10	if	if	IN
cord-326631-7gd3hjc3	131	11	the	the	DT
cord-326631-7gd3hjc3	131	12	stage	stage	NN
cord-326631-7gd3hjc3	131	13	durations	duration	NNS
cord-326631-7gd3hjc3	131	14	follow	follow	VBP
cord-326631-7gd3hjc3	131	15	a	a	DT
cord-326631-7gd3hjc3	131	16	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	131	17	distribution	distribution	NN
cord-326631-7gd3hjc3	131	18	,	,	,
cord-326631-7gd3hjc3	131	19	which	which	WDT
cord-326631-7gd3hjc3	131	20	has	have	VBZ
cord-326631-7gd3hjc3	131	21	probability	probability	NN
cord-326631-7gd3hjc3	131	22	density	density	NN
cord-326631-7gd3hjc3	131	23	Here	here	RB
cord-326631-7gd3hjc3	132	1	,	,	,
cord-326631-7gd3hjc3	132	2	the	the	DT
cord-326631-7gd3hjc3	132	3	shape	shape	NN
cord-326631-7gd3hjc3	132	4	parameter	parameter	NN
cord-326631-7gd3hjc3	132	5	k	k	NN
cord-326631-7gd3hjc3	132	6	is	be	VBZ
cord-326631-7gd3hjc3	132	7	a	a	DT
cord-326631-7gd3hjc3	132	8	positive	positive	JJ
cord-326631-7gd3hjc3	132	9	integer	integer	NN
cord-326631-7gd3hjc3	132	10	and	and	CC
cord-326631-7gd3hjc3	132	11	the	the	DT
cord-326631-7gd3hjc3	132	12	scale	scale	NN
cord-326631-7gd3hjc3	132	13	parameter	parameter	NN
cord-326631-7gd3hjc3	132	14	φ	φ	NN
cord-326631-7gd3hjc3	132	15	>	>	XX
cord-326631-7gd3hjc3	132	16	0	0	NFP
cord-326631-7gd3hjc3	132	17	.	.	.
cord-326631-7gd3hjc3	133	1	The	the	DT
cord-326631-7gd3hjc3	133	2	mean	mean	NN
cord-326631-7gd3hjc3	133	3	is	be	VBZ
cord-326631-7gd3hjc3	133	4	k	k	NN
cord-326631-7gd3hjc3	133	5	/	/	SYM
cord-326631-7gd3hjc3	133	6	φ	φ	NN
cord-326631-7gd3hjc3	133	7	and	and	CC
cord-326631-7gd3hjc3	133	8	the	the	DT
cord-326631-7gd3hjc3	133	9	variance	variance	NN
cord-326631-7gd3hjc3	134	1	is	be	VBZ
cord-326631-7gd3hjc3	134	2	k	k	NNP
cord-326631-7gd3hjc3	134	3	/	/	SYM
cord-326631-7gd3hjc3	134	4	φ	φ	NN
cord-326631-7gd3hjc3	134	5	2	2	CD
cord-326631-7gd3hjc3	134	6	.	.	.
cord-326631-7gd3hjc3	135	1	This	this	DT
cord-326631-7gd3hjc3	135	2	family	family	NN
cord-326631-7gd3hjc3	135	3	of	of	IN
cord-326631-7gd3hjc3	135	4	distributions	distribution	NNS
cord-326631-7gd3hjc3	135	5	includes	include	VBZ
cord-326631-7gd3hjc3	135	6	the	the	DT
cord-326631-7gd3hjc3	135	7	exponential	exponential	JJ
cord-326631-7gd3hjc3	135	8	distribution	distribution	NN
cord-326631-7gd3hjc3	135	9	(	(	-LRB-
cord-326631-7gd3hjc3	135	10	k	k	NN
cord-326631-7gd3hjc3	135	11	=	=	SYM
cord-326631-7gd3hjc3	135	12	1	1	CD
cord-326631-7gd3hjc3	135	13	)	)	-RRB-
cord-326631-7gd3hjc3	135	14	,	,	,
cord-326631-7gd3hjc3	135	15	nearly	nearly	RB
cord-326631-7gd3hjc3	135	16	normal	normal	JJ
cord-326631-7gd3hjc3	135	17	distributions	distribution	NNS
cord-326631-7gd3hjc3	135	18	(	(	-LRB-
cord-326631-7gd3hjc3	135	19	k	k	IN
cord-326631-7gd3hjc3	135	20	large	large	NNP
cord-326631-7gd3hjc3	135	21	)	)	-RRB-
cord-326631-7gd3hjc3	135	22	and	and	CC
cord-326631-7gd3hjc3	135	23	the	the	DT
cord-326631-7gd3hjc3	135	24	Delta	Delta	NNP
cord-326631-7gd3hjc3	135	25	distribution	distribution	NN
cord-326631-7gd3hjc3	135	26	,	,	,
cord-326631-7gd3hjc3	135	27	which	which	WDT
cord-326631-7gd3hjc3	135	28	yields	yield	VBZ
cord-326631-7gd3hjc3	135	29	a	a	DT
cord-326631-7gd3hjc3	135	30	fixed	fix	VBN
cord-326631-7gd3hjc3	135	31	duration	duration	NN
cord-326631-7gd3hjc3	135	32	(	(	-LRB-
cord-326631-7gd3hjc3	135	33	k	k	NN
cord-326631-7gd3hjc3	135	34	→	→	NN
cord-326631-7gd3hjc3	135	35	∞	∞	NNP
cord-326631-7gd3hjc3	135	36	)	)	-RRB-
cord-326631-7gd3hjc3	135	37	.	.	.
cord-326631-7gd3hjc3	136	1	The	the	DT
cord-326631-7gd3hjc3	136	2	term	term	NN
cord-326631-7gd3hjc3	136	3	−γ	−γ	VBN
cord-326631-7gd3hjc3	136	4	I	-PRON-	PRP
cord-326631-7gd3hjc3	136	5	in	in	IN
cord-326631-7gd3hjc3	136	6	Eq	Eq	NNP
cord-326631-7gd3hjc3	136	7	.	.	.
cord-326631-7gd3hjc3	137	1	(	(	-LRB-
cord-326631-7gd3hjc3	137	2	1b	1b	LS
cord-326631-7gd3hjc3	137	3	)	)	-RRB-
cord-326631-7gd3hjc3	137	4	for	for	IN
cord-326631-7gd3hjc3	137	5	the	the	DT
cord-326631-7gd3hjc3	137	6	simple	simple	JJ
cord-326631-7gd3hjc3	137	7	SIR	SIR	NNP
cord-326631-7gd3hjc3	137	8	model	model	NN
cord-326631-7gd3hjc3	137	9	implies	imply	VBZ
cord-326631-7gd3hjc3	137	10	that	that	IN
cord-326631-7gd3hjc3	137	11	the	the	DT
cord-326631-7gd3hjc3	137	12	durations	duration	NNS
cord-326631-7gd3hjc3	137	13	of	of	IN
cord-326631-7gd3hjc3	137	14	infectious	infectious	JJ
cord-326631-7gd3hjc3	137	15	periods	period	NNS
cord-326631-7gd3hjc3	137	16	are	be	VBP
cord-326631-7gd3hjc3	137	17	exponentially	exponentially	RB
cord-326631-7gd3hjc3	137	18	distributed	distribute	VBN
cord-326631-7gd3hjc3	137	19	with	with	IN
cord-326631-7gd3hjc3	137	20	mean	mean	JJ
cord-326631-7gd3hjc3	137	21	1	1	CD
cord-326631-7gd3hjc3	137	22	/	/	SYM
cord-326631-7gd3hjc3	137	23	γ	γ	NN
cord-326631-7gd3hjc3	137	24	(	(	-LRB-
cord-326631-7gd3hjc3	137	25	Brauer	Brauer	NNP
cord-326631-7gd3hjc3	137	26	and	and	CC
cord-326631-7gd3hjc3	137	27	Castillo	Castillo	NNP
cord-326631-7gd3hjc3	137	28	-	-	HYPH
cord-326631-7gd3hjc3	137	29	Chavez	Chavez	NNP
cord-326631-7gd3hjc3	137	30	,	,	,
cord-326631-7gd3hjc3	137	31	2001	2001	CD
cord-326631-7gd3hjc3	137	32	)	)	-RRB-
cord-326631-7gd3hjc3	137	33	.	.	.
cord-326631-7gd3hjc3	138	1	Since	since	IN
cord-326631-7gd3hjc3	138	2	the	the	DT
cord-326631-7gd3hjc3	138	3	sum	sum	NN
cord-326631-7gd3hjc3	138	4	of	of	IN
cord-326631-7gd3hjc3	138	5	exponentially	exponentially	RB
cord-326631-7gd3hjc3	138	6	distributed	distribute	VBN
cord-326631-7gd3hjc3	138	7	random	random	JJ
cord-326631-7gd3hjc3	138	8	variables	variable	NNS
cord-326631-7gd3hjc3	138	9	is	be	VBZ
cord-326631-7gd3hjc3	138	10	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	138	11	distributed	distribute	VBN
cord-326631-7gd3hjc3	138	12	,	,	,
cord-326631-7gd3hjc3	138	13	a	a	DT
cord-326631-7gd3hjc3	138	14	standard	standard	JJ
cord-326631-7gd3hjc3	138	15	trick	trick	NN
cord-326631-7gd3hjc3	138	16	(	(	-LRB-
cord-326631-7gd3hjc3	138	17	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	138	18	and	and	CC
cord-326631-7gd3hjc3	138	19	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	138	20	,	,	,
cord-326631-7gd3hjc3	138	21	1980	1980	CD
cord-326631-7gd3hjc3	138	22	;	;	:
cord-326631-7gd3hjc3	138	23	Lloyd	Lloyd	NNP
cord-326631-7gd3hjc3	138	24	,	,	,
cord-326631-7gd3hjc3	138	25	2001a	2001a	CD
cord-326631-7gd3hjc3	138	26	,	,	,
cord-326631-7gd3hjc3	138	27	b	b	LS
cord-326631-7gd3hjc3	138	28	)	)	-RRB-
cord-326631-7gd3hjc3	139	1	enables	enable	VBZ
cord-326631-7gd3hjc3	139	2	us	-PRON-	PRP
cord-326631-7gd3hjc3	139	3	to	to	TO
cord-326631-7gd3hjc3	139	4	replace	replace	VB
cord-326631-7gd3hjc3	139	5	an	an	DT
cord-326631-7gd3hjc3	139	6	exponential	exponential	JJ
cord-326631-7gd3hjc3	139	7	distribution	distribution	NN
cord-326631-7gd3hjc3	139	8	with	with	IN
cord-326631-7gd3hjc3	139	9	mean	mean	JJ
cord-326631-7gd3hjc3	139	10	1	1	CD
cord-326631-7gd3hjc3	139	11	/	/	SYM
cord-326631-7gd3hjc3	139	12	γ	γ	NN
cord-326631-7gd3hjc3	139	13	by	by	IN
cord-326631-7gd3hjc3	139	14	a	a	DT
cord-326631-7gd3hjc3	139	15	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	139	16	distribution	distribution	NN
cord-326631-7gd3hjc3	139	17	g	g	NN
cord-326631-7gd3hjc3	139	18	k	k	XX
cord-326631-7gd3hjc3	139	19	,	,	,
cord-326631-7gd3hjc3	139	20	kγ	kγ	PRP
cord-326631-7gd3hjc3	139	21	(	(	-LRB-
cord-326631-7gd3hjc3	139	22	which	which	WDT
cord-326631-7gd3hjc3	139	23	also	also	RB
cord-326631-7gd3hjc3	139	24	has	have	VBZ
cord-326631-7gd3hjc3	139	25	mean	mean	JJ
cord-326631-7gd3hjc3	139	26	1	1	CD
cord-326631-7gd3hjc3	139	27	/	/	SYM
cord-326631-7gd3hjc3	139	28	γ	γ	NN
cord-326631-7gd3hjc3	139	29	)	)	-RRB-
cord-326631-7gd3hjc3	139	30	.	.	.
cord-326631-7gd3hjc3	140	1	The	the	DT
cord-326631-7gd3hjc3	140	2	trick	trick	NN
cord-326631-7gd3hjc3	140	3	is	be	VBZ
cord-326631-7gd3hjc3	140	4	to	to	TO
cord-326631-7gd3hjc3	140	5	replace	replace	VB
cord-326631-7gd3hjc3	140	6	a	a	DT
cord-326631-7gd3hjc3	140	7	single	single	JJ
cord-326631-7gd3hjc3	140	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	140	9	stage	stage	NN
cord-326631-7gd3hjc3	140	10	with	with	IN
cord-326631-7gd3hjc3	140	11	k	k	NNP
cord-326631-7gd3hjc3	140	12	identical	identical	JJ
cord-326631-7gd3hjc3	140	13	exponentially	exponentially	RB
cord-326631-7gd3hjc3	140	14	distributed	distribute	VBN
cord-326631-7gd3hjc3	140	15	substages	substage	NNS
cord-326631-7gd3hjc3	140	16	of	of	IN
cord-326631-7gd3hjc3	140	17	mean	mean	JJ
cord-326631-7gd3hjc3	140	18	duration	duration	NN
cord-326631-7gd3hjc3	140	19	1/(kγ	1/(kγ	CD
cord-326631-7gd3hjc3	140	20	)	)	-RRB-
cord-326631-7gd3hjc3	140	21	.	.	.
cord-326631-7gd3hjc3	141	1	The	the	DT
cord-326631-7gd3hjc3	141	2	model	model	NN
cord-326631-7gd3hjc3	141	3	then	then	RB
cord-326631-7gd3hjc3	141	4	has	have	VBZ
cord-326631-7gd3hjc3	141	5	precisely	precisely	RB
cord-326631-7gd3hjc3	141	6	the	the	DT
cord-326631-7gd3hjc3	141	7	form	form	NN
cord-326631-7gd3hjc3	141	8	the	the	DT
cord-326631-7gd3hjc3	141	9	SI	SI	NNP
cord-326631-7gd3hjc3	141	10	n	n	NNP
cord-326631-7gd3hjc3	141	11	R	r	NN
cord-326631-7gd3hjc3	141	12	model	model	NN
cord-326631-7gd3hjc3	141	13	(	(	-LRB-
cord-326631-7gd3hjc3	141	14	6	6	CD
cord-326631-7gd3hjc3	141	15	)	)	-RRB-
cord-326631-7gd3hjc3	141	16	,	,	,
cord-326631-7gd3hjc3	141	17	but	but	CC
cord-326631-7gd3hjc3	141	18	with	with	IN
cord-326631-7gd3hjc3	141	19	the	the	DT
cord-326631-7gd3hjc3	141	20	sequence	sequence	NN
cord-326631-7gd3hjc3	141	21	of	of	IN
cord-326631-7gd3hjc3	141	22	infectious	infectious	JJ
cord-326631-7gd3hjc3	141	23	stages	stage	NNS
cord-326631-7gd3hjc3	141	24	being	be	VBG
cord-326631-7gd3hjc3	141	25	mathematical	mathematical	JJ
cord-326631-7gd3hjc3	141	26	artefacts	artefact	NNS
cord-326631-7gd3hjc3	141	27	rather	rather	RB
cord-326631-7gd3hjc3	141	28	than	than	IN
cord-326631-7gd3hjc3	141	29	biologically	biologically	RB
cord-326631-7gd3hjc3	141	30	meaningful	meaningful	JJ
cord-326631-7gd3hjc3	141	31	.	.	.
cord-326631-7gd3hjc3	142	1	Since	since	IN
cord-326631-7gd3hjc3	142	2	this	this	DT
cord-326631-7gd3hjc3	142	3	substage	substage	NN
cord-326631-7gd3hjc3	142	4	trick	trick	NN
cord-326631-7gd3hjc3	142	5	can	can	MD
cord-326631-7gd3hjc3	142	6	be	be	VB
cord-326631-7gd3hjc3	142	7	applied	apply	VBN
cord-326631-7gd3hjc3	142	8	equally	equally	RB
cord-326631-7gd3hjc3	142	9	well	well	RB
cord-326631-7gd3hjc3	142	10	to	to	IN
cord-326631-7gd3hjc3	142	11	any	any	DT
cord-326631-7gd3hjc3	142	12	infectious	infectious	JJ
cord-326631-7gd3hjc3	142	13	stage	stage	NN
cord-326631-7gd3hjc3	142	14	,	,	,
cord-326631-7gd3hjc3	142	15	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	142	16	and	and	CC
cord-326631-7gd3hjc3	142	17	Watson	Watson	NNP
cord-326631-7gd3hjc3	142	18	's	's	POS
cord-326631-7gd3hjc3	142	19	(	(	-LRB-
cord-326631-7gd3hjc3	142	20	1980	1980	CD
cord-326631-7gd3hjc3	142	21	)	)	-RRB-
cord-326631-7gd3hjc3	142	22	conclusion	conclusion	NN
cord-326631-7gd3hjc3	142	23	that	that	IN
cord-326631-7gd3hjc3	142	24	the	the	DT
cord-326631-7gd3hjc3	142	25	final	final	JJ
cord-326631-7gd3hjc3	142	26	size	size	NN
cord-326631-7gd3hjc3	142	27	in	in	IN
cord-326631-7gd3hjc3	142	28	an	an	DT
cord-326631-7gd3hjc3	142	29	SIR	SIR	NNP
cord-326631-7gd3hjc3	142	30	model	model	NN
cord-326631-7gd3hjc3	142	31	with	with	IN
cord-326631-7gd3hjc3	142	32	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	142	33	distributed	distribute	VBD
cord-326631-7gd3hjc3	142	34	infectious	infectious	JJ
cord-326631-7gd3hjc3	142	35	periods	period	NNS
cord-326631-7gd3hjc3	142	36	is	be	VBZ
cord-326631-7gd3hjc3	142	37	given	give	VBN
cord-326631-7gd3hjc3	142	38	by	by	IN
cord-326631-7gd3hjc3	142	39	the	the	DT
cord-326631-7gd3hjc3	142	40	usual	usual	JJ
cord-326631-7gd3hjc3	142	41	formula	formula	NN
cord-326631-7gd3hjc3	142	42	(	(	-LRB-
cord-326631-7gd3hjc3	142	43	5	5	LS
cord-326631-7gd3hjc3	142	44	)	)	-RRB-
cord-326631-7gd3hjc3	142	45	now	now	RB
cord-326631-7gd3hjc3	142	46	generalizes	generalize	VBZ
cord-326631-7gd3hjc3	142	47	to	to	IN
cord-326631-7gd3hjc3	142	48	an	an	DT
cord-326631-7gd3hjc3	142	49	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	142	50	number	number	NN
cord-326631-7gd3hjc3	142	51	of	of	IN
cord-326631-7gd3hjc3	142	52	stages	stage	NNS
cord-326631-7gd3hjc3	142	53	,	,	,
cord-326631-7gd3hjc3	142	54	each	each	DT
cord-326631-7gd3hjc3	142	55	with	with	IN
cord-326631-7gd3hjc3	142	56	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	142	57	distributed	distribute	VBN
cord-326631-7gd3hjc3	142	58	durations	duration	NNS
cord-326631-7gd3hjc3	142	59	.	.	.
cord-326631-7gd3hjc3	143	1	Although	although	IN
cord-326631-7gd3hjc3	143	2	expressed	express	VBN
cord-326631-7gd3hjc3	143	3	differently	differently	RB
cord-326631-7gd3hjc3	143	4	,	,	,
cord-326631-7gd3hjc3	143	5	in	in	IN
cord-326631-7gd3hjc3	143	6	their	-PRON-	PRP$
cord-326631-7gd3hjc3	143	7	original	original	JJ
cord-326631-7gd3hjc3	143	8	paper	paper	NN
cord-326631-7gd3hjc3	143	9	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	143	10	and	and	CC
cord-326631-7gd3hjc3	143	11	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	143	12	(	(	-LRB-
cord-326631-7gd3hjc3	143	13	1927	1927	CD
cord-326631-7gd3hjc3	143	14	)	)	-RRB-
cord-326631-7gd3hjc3	143	15	studied	study	VBD
cord-326631-7gd3hjc3	143	16	a	a	DT
cord-326631-7gd3hjc3	143	17	particular	particular	JJ
cord-326631-7gd3hjc3	143	18	limit	limit	NN
cord-326631-7gd3hjc3	143	19	of	of	IN
cord-326631-7gd3hjc3	143	20	the	the	DT
cord-326631-7gd3hjc3	143	21	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	143	22	distributed	distribute	VBD
cord-326631-7gd3hjc3	143	23	multiple	multiple	JJ
cord-326631-7gd3hjc3	143	24	stage	stage	NN
cord-326631-7gd3hjc3	143	25	model	model	NN
cord-326631-7gd3hjc3	143	26	described	describe	VBN
cord-326631-7gd3hjc3	143	27	in	in	IN
cord-326631-7gd3hjc3	143	28	the	the	DT
cord-326631-7gd3hjc3	143	29	previous	previous	JJ
cord-326631-7gd3hjc3	143	30	section	section	NN
cord-326631-7gd3hjc3	143	31	.	.	.
cord-326631-7gd3hjc3	144	1	Suppose	suppose	VB
cord-326631-7gd3hjc3	144	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	144	3	have	have	VBP
cord-326631-7gd3hjc3	144	4	a	a	DT
cord-326631-7gd3hjc3	144	5	sequence	sequence	NN
cord-326631-7gd3hjc3	144	6	of	of	IN
cord-326631-7gd3hjc3	144	7	n	n	NN
cord-326631-7gd3hjc3	144	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	144	9	stages	stage	NNS
cord-326631-7gd3hjc3	144	10	,	,	,
cord-326631-7gd3hjc3	144	11	each	each	DT
cord-326631-7gd3hjc3	144	12	with	with	IN
cord-326631-7gd3hjc3	144	13	the	the	DT
cord-326631-7gd3hjc3	144	14	same	same	JJ
cord-326631-7gd3hjc3	144	15	,	,	,
cord-326631-7gd3hjc3	144	16	fixed	fix	VBN
cord-326631-7gd3hjc3	144	17	stage	stage	NN
cord-326631-7gd3hjc3	144	18	duration	duration	NN
cord-326631-7gd3hjc3	144	19	τ	τ	NN
cord-326631-7gd3hjc3	144	20	.	.	.
cord-326631-7gd3hjc3	145	1	Thus	thus	RB
cord-326631-7gd3hjc3	145	2	,	,	,
cord-326631-7gd3hjc3	145	3	this	this	DT
cord-326631-7gd3hjc3	145	4	is	be	VBZ
cord-326631-7gd3hjc3	145	5	the	the	DT
cord-326631-7gd3hjc3	145	6	limit	limit	NN
cord-326631-7gd3hjc3	145	7	k	k	NN
cord-326631-7gd3hjc3	146	1	→	→	IN
cord-326631-7gd3hjc3	146	2	∞	∞	NNP
cord-326631-7gd3hjc3	146	3	in	in	IN
cord-326631-7gd3hjc3	146	4	the	the	DT
cord-326631-7gd3hjc3	146	5	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	146	6	distribution	distribution	NN
cord-326631-7gd3hjc3	146	7	(	(	-LRB-
cord-326631-7gd3hjc3	146	8	10	10	CD
cord-326631-7gd3hjc3	146	9	)	)	-RRB-
cord-326631-7gd3hjc3	146	10	,	,	,
cord-326631-7gd3hjc3	146	11	with	with	IN
cord-326631-7gd3hjc3	146	12	φ	φ	NN
cord-326631-7gd3hjc3	146	13	=	=	SYM
cord-326631-7gd3hjc3	146	14	1	1	CD
cord-326631-7gd3hjc3	146	15	/	/	SYM
cord-326631-7gd3hjc3	146	16	τ	τ	NN
cord-326631-7gd3hjc3	146	17	.	.	.
cord-326631-7gd3hjc3	147	1	During	during	IN
cord-326631-7gd3hjc3	147	2	stage	stage	NN
cord-326631-7gd3hjc3	147	3	i	i	PRP
cord-326631-7gd3hjc3	147	4	,	,	,
cord-326631-7gd3hjc3	147	5	the	the	DT
cord-326631-7gd3hjc3	147	6	transmission	transmission	NN
cord-326631-7gd3hjc3	147	7	rate	rate	NN
cord-326631-7gd3hjc3	147	8	is	be	VBZ
cord-326631-7gd3hjc3	147	9	β	β	NN
cord-326631-7gd3hjc3	148	1	i	i	PRP
cord-326631-7gd3hjc3	148	2	(	(	-LRB-
cord-326631-7gd3hjc3	148	3	i	i	NN
cord-326631-7gd3hjc3	148	4	=	=	SYM
cord-326631-7gd3hjc3	148	5	1	1	CD
cord-326631-7gd3hjc3	148	6	,	,	,
cord-326631-7gd3hjc3	148	7	.	.	.
cord-326631-7gd3hjc3	148	8	.	.	.
cord-326631-7gd3hjc3	148	9	.	.	.
cord-326631-7gd3hjc3	148	10	,	,	,
cord-326631-7gd3hjc3	148	11	n	n	LS
cord-326631-7gd3hjc3	148	12	)	)	-RRB-
cord-326631-7gd3hjc3	148	13	.	.	.
cord-326631-7gd3hjc3	149	1	If	if	IN
cord-326631-7gd3hjc3	149	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	149	3	now	now	RB
cord-326631-7gd3hjc3	149	4	let	let	VBP
cord-326631-7gd3hjc3	149	5	the	the	DT
cord-326631-7gd3hjc3	149	6	number	number	NN
cord-326631-7gd3hjc3	149	7	of	of	IN
cord-326631-7gd3hjc3	149	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	149	9	stages	stage	NNS
cord-326631-7gd3hjc3	149	10	increase	increase	VBP
cord-326631-7gd3hjc3	149	11	(	(	-LRB-
cord-326631-7gd3hjc3	149	12	n	n	NN
cord-326631-7gd3hjc3	149	13	→	→	NN
cord-326631-7gd3hjc3	149	14	∞	∞	NNP
cord-326631-7gd3hjc3	149	15	)	)	-RRB-
cord-326631-7gd3hjc3	149	16	and	and	CC
cord-326631-7gd3hjc3	149	17	the	the	DT
cord-326631-7gd3hjc3	149	18	length	length	NN
cord-326631-7gd3hjc3	149	19	of	of	IN
cord-326631-7gd3hjc3	149	20	each	each	DT
cord-326631-7gd3hjc3	149	21	stage	stage	NN
cord-326631-7gd3hjc3	149	22	decrease	decrease	NN
cord-326631-7gd3hjc3	149	23	(	(	-LRB-
cord-326631-7gd3hjc3	149	24	τ	τ	NN
cord-326631-7gd3hjc3	149	25	→	→	IN
cord-326631-7gd3hjc3	149	26	0	0	CD
cord-326631-7gd3hjc3	149	27	)	)	-RRB-
cord-326631-7gd3hjc3	149	28	,	,	,
cord-326631-7gd3hjc3	149	29	keeping	keep	VBG
cord-326631-7gd3hjc3	149	30	the	the	DT
cord-326631-7gd3hjc3	149	31	total	total	JJ
cord-326631-7gd3hjc3	149	32	infectious	infectious	JJ
cord-326631-7gd3hjc3	149	33	period	period	NN
cord-326631-7gd3hjc3	149	34	(	(	-LRB-
cord-326631-7gd3hjc3	149	35	T	t	NN
cord-326631-7gd3hjc3	149	36	=	=	SYM
cord-326631-7gd3hjc3	149	37	nτ	nτ	NN
cord-326631-7gd3hjc3	149	38	)	)	-RRB-
cord-326631-7gd3hjc3	149	39	constant	constant	JJ
cord-326631-7gd3hjc3	149	40	,	,	,
cord-326631-7gd3hjc3	149	41	then	then	RB
cord-326631-7gd3hjc3	149	42	we	-PRON-	PRP
cord-326631-7gd3hjc3	149	43	arrive	arrive	VBP
cord-326631-7gd3hjc3	149	44	at	at	IN
cord-326631-7gd3hjc3	149	45	a	a	DT
cord-326631-7gd3hjc3	149	46	model	model	NN
cord-326631-7gd3hjc3	149	47	in	in	IN
cord-326631-7gd3hjc3	149	48	which	which	WDT
cord-326631-7gd3hjc3	149	49	the	the	DT
cord-326631-7gd3hjc3	149	50	transmission	transmission	NN
cord-326631-7gd3hjc3	149	51	rate	rate	NN
cord-326631-7gd3hjc3	149	52	(	(	-LRB-
cord-326631-7gd3hjc3	149	53	β	β	NN
cord-326631-7gd3hjc3	149	54	)	)	-RRB-
cord-326631-7gd3hjc3	149	55	varies	vary	VBZ
cord-326631-7gd3hjc3	149	56	continuously	continuously	RB
cord-326631-7gd3hjc3	149	57	through	through	IN
cord-326631-7gd3hjc3	149	58	the	the	DT
cord-326631-7gd3hjc3	149	59	infectious	infectious	JJ
cord-326631-7gd3hjc3	149	60	period	period	NN
cord-326631-7gd3hjc3	149	61	.	.	.
cord-326631-7gd3hjc3	150	1	In	in	IN
cord-326631-7gd3hjc3	150	2	such	such	PDT
cord-326631-7gd3hjc3	150	3	a	a	DT
cord-326631-7gd3hjc3	150	4	model	model	NN
cord-326631-7gd3hjc3	150	5	,	,	,
cord-326631-7gd3hjc3	150	6	an	an	DT
cord-326631-7gd3hjc3	150	7	individual	individual	NN
cord-326631-7gd3hjc3	150	8	's	's	POS
cord-326631-7gd3hjc3	150	9	infectivity	infectivity	NN
cord-326631-7gd3hjc3	150	10	depends	depend	VBZ
cord-326631-7gd3hjc3	150	11	on	on	IN
cord-326631-7gd3hjc3	150	12	his	-PRON-	PRP$
cord-326631-7gd3hjc3	150	13	/	/	SYM
cord-326631-7gd3hjc3	150	14	her	-PRON-	PRP$
cord-326631-7gd3hjc3	150	15	stage	stage	NN
cord-326631-7gd3hjc3	150	16	-	-	HYPH
cord-326631-7gd3hjc3	150	17	age	age	NN
cord-326631-7gd3hjc3	150	18	,	,	,
cord-326631-7gd3hjc3	150	19	i.e.	i.e.	FW
cord-326631-7gd3hjc3	150	20	,	,	,
cord-326631-7gd3hjc3	150	21	the	the	DT
cord-326631-7gd3hjc3	150	22	amount	amount	NN
cord-326631-7gd3hjc3	150	23	of	of	IN
cord-326631-7gd3hjc3	150	24	time	time	NN
cord-326631-7gd3hjc3	150	25	since	since	IN
cord-326631-7gd3hjc3	150	26	initial	initial	JJ
cord-326631-7gd3hjc3	150	27	infection	infection	NN
cord-326631-7gd3hjc3	150	28	.	.	.
cord-326631-7gd3hjc3	151	1	Using	use	VBG
cord-326631-7gd3hjc3	151	2	a	a	DT
cord-326631-7gd3hjc3	151	3	stage	stage	NN
cord-326631-7gd3hjc3	151	4	-	-	HYPH
cord-326631-7gd3hjc3	151	5	age	age	NN
cord-326631-7gd3hjc3	151	6	SIR	SIR	NNP
cord-326631-7gd3hjc3	151	7	formulation	formulation	NN
cord-326631-7gd3hjc3	151	8	,	,	,
cord-326631-7gd3hjc3	151	9	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	151	10	and	and	CC
cord-326631-7gd3hjc3	151	11	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	151	12	(	(	-LRB-
cord-326631-7gd3hjc3	151	13	1927	1927	CD
cord-326631-7gd3hjc3	151	14	)	)	-RRB-
cord-326631-7gd3hjc3	151	15	derived	derive	VBD
cord-326631-7gd3hjc3	151	16	the	the	DT
cord-326631-7gd3hjc3	151	17	final	final	JJ
cord-326631-7gd3hjc3	151	18	size	size	NN
cord-326631-7gd3hjc3	151	19	formula	formula	NN
cord-326631-7gd3hjc3	151	20	(	(	-LRB-
cord-326631-7gd3hjc3	151	21	5	5	CD
cord-326631-7gd3hjc3	151	22	)	)	-RRB-
cord-326631-7gd3hjc3	151	23	and	and	CC
cord-326631-7gd3hjc3	151	24	showed	show	VBD
cord-326631-7gd3hjc3	151	25	that	that	IN
cord-326631-7gd3hjc3	151	26	its	-PRON-	PRP$
cord-326631-7gd3hjc3	151	27	form	form	NN
cord-326631-7gd3hjc3	151	28	is	be	VBZ
cord-326631-7gd3hjc3	151	29	independent	independent	JJ
cord-326631-7gd3hjc3	151	30	of	of	IN
cord-326631-7gd3hjc3	151	31	how	how	WRB
cord-326631-7gd3hjc3	151	32	the	the	DT
cord-326631-7gd3hjc3	151	33	transmission	transmission	NN
cord-326631-7gd3hjc3	151	34	rate	rate	NN
cord-326631-7gd3hjc3	151	35	depends	depend	VBZ
cord-326631-7gd3hjc3	151	36	on	on	IN
cord-326631-7gd3hjc3	151	37	stage	stage	NN
cord-326631-7gd3hjc3	151	38	-	-	HYPH
cord-326631-7gd3hjc3	151	39	age	age	NN
cord-326631-7gd3hjc3	151	40	.	.	.
cord-326631-7gd3hjc3	152	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	152	2	have	have	VBP
cord-326631-7gd3hjc3	152	3	seen	see	VBN
cord-326631-7gd3hjc3	152	4	that	that	IN
cord-326631-7gd3hjc3	152	5	the	the	DT
cord-326631-7gd3hjc3	152	6	final	final	JJ
cord-326631-7gd3hjc3	152	7	size	size	NN
cord-326631-7gd3hjc3	152	8	formula	formula	NN
cord-326631-7gd3hjc3	152	9	(	(	-LRB-
cord-326631-7gd3hjc3	152	10	5	5	LS
cord-326631-7gd3hjc3	152	11	)	)	-RRB-
cord-326631-7gd3hjc3	152	12	is	be	VBZ
cord-326631-7gd3hjc3	152	13	the	the	DT
cord-326631-7gd3hjc3	152	14	same	same	JJ
cord-326631-7gd3hjc3	152	15	if	if	IN
cord-326631-7gd3hjc3	152	16	stage	stage	NN
cord-326631-7gd3hjc3	152	17	durations	duration	NNS
cord-326631-7gd3hjc3	152	18	are	be	VBP
cord-326631-7gd3hjc3	152	19	distributed	distribute	VBN
cord-326631-7gd3hjc3	152	20	according	accord	VBG
cord-326631-7gd3hjc3	152	21	to	to	IN
cord-326631-7gd3hjc3	152	22	any	any	DT
cord-326631-7gd3hjc3	152	23	member	member	NN
cord-326631-7gd3hjc3	152	24	of	of	IN
cord-326631-7gd3hjc3	152	25	the	the	DT
cord-326631-7gd3hjc3	152	26	family	family	NN
cord-326631-7gd3hjc3	152	27	of	of	IN
cord-326631-7gd3hjc3	152	28	the	the	DT
cord-326631-7gd3hjc3	152	29	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	152	30	distributions	distribution	NNS
cord-326631-7gd3hjc3	152	31	(	(	-LRB-
cord-326631-7gd3hjc3	152	32	10	10	CD
cord-326631-7gd3hjc3	152	33	)	)	-RRB-
cord-326631-7gd3hjc3	152	34	.	.	.
cord-326631-7gd3hjc3	153	1	This	this	DT
cord-326631-7gd3hjc3	153	2	suggests	suggest	VBZ
cord-326631-7gd3hjc3	153	3	that	that	IN
cord-326631-7gd3hjc3	153	4	any	any	DT
cord-326631-7gd3hjc3	153	5	distribution	distribution	NN
cord-326631-7gd3hjc3	153	6	of	of	IN
cord-326631-7gd3hjc3	153	7	stage	stage	NN
cord-326631-7gd3hjc3	153	8	durations	duration	NNS
cord-326631-7gd3hjc3	153	9	will	will	MD
cord-326631-7gd3hjc3	153	10	yield	yield	VB
cord-326631-7gd3hjc3	153	11	the	the	DT
cord-326631-7gd3hjc3	153	12	same	same	JJ
cord-326631-7gd3hjc3	153	13	final	final	JJ
cord-326631-7gd3hjc3	153	14	size	size	NN
cord-326631-7gd3hjc3	153	15	.	.	.
cord-326631-7gd3hjc3	154	1	Unlike	unlike	IN
cord-326631-7gd3hjc3	154	2	the	the	DT
cord-326631-7gd3hjc3	154	3	situation	situation	NN
cord-326631-7gd3hjc3	154	4	for	for	IN
cord-326631-7gd3hjc3	154	5	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	154	6	distributed	distribute	VBD
cord-326631-7gd3hjc3	154	7	infectious	infectious	JJ
cord-326631-7gd3hjc3	154	8	periods	period	NNS
cord-326631-7gd3hjc3	154	9	,	,	,
cord-326631-7gd3hjc3	154	10	with	with	IN
cord-326631-7gd3hjc3	154	11	an	an	DT
cord-326631-7gd3hjc3	154	12	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	154	13	distribution	distribution	NN
cord-326631-7gd3hjc3	154	14	the	the	DT
cord-326631-7gd3hjc3	154	15	time	time	NN
cord-326631-7gd3hjc3	154	16	-	-	HYPH
cord-326631-7gd3hjc3	154	17	evolution	evolution	NN
cord-326631-7gd3hjc3	154	18	of	of	IN
cord-326631-7gd3hjc3	154	19	the	the	DT
cord-326631-7gd3hjc3	154	20	infectious	infectious	JJ
cord-326631-7gd3hjc3	154	21	class	class	NN
cord-326631-7gd3hjc3	154	22	can	can	MD
cord-326631-7gd3hjc3	154	23	no	no	RB
cord-326631-7gd3hjc3	154	24	longer	longer	RB
cord-326631-7gd3hjc3	154	25	be	be	VB
cord-326631-7gd3hjc3	154	26	expressed	express	VBN
cord-326631-7gd3hjc3	154	27	using	use	VBG
cord-326631-7gd3hjc3	154	28	ordinary	ordinary	JJ
cord-326631-7gd3hjc3	154	29	differential	differential	JJ
cord-326631-7gd3hjc3	154	30	equations	equation	NNS
cord-326631-7gd3hjc3	154	31	(	(	-LRB-
cord-326631-7gd3hjc3	154	32	ODEs	ode	NNS
cord-326631-7gd3hjc3	154	33	)	)	-RRB-
cord-326631-7gd3hjc3	154	34	.	.	.
cord-326631-7gd3hjc3	155	1	Instead	instead	RB
cord-326631-7gd3hjc3	155	2	,	,	,
cord-326631-7gd3hjc3	155	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	155	4	must	must	MD
cord-326631-7gd3hjc3	155	5	construct	construct	VB
cord-326631-7gd3hjc3	155	6	a	a	DT
cord-326631-7gd3hjc3	155	7	system	system	NN
cord-326631-7gd3hjc3	155	8	of	of	IN
cord-326631-7gd3hjc3	155	9	integro	integro	JJ
cord-326631-7gd3hjc3	155	10	-	-	HYPH
cord-326631-7gd3hjc3	155	11	differential	differential	JJ
cord-326631-7gd3hjc3	155	12	equations	equation	NNS
cord-326631-7gd3hjc3	155	13	(	(	-LRB-
cord-326631-7gd3hjc3	155	14	Feng	Feng	NNP
cord-326631-7gd3hjc3	155	15	and	and	CC
cord-326631-7gd3hjc3	155	16	Thieme	Thieme	NNP
cord-326631-7gd3hjc3	155	17	,	,	,
cord-326631-7gd3hjc3	155	18	2000	2000	CD
cord-326631-7gd3hjc3	155	19	)	)	-RRB-
cord-326631-7gd3hjc3	155	20	.	.	.
cord-326631-7gd3hjc3	156	1	Let	let	VB
cord-326631-7gd3hjc3	156	2	U(t	u(t	CD
cord-326631-7gd3hjc3	156	3	)	)	-RRB-
cord-326631-7gd3hjc3	156	4	be	be	VB
cord-326631-7gd3hjc3	156	5	the	the	DT
cord-326631-7gd3hjc3	156	6	rate	rate	NN
cord-326631-7gd3hjc3	156	7	at	at	IN
cord-326631-7gd3hjc3	156	8	which	which	WDT
cord-326631-7gd3hjc3	156	9	individuals	individual	NNS
cord-326631-7gd3hjc3	156	10	become	become	VBP
cord-326631-7gd3hjc3	156	11	infectious	infectious	JJ
cord-326631-7gd3hjc3	156	12	(	(	-LRB-
cord-326631-7gd3hjc3	156	13	enter	enter	VB
cord-326631-7gd3hjc3	156	14	class	class	NN
cord-326631-7gd3hjc3	156	15	I	i	NN
cord-326631-7gd3hjc3	156	16	)	)	-RRB-
cord-326631-7gd3hjc3	156	17	at	at	IN
cord-326631-7gd3hjc3	156	18	time	time	NN
cord-326631-7gd3hjc3	156	19	t	t	NNP
cord-326631-7gd3hjc3	156	20	≥	≥	CD
cord-326631-7gd3hjc3	156	21	0	0	CD
cord-326631-7gd3hjc3	156	22	,	,	,
cord-326631-7gd3hjc3	156	23	i.e.	i.e.	FW
cord-326631-7gd3hjc3	156	24	,	,	,
cord-326631-7gd3hjc3	156	25	The	the	DT
cord-326631-7gd3hjc3	156	26	equation	equation	NN
cord-326631-7gd3hjc3	156	27	for	for	IN
cord-326631-7gd3hjc3	156	28	the	the	DT
cord-326631-7gd3hjc3	156	29	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	156	30	class	class	NN
cord-326631-7gd3hjc3	156	31	is	be	VBZ
cord-326631-7gd3hjc3	156	32	the	the	DT
cord-326631-7gd3hjc3	156	33	same	same	JJ
cord-326631-7gd3hjc3	156	34	as	as	IN
cord-326631-7gd3hjc3	156	35	in	in	IN
cord-326631-7gd3hjc3	156	36	the	the	DT
cord-326631-7gd3hjc3	156	37	standard	standard	JJ
cord-326631-7gd3hjc3	156	38	SIR	SIR	NNP
cord-326631-7gd3hjc3	156	39	model	model	NN
cord-326631-7gd3hjc3	156	40	,	,	,
cord-326631-7gd3hjc3	156	41	We	-PRON-	PRP
cord-326631-7gd3hjc3	156	42	also	also	RB
cord-326631-7gd3hjc3	156	43	define	define	VBP
cord-326631-7gd3hjc3	156	44	U(t	U(t	NNP
cord-326631-7gd3hjc3	156	45	)	)	-RRB-
cord-326631-7gd3hjc3	156	46	for	for	IN
cord-326631-7gd3hjc3	156	47	t	t	NN
cord-326631-7gd3hjc3	156	48	<	<	XX
cord-326631-7gd3hjc3	156	49	0	0	NFP
cord-326631-7gd3hjc3	156	50	since	since	IN
cord-326631-7gd3hjc3	156	51	this	this	DT
cord-326631-7gd3hjc3	156	52	will	will	MD
cord-326631-7gd3hjc3	156	53	allow	allow	VB
cord-326631-7gd3hjc3	156	54	us	-PRON-	PRP
cord-326631-7gd3hjc3	156	55	to	to	TO
cord-326631-7gd3hjc3	156	56	specify	specify	VB
cord-326631-7gd3hjc3	156	57	the	the	DT
cord-326631-7gd3hjc3	156	58	initial	initial	JJ
cord-326631-7gd3hjc3	156	59	conditions	condition	NNS
cord-326631-7gd3hjc3	156	60	.	.	.
cord-326631-7gd3hjc3	157	1	For	for	IN
cord-326631-7gd3hjc3	157	2	t	t	NN
cord-326631-7gd3hjc3	157	3	<	<	XX
cord-326631-7gd3hjc3	157	4	0	0	CD
cord-326631-7gd3hjc3	157	5	,	,	,
cord-326631-7gd3hjc3	157	6	U(t	U(t	NNP
cord-326631-7gd3hjc3	157	7	)	)	-RRB-
cord-326631-7gd3hjc3	157	8	is	be	VBZ
cord-326631-7gd3hjc3	157	9	the	the	DT
cord-326631-7gd3hjc3	157	10	rate	rate	NN
cord-326631-7gd3hjc3	157	11	at	at	IN
cord-326631-7gd3hjc3	157	12	which	which	WDT
cord-326631-7gd3hjc3	157	13	individuals	individual	NNS
cord-326631-7gd3hjc3	157	14	who	who	WP
cord-326631-7gd3hjc3	157	15	were	be	VBD
cord-326631-7gd3hjc3	157	16	still	still	RB
cord-326631-7gd3hjc3	157	17	infectious	infectious	JJ
cord-326631-7gd3hjc3	157	18	at	at	IN
cord-326631-7gd3hjc3	157	19	the	the	DT
cord-326631-7gd3hjc3	157	20	initial	initial	JJ
cord-326631-7gd3hjc3	157	21	time	time	NN
cord-326631-7gd3hjc3	157	22	(	(	-LRB-
cord-326631-7gd3hjc3	157	23	time	time	NN
cord-326631-7gd3hjc3	157	24	0	0	CD
cord-326631-7gd3hjc3	157	25	)	)	-RRB-
cord-326631-7gd3hjc3	157	26	became	become	VBD
cord-326631-7gd3hjc3	157	27	infectious	infectious	JJ
cord-326631-7gd3hjc3	157	28	at	at	IN
cord-326631-7gd3hjc3	157	29	time	time	NN
cord-326631-7gd3hjc3	157	30	t.	t.	NNP
cord-326631-7gd3hjc3	158	1	Hence	hence	RB
cord-326631-7gd3hjc3	158	2	,	,	,
cord-326631-7gd3hjc3	158	3	the	the	DT
cord-326631-7gd3hjc3	158	4	number	number	NN
cord-326631-7gd3hjc3	158	5	of	of	IN
cord-326631-7gd3hjc3	158	6	infectious	infectious	JJ
cord-326631-7gd3hjc3	158	7	individuals	individual	NNS
cord-326631-7gd3hjc3	158	8	at	at	IN
cord-326631-7gd3hjc3	158	9	time	time	NN
cord-326631-7gd3hjc3	158	10	t	t	NN
cord-326631-7gd3hjc3	158	11	=	=	SYM
cord-326631-7gd3hjc3	158	12	0	0	NFP
cord-326631-7gd3hjc3	158	13	is	be	VBZ
cord-326631-7gd3hjc3	158	14	Let	let	VB
cord-326631-7gd3hjc3	158	15	f	f	LS
cord-326631-7gd3hjc3	158	16	(	(	-LRB-
cord-326631-7gd3hjc3	158	17	t	t	NN
cord-326631-7gd3hjc3	158	18	)	)	-RRB-
cord-326631-7gd3hjc3	158	19	be	be	VB
cord-326631-7gd3hjc3	158	20	the	the	DT
cord-326631-7gd3hjc3	158	21	probability	probability	NN
cord-326631-7gd3hjc3	158	22	density	density	NN
cord-326631-7gd3hjc3	158	23	of	of	IN
cord-326631-7gd3hjc3	158	24	the	the	DT
cord-326631-7gd3hjc3	158	25	infectious	infectious	JJ
cord-326631-7gd3hjc3	158	26	period	period	NN
cord-326631-7gd3hjc3	158	27	(	(	-LRB-
cord-326631-7gd3hjc3	159	1	so	so	RB
cord-326631-7gd3hjc3	159	2	,	,	,
cord-326631-7gd3hjc3	159	3	for	for	IN
cord-326631-7gd3hjc3	159	4	the	the	DT
cord-326631-7gd3hjc3	159	5	special	special	JJ
cord-326631-7gd3hjc3	159	6	case	case	NN
cord-326631-7gd3hjc3	159	7	of	of	IN
cord-326631-7gd3hjc3	159	8	a	a	DT
cord-326631-7gd3hjc3	159	9	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	159	10	distribution	distribution	NN
cord-326631-7gd3hjc3	159	11	,	,	,
cord-326631-7gd3hjc3	159	12	f	f	NNP
cord-326631-7gd3hjc3	159	13	(	(	-LRB-
cord-326631-7gd3hjc3	159	14	t	t	NN
cord-326631-7gd3hjc3	159	15	)	)	-RRB-
cord-326631-7gd3hjc3	159	16	is	be	VBZ
cord-326631-7gd3hjc3	159	17	given	give	VBN
cord-326631-7gd3hjc3	159	18	by	by	IN
cord-326631-7gd3hjc3	159	19	g	g	NNP
cord-326631-7gd3hjc3	159	20	k	k	NNP
cord-326631-7gd3hjc3	159	21	,	,	,
cord-326631-7gd3hjc3	159	22	φ	φ	NNP
cord-326631-7gd3hjc3	159	23	(	(	-LRB-
cord-326631-7gd3hjc3	159	24	t	t	NN
cord-326631-7gd3hjc3	159	25	)	)	-RRB-
cord-326631-7gd3hjc3	159	26	in	in	IN
cord-326631-7gd3hjc3	159	27	Eq	Eq	NNP
cord-326631-7gd3hjc3	159	28	.	.	NNP
cord-326631-7gd3hjc3	159	29	10	10	CD
cord-326631-7gd3hjc3	159	30	)	)	-RRB-
cord-326631-7gd3hjc3	159	31	.	.	.
cord-326631-7gd3hjc3	160	1	For	for	IN
cord-326631-7gd3hjc3	160	2	an	an	DT
cord-326631-7gd3hjc3	160	3	individual	individual	NN
cord-326631-7gd3hjc3	160	4	who	who	WP
cord-326631-7gd3hjc3	160	5	becomes	become	VBZ
cord-326631-7gd3hjc3	160	6	infectious	infectious	JJ
cord-326631-7gd3hjc3	160	7	at	at	IN
cord-326631-7gd3hjc3	160	8	time	time	NN
cord-326631-7gd3hjc3	160	9	τ	τ	NN
cord-326631-7gd3hjc3	160	10	≥	≥	CD
cord-326631-7gd3hjc3	160	11	0	0	CD
cord-326631-7gd3hjc3	160	12	,	,	,
cord-326631-7gd3hjc3	160	13	the	the	DT
cord-326631-7gd3hjc3	160	14	probability	probability	NN
cord-326631-7gd3hjc3	160	15	density	density	NN
cord-326631-7gd3hjc3	160	16	that	that	WDT
cord-326631-7gd3hjc3	160	17	s	s	NN
cord-326631-7gd3hjc3	160	18	/	/	SYM
cord-326631-7gd3hjc3	160	19	he	-PRON-	PRP
cord-326631-7gd3hjc3	160	20	recovers	recover	VBZ
cord-326631-7gd3hjc3	160	21	(	(	-LRB-
cord-326631-7gd3hjc3	160	22	leaves	leave	VBZ
cord-326631-7gd3hjc3	160	23	the	the	DT
cord-326631-7gd3hjc3	160	24	I	I	NNP
cord-326631-7gd3hjc3	160	25	class	class	NN
cord-326631-7gd3hjc3	160	26	)	)	-RRB-
cord-326631-7gd3hjc3	160	27	at	at	IN
cord-326631-7gd3hjc3	160	28	time	time	NN
cord-326631-7gd3hjc3	160	29	t	t	NNP
cord-326631-7gd3hjc3	161	1	>	>	XX
cord-326631-7gd3hjc3	162	1	τ	τ	NN
cord-326631-7gd3hjc3	162	2	is	be	VBZ
cord-326631-7gd3hjc3	162	3	However	however	RB
cord-326631-7gd3hjc3	162	4	,	,	,
cord-326631-7gd3hjc3	162	5	for	for	IN
cord-326631-7gd3hjc3	162	6	individuals	individual	NNS
cord-326631-7gd3hjc3	162	7	who	who	WP
cord-326631-7gd3hjc3	162	8	became	become	VBD
cord-326631-7gd3hjc3	162	9	infectious	infectious	JJ
cord-326631-7gd3hjc3	162	10	at	at	IN
cord-326631-7gd3hjc3	162	11	time	time	NN
cord-326631-7gd3hjc3	162	12	τ	τ	NN
cord-326631-7gd3hjc3	162	13	<	<	XX
cord-326631-7gd3hjc3	162	14	0	0	NFP
cord-326631-7gd3hjc3	162	15	,	,	,
cord-326631-7gd3hjc3	162	16	the	the	DT
cord-326631-7gd3hjc3	162	17	probability	probability	NN
cord-326631-7gd3hjc3	162	18	density	density	NN
cord-326631-7gd3hjc3	162	19	to	to	TO
cord-326631-7gd3hjc3	162	20	leave	leave	VB
cord-326631-7gd3hjc3	162	21	class	class	NN
cord-326631-7gd3hjc3	162	22	I	-PRON-	PRP
cord-326631-7gd3hjc3	162	23	at	at	IN
cord-326631-7gd3hjc3	162	24	time	time	NN
cord-326631-7gd3hjc3	162	25	t	t	NNP
cord-326631-7gd3hjc3	162	26	must	must	MD
cord-326631-7gd3hjc3	162	27	be	be	VB
cord-326631-7gd3hjc3	162	28	conditioned	condition	VBN
cord-326631-7gd3hjc3	162	29	by	by	IN
cord-326631-7gd3hjc3	162	30	still	still	RB
cord-326631-7gd3hjc3	162	31	being	be	VBG
cord-326631-7gd3hjc3	162	32	infectious	infectious	JJ
cord-326631-7gd3hjc3	162	33	at	at	IN
cord-326631-7gd3hjc3	162	34	time	time	NN
cord-326631-7gd3hjc3	162	35	0	0	CD
cord-326631-7gd3hjc3	162	36	,	,	,
cord-326631-7gd3hjc3	162	37	Hence	hence	RB
cord-326631-7gd3hjc3	163	1	,	,	,
cord-326631-7gd3hjc3	163	2	the	the	DT
cord-326631-7gd3hjc3	163	3	rate	rate	NN
cord-326631-7gd3hjc3	163	4	of	of	IN
cord-326631-7gd3hjc3	163	5	change	change	NN
cord-326631-7gd3hjc3	163	6	of	of	IN
cord-326631-7gd3hjc3	163	7	the	the	DT
cord-326631-7gd3hjc3	163	8	number	number	NN
cord-326631-7gd3hjc3	163	9	of	of	IN
cord-326631-7gd3hjc3	163	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	163	11	individuals	individual	NNS
cord-326631-7gd3hjc3	163	12	at	at	IN
cord-326631-7gd3hjc3	163	13	time	time	NN
cord-326631-7gd3hjc3	163	14	t	t	NN
cord-326631-7gd3hjc3	163	15	is	be	VBZ
cord-326631-7gd3hjc3	163	16	Those	those	DT
cord-326631-7gd3hjc3	163	17	who	who	WP
cord-326631-7gd3hjc3	163	18	leave	leave	VBP
cord-326631-7gd3hjc3	163	19	class	class	NN
cord-326631-7gd3hjc3	163	20	I	-PRON-	PRP
cord-326631-7gd3hjc3	163	21	enter	enter	VBP
cord-326631-7gd3hjc3	163	22	class	class	NN
cord-326631-7gd3hjc3	163	23	R	r	NN
cord-326631-7gd3hjc3	163	24	,	,	,
cord-326631-7gd3hjc3	163	25	hence	hence	RB
cord-326631-7gd3hjc3	164	1	In	in	IN
cord-326631-7gd3hjc3	164	2	Appendix	Appendix	NNP
cord-326631-7gd3hjc3	164	3	B	B	NNP
cord-326631-7gd3hjc3	164	4	,	,	,
cord-326631-7gd3hjc3	164	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	164	6	show	show	VBP
cord-326631-7gd3hjc3	164	7	that	that	IN
cord-326631-7gd3hjc3	164	8	if	if	IN
cord-326631-7gd3hjc3	164	9	the	the	DT
cord-326631-7gd3hjc3	164	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	164	11	period	period	NN
cord-326631-7gd3hjc3	164	12	is	be	VBZ
cord-326631-7gd3hjc3	164	13	exponentially	exponentially	RB
cord-326631-7gd3hjc3	164	14	distributed	distribute	VBN
cord-326631-7gd3hjc3	164	15	then	then	RB
cord-326631-7gd3hjc3	164	16	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	164	17	.	.	.
cord-326631-7gd3hjc3	165	1	(	(	-LRB-
cord-326631-7gd3hjc3	165	2	11	11	CD
cord-326631-7gd3hjc3	165	3	)	)	-RRB-
cord-326631-7gd3hjc3	165	4	reduce	reduce	VB
cord-326631-7gd3hjc3	165	5	to	to	IN
cord-326631-7gd3hjc3	165	6	the	the	DT
cord-326631-7gd3hjc3	165	7	the	the	DT
cord-326631-7gd3hjc3	165	8	standard	standard	JJ
cord-326631-7gd3hjc3	165	9	SIR	SIR	NNP
cord-326631-7gd3hjc3	165	10	model	model	NN
cord-326631-7gd3hjc3	165	11	(	(	-LRB-
cord-326631-7gd3hjc3	165	12	1	1	CD
cord-326631-7gd3hjc3	165	13	)	)	-RRB-
cord-326631-7gd3hjc3	165	14	.	.	.
cord-326631-7gd3hjc3	166	1	As	as	IN
cord-326631-7gd3hjc3	166	2	in	in	IN
cord-326631-7gd3hjc3	166	3	the	the	DT
cord-326631-7gd3hjc3	166	4	standard	standard	JJ
cord-326631-7gd3hjc3	166	5	SIR	SIR	NNP
cord-326631-7gd3hjc3	166	6	model	model	NN
cord-326631-7gd3hjc3	166	7	(	(	-LRB-
cord-326631-7gd3hjc3	166	8	1	1	CD
cord-326631-7gd3hjc3	166	9	)	)	-RRB-
cord-326631-7gd3hjc3	166	10	,	,	,
cord-326631-7gd3hjc3	166	11	the	the	DT
cord-326631-7gd3hjc3	166	12	population	population	NN
cord-326631-7gd3hjc3	166	13	size	size	NN
cord-326631-7gd3hjc3	166	14	is	be	VBZ
cord-326631-7gd3hjc3	166	15	invariant	invariant	JJ
cord-326631-7gd3hjc3	167	1	(	(	-LRB-
cord-326631-7gd3hjc3	167	2	S	S	NNP
cord-326631-7gd3hjc3	168	1	+	+	CC
cord-326631-7gd3hjc3	169	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	169	2	+	+	CC
cord-326631-7gd3hjc3	169	3	R	r	NN
cord-326631-7gd3hjc3	169	4	=	=	SYM
cord-326631-7gd3hjc3	169	5	1	1	CD
cord-326631-7gd3hjc3	169	6	)	)	-RRB-
cord-326631-7gd3hjc3	169	7	,	,	,
cord-326631-7gd3hjc3	169	8	S	s	NN
cord-326631-7gd3hjc3	169	9	≥	≥	NNP
cord-326631-7gd3hjc3	169	10	0	0	NNP
cord-326631-7gd3hjc3	169	11	,	,	,
cord-326631-7gd3hjc3	169	12	and	and	CC
cord-326631-7gd3hjc3	169	13	S(∞	S(∞	NNP
cord-326631-7gd3hjc3	169	14	)	)	-RRB-
cord-326631-7gd3hjc3	169	15	exists	exist	VBZ
cord-326631-7gd3hjc3	169	16	.	.	.
cord-326631-7gd3hjc3	170	1	Establishing	establish	VBG
cord-326631-7gd3hjc3	170	2	that	that	IN
cord-326631-7gd3hjc3	170	3	I(∞	I(∞	NNP
cord-326631-7gd3hjc3	170	4	)	)	-RRB-
cord-326631-7gd3hjc3	170	5	=	=	SYM
cord-326631-7gd3hjc3	170	6	0	0	NFP
cord-326631-7gd3hjc3	171	1	(	(	-LRB-
cord-326631-7gd3hjc3	171	2	so	so	IN
cord-326631-7gd3hjc3	171	3	the	the	DT
cord-326631-7gd3hjc3	171	4	disease	disease	NN
cord-326631-7gd3hjc3	171	5	will	will	MD
cord-326631-7gd3hjc3	171	6	burn	burn	VB
cord-326631-7gd3hjc3	171	7	out	out	RP
cord-326631-7gd3hjc3	171	8	regardless	regardless	RB
cord-326631-7gd3hjc3	171	9	of	of	IN
cord-326631-7gd3hjc3	171	10	the	the	DT
cord-326631-7gd3hjc3	171	11	infectious	infectious	JJ
cord-326631-7gd3hjc3	171	12	period	period	NN
cord-326631-7gd3hjc3	171	13	distribution	distribution	NN
cord-326631-7gd3hjc3	171	14	)	)	-RRB-
cord-326631-7gd3hjc3	171	15	requires	require	VBZ
cord-326631-7gd3hjc3	171	16	a	a	DT
cord-326631-7gd3hjc3	171	17	little	little	JJ
cord-326631-7gd3hjc3	171	18	more	more	JJR
cord-326631-7gd3hjc3	171	19	work	work	NN
cord-326631-7gd3hjc3	171	20	.	.	.
cord-326631-7gd3hjc3	172	1	Since	since	IN
cord-326631-7gd3hjc3	172	2	f	f	LS
cord-326631-7gd3hjc3	172	3	(	(	-LRB-
cord-326631-7gd3hjc3	172	4	t	t	NN
cord-326631-7gd3hjc3	172	5	)	)	-RRB-
cord-326631-7gd3hjc3	172	6	and	and	CC
cord-326631-7gd3hjc3	172	7	l(τ	l(τ	NNP
cord-326631-7gd3hjc3	172	8	,	,	,
cord-326631-7gd3hjc3	172	9	t	t	NNP
cord-326631-7gd3hjc3	172	10	)	)	-RRB-
cord-326631-7gd3hjc3	172	11	are	be	VBP
cord-326631-7gd3hjc3	172	12	probability	probability	NN
cord-326631-7gd3hjc3	172	13	densities	density	NNS
cord-326631-7gd3hjc3	172	14	,	,	,
cord-326631-7gd3hjc3	172	15	∞	∞	NN
cord-326631-7gd3hjc3	172	16	0	0	NFP
cord-326631-7gd3hjc3	172	17	f	f	NNP
cord-326631-7gd3hjc3	172	18	(	(	-LRB-
cord-326631-7gd3hjc3	172	19	t	t	NN
cord-326631-7gd3hjc3	172	20	)	)	-RRB-
cord-326631-7gd3hjc3	172	21	dt	dt	NN
cord-326631-7gd3hjc3	172	22	=	=	NN
cord-326631-7gd3hjc3	172	23	∞	∞	NNP
cord-326631-7gd3hjc3	172	24	0	0	NFP
cord-326631-7gd3hjc3	172	25	l(τ	l(τ	NNP
cord-326631-7gd3hjc3	172	26	,	,	,
cord-326631-7gd3hjc3	172	27	t	t	NNP
cord-326631-7gd3hjc3	172	28	)	)	-RRB-
cord-326631-7gd3hjc3	172	29	dt	dt	NN
cord-326631-7gd3hjc3	172	30	=	=	NN
cord-326631-7gd3hjc3	172	31	1	1	CD
cord-326631-7gd3hjc3	172	32	;	;	:
cord-326631-7gd3hjc3	172	33	consequently	consequently	RB
cord-326631-7gd3hjc3	172	34	,	,	,
cord-326631-7gd3hjc3	172	35	switching	switch	VBG
cord-326631-7gd3hjc3	172	36	the	the	DT
cord-326631-7gd3hjc3	172	37	order	order	NN
cord-326631-7gd3hjc3	172	38	of	of	IN
cord-326631-7gd3hjc3	172	39	integrations	integration	NNS
cord-326631-7gd3hjc3	172	40	,	,	,
cord-326631-7gd3hjc3	172	41	we	-PRON-	PRP
cord-326631-7gd3hjc3	172	42	find	find	VBP
cord-326631-7gd3hjc3	172	43	Next	Next	NNP
cord-326631-7gd3hjc3	172	44	,	,	,
cord-326631-7gd3hjc3	172	45	integrating	integrate	VBG
cord-326631-7gd3hjc3	172	46	from	from	IN
cord-326631-7gd3hjc3	172	47	0	0	CD
cord-326631-7gd3hjc3	172	48	to	to	IN
cord-326631-7gd3hjc3	172	49	∞	∞	NNP
cord-326631-7gd3hjc3	172	50	on	on	IN
cord-326631-7gd3hjc3	172	51	both	both	DT
cord-326631-7gd3hjc3	172	52	sides	side	NNS
cord-326631-7gd3hjc3	172	53	of	of	IN
cord-326631-7gd3hjc3	172	54	Eq	Eq	NNP
cord-326631-7gd3hjc3	172	55	.	.	.
cord-326631-7gd3hjc3	173	1	(	(	-LRB-
cord-326631-7gd3hjc3	173	2	11f	11f	CD
cord-326631-7gd3hjc3	173	3	)	)	-RRB-
cord-326631-7gd3hjc3	173	4	,	,	,
cord-326631-7gd3hjc3	173	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	173	6	have	have	VBP
cord-326631-7gd3hjc3	173	7	I(∞	i(∞	CD
cord-326631-7gd3hjc3	173	8	)	)	-RRB-
cord-326631-7gd3hjc3	174	1	=	=	SYM
cord-326631-7gd3hjc3	174	2	0	0	NFP
cord-326631-7gd3hjc3	174	3	.	.	.
cord-326631-7gd3hjc3	175	1	To	to	TO
cord-326631-7gd3hjc3	175	2	relate	relate	VB
cord-326631-7gd3hjc3	175	3	the	the	DT
cord-326631-7gd3hjc3	175	4	final	final	JJ
cord-326631-7gd3hjc3	175	5	size	size	NN
cord-326631-7gd3hjc3	175	6	in	in	IN
cord-326631-7gd3hjc3	175	7	the	the	DT
cord-326631-7gd3hjc3	175	8	present	present	JJ
cord-326631-7gd3hjc3	175	9	model	model	NN
cord-326631-7gd3hjc3	175	10	to	to	IN
cord-326631-7gd3hjc3	175	11	the	the	DT
cord-326631-7gd3hjc3	175	12	usual	usual	JJ
cord-326631-7gd3hjc3	175	13	formula	formula	NN
cord-326631-7gd3hjc3	175	14	(	(	-LRB-
cord-326631-7gd3hjc3	175	15	5	5	CD
cord-326631-7gd3hjc3	175	16	)	)	-RRB-
cord-326631-7gd3hjc3	175	17	,	,	,
cord-326631-7gd3hjc3	175	18	we	-PRON-	PRP
cord-326631-7gd3hjc3	175	19	need	need	VBP
cord-326631-7gd3hjc3	175	20	an	an	DT
cord-326631-7gd3hjc3	175	21	expression	expression	NN
cord-326631-7gd3hjc3	175	22	for	for	IN
cord-326631-7gd3hjc3	175	23	the	the	DT
cord-326631-7gd3hjc3	175	24	basic	basic	JJ
cord-326631-7gd3hjc3	175	25	reproduction	reproduction	NN
cord-326631-7gd3hjc3	175	26	number	number	NN
cord-326631-7gd3hjc3	175	27	R	r	NN
cord-326631-7gd3hjc3	175	28	0	0	CD
cord-326631-7gd3hjc3	175	29	.	.	.
cord-326631-7gd3hjc3	176	1	Feng	Feng	NNP
cord-326631-7gd3hjc3	176	2	and	and	CC
cord-326631-7gd3hjc3	176	3	Thieme	Thieme	NNP
cord-326631-7gd3hjc3	176	4	(	(	-LRB-
cord-326631-7gd3hjc3	176	5	2000	2000	CD
cord-326631-7gd3hjc3	176	6	)	)	-RRB-
cord-326631-7gd3hjc3	176	7	have	have	VBP
cord-326631-7gd3hjc3	176	8	We	-PRON-	PRP
cord-326631-7gd3hjc3	176	9	now	now	RB
cord-326631-7gd3hjc3	176	10	divide	divide	VB
cord-326631-7gd3hjc3	176	11	Eq	Eq	NNP
cord-326631-7gd3hjc3	176	12	.	.	.
cord-326631-7gd3hjc3	177	1	(	(	-LRB-
cord-326631-7gd3hjc3	177	2	11b	11b	NNS
cord-326631-7gd3hjc3	177	3	)	)	-RRB-
cord-326631-7gd3hjc3	177	4	by	by	IN
cord-326631-7gd3hjc3	177	5	S	S	NNP
cord-326631-7gd3hjc3	177	6	and	and	CC
cord-326631-7gd3hjc3	177	7	integrate	integrate	VB
cord-326631-7gd3hjc3	177	8	,	,	,
cord-326631-7gd3hjc3	177	9	yielding	yield	VBG
cord-326631-7gd3hjc3	177	10	Therefore	therefore	RB
cord-326631-7gd3hjc3	177	11	,	,	,
cord-326631-7gd3hjc3	177	12	the	the	DT
cord-326631-7gd3hjc3	177	13	usual	usual	JJ
cord-326631-7gd3hjc3	177	14	final	final	JJ
cord-326631-7gd3hjc3	177	15	size	size	NN
cord-326631-7gd3hjc3	177	16	formula	formula	NN
cord-326631-7gd3hjc3	177	17	(	(	-LRB-
cord-326631-7gd3hjc3	177	18	5	5	LS
cord-326631-7gd3hjc3	177	19	)	)	-RRB-
cord-326631-7gd3hjc3	177	20	will	will	MD
cord-326631-7gd3hjc3	177	21	follow	follow	VB
cord-326631-7gd3hjc3	177	22	if	if	IN
cord-326631-7gd3hjc3	177	23	∞	∞	NNP
cord-326631-7gd3hjc3	177	24	0	0	CD
cord-326631-7gd3hjc3	177	25	I(t	I(t	NNP
cord-326631-7gd3hjc3	177	26	)	)	-RRB-
cord-326631-7gd3hjc3	177	27	dt	dt	NN
cord-326631-7gd3hjc3	177	28	=	=	NN
cord-326631-7gd3hjc3	178	1	T	T	NNP
cord-326631-7gd3hjc3	178	2	Z.	Z.	NNP
cord-326631-7gd3hjc3	179	1	This	this	DT
cord-326631-7gd3hjc3	179	2	is	be	VBZ
cord-326631-7gd3hjc3	179	3	plausible	plausible	JJ
cord-326631-7gd3hjc3	179	4	,	,	,
cord-326631-7gd3hjc3	179	5	intuitively	intuitively	RB
cord-326631-7gd3hjc3	179	6	,	,	,
cord-326631-7gd3hjc3	179	7	since	since	IN
cord-326631-7gd3hjc3	179	8	the	the	DT
cord-326631-7gd3hjc3	179	9	integral	integral	JJ
cord-326631-7gd3hjc3	179	10	∞	∞	NNP
cord-326631-7gd3hjc3	179	11	0	0	CD
cord-326631-7gd3hjc3	179	12	I(t	I(t	NNP
cord-326631-7gd3hjc3	179	13	)	)	-RRB-
cord-326631-7gd3hjc3	179	14	dt	dt	NN
cord-326631-7gd3hjc3	179	15	sums	sum	VBZ
cord-326631-7gd3hjc3	179	16	all	all	DT
cord-326631-7gd3hjc3	179	17	infectious	infectious	JJ
cord-326631-7gd3hjc3	179	18	individuals	individual	NNS
cord-326631-7gd3hjc3	179	19	,	,	,
cord-326631-7gd3hjc3	179	20	weighted	weight	VBN
cord-326631-7gd3hjc3	179	21	by	by	IN
cord-326631-7gd3hjc3	179	22	the	the	DT
cord-326631-7gd3hjc3	179	23	time	time	NN
cord-326631-7gd3hjc3	179	24	they	-PRON-	PRP
cord-326631-7gd3hjc3	179	25	are	be	VBP
cord-326631-7gd3hjc3	179	26	infectious	infectious	JJ
cord-326631-7gd3hjc3	179	27	;	;	:
cord-326631-7gd3hjc3	179	28	this	this	DT
cord-326631-7gd3hjc3	179	29	must	must	MD
cord-326631-7gd3hjc3	179	30	also	also	RB
cord-326631-7gd3hjc3	179	31	equal	equal	VB
cord-326631-7gd3hjc3	179	32	the	the	DT
cord-326631-7gd3hjc3	179	33	mean	mean	JJ
cord-326631-7gd3hjc3	179	34	infectious	infectious	JJ
cord-326631-7gd3hjc3	179	35	period	period	NN
cord-326631-7gd3hjc3	179	36	T	T	NNP
cord-326631-7gd3hjc3	179	37	times	time	NNS
cord-326631-7gd3hjc3	179	38	the	the	DT
cord-326631-7gd3hjc3	179	39	number	number	NN
cord-326631-7gd3hjc3	179	40	of	of	IN
cord-326631-7gd3hjc3	179	41	individuals	individual	NNS
cord-326631-7gd3hjc3	179	42	infected	infect	VBN
cord-326631-7gd3hjc3	179	43	over	over	IN
cord-326631-7gd3hjc3	179	44	the	the	DT
cord-326631-7gd3hjc3	179	45	course	course	NN
cord-326631-7gd3hjc3	179	46	of	of	IN
cord-326631-7gd3hjc3	179	47	the	the	DT
cord-326631-7gd3hjc3	179	48	entire	entire	JJ
cord-326631-7gd3hjc3	179	49	epidemic	epidemic	NN
cord-326631-7gd3hjc3	179	50	(	(	-LRB-
cord-326631-7gd3hjc3	179	51	the	the	DT
cord-326631-7gd3hjc3	179	52	final	final	JJ
cord-326631-7gd3hjc3	179	53	size	size	NN
cord-326631-7gd3hjc3	179	54	Z	Z	NNP
cord-326631-7gd3hjc3	179	55	)	)	-RRB-
cord-326631-7gd3hjc3	179	56	.	.	.
cord-326631-7gd3hjc3	180	1	More	more	RBR
cord-326631-7gd3hjc3	180	2	rigorously	rigorously	RB
cord-326631-7gd3hjc3	180	3	,	,	,
cord-326631-7gd3hjc3	180	4	in	in	IN
cord-326631-7gd3hjc3	180	5	Appendix	Appendix	NNP
cord-326631-7gd3hjc3	180	6	B	B	NNP
cord-326631-7gd3hjc3	180	7	we	-PRON-	PRP
cord-326631-7gd3hjc3	180	8	prove	prove	VBP
cord-326631-7gd3hjc3	180	9	Lemma	Lemma	NNP
cord-326631-7gd3hjc3	180	10	6.1	6.1	CD
cord-326631-7gd3hjc3	180	11	.	.	.
cord-326631-7gd3hjc3	181	1	For	for	IN
cord-326631-7gd3hjc3	181	2	the	the	DT
cord-326631-7gd3hjc3	181	3	model	model	NN
cord-326631-7gd3hjc3	181	4	specified	specify	VBN
cord-326631-7gd3hjc3	181	5	by	by	IN
cord-326631-7gd3hjc3	181	6	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	181	7	.	.	.
cord-326631-7gd3hjc3	182	1	(	(	-LRB-
cord-326631-7gd3hjc3	182	2	11	11	CD
cord-326631-7gd3hjc3	182	3	)	)	-RRB-
cord-326631-7gd3hjc3	182	4	,	,	,
cord-326631-7gd3hjc3	182	5	in	in	IN
cord-326631-7gd3hjc3	182	6	the	the	DT
cord-326631-7gd3hjc3	182	7	limit	limit	NN
cord-326631-7gd3hjc3	182	8	(	(	-LRB-
cord-326631-7gd3hjc3	182	9	11	11	CD
cord-326631-7gd3hjc3	182	10	)	)	-RRB-
cord-326631-7gd3hjc3	182	11	.	.	.
cord-326631-7gd3hjc3	183	1	If	if	IN
cord-326631-7gd3hjc3	183	2	the	the	DT
cord-326631-7gd3hjc3	183	3	initial	initial	JJ
cord-326631-7gd3hjc3	183	4	number	number	NN
cord-326631-7gd3hjc3	183	5	of	of	IN
cord-326631-7gd3hjc3	183	6	infectious	infectious	JJ
cord-326631-7gd3hjc3	183	7	individuals	individual	NNS
cord-326631-7gd3hjc3	183	8	is	be	VBZ
cord-326631-7gd3hjc3	183	9	small	small	JJ
cord-326631-7gd3hjc3	183	10	(	(	-LRB-
cord-326631-7gd3hjc3	183	11	I(0	I(0	NNP
cord-326631-7gd3hjc3	183	12	)	)	-RRB-
cord-326631-7gd3hjc3	184	1	→	→	SYM
cord-326631-7gd3hjc3	184	2	0	0	CD
cord-326631-7gd3hjc3	184	3	)	)	-RRB-
cord-326631-7gd3hjc3	184	4	,	,	,
cord-326631-7gd3hjc3	184	5	then	then	RB
cord-326631-7gd3hjc3	184	6	the	the	DT
cord-326631-7gd3hjc3	184	7	final	final	JJ
cord-326631-7gd3hjc3	184	8	size	size	NN
cord-326631-7gd3hjc3	184	9	of	of	IN
cord-326631-7gd3hjc3	184	10	the	the	DT
cord-326631-7gd3hjc3	184	11	epidemic	epidemic	NN
cord-326631-7gd3hjc3	184	12	(	(	-LRB-
cord-326631-7gd3hjc3	184	13	Z	z	NN
cord-326631-7gd3hjc3	184	14	)	)	-RRB-
cord-326631-7gd3hjc3	184	15	is	be	VBZ
cord-326631-7gd3hjc3	184	16	given	give	VBN
cord-326631-7gd3hjc3	184	17	by	by	IN
cord-326631-7gd3hjc3	184	18	the	the	DT
cord-326631-7gd3hjc3	184	19	classical	classical	JJ
cord-326631-7gd3hjc3	184	20	formula	formula	NN
cord-326631-7gd3hjc3	184	21	(	(	-LRB-
cord-326631-7gd3hjc3	184	22	5	5	CD
cord-326631-7gd3hjc3	184	23	)	)	-RRB-
cord-326631-7gd3hjc3	184	24	.	.	.
cord-326631-7gd3hjc3	185	1	In	in	IN
cord-326631-7gd3hjc3	185	2	this	this	DT
cord-326631-7gd3hjc3	185	3	formula	formula	NN
cord-326631-7gd3hjc3	185	4	,	,	,
cord-326631-7gd3hjc3	185	5	the	the	DT
cord-326631-7gd3hjc3	185	6	basic	basic	JJ
cord-326631-7gd3hjc3	185	7	reproduction	reproduction	NN
cord-326631-7gd3hjc3	185	8	number	number	NN
cord-326631-7gd3hjc3	185	9	is	be	VBZ
cord-326631-7gd3hjc3	185	10	R	r	NN
cord-326631-7gd3hjc3	185	11	0	0	CD
cord-326631-7gd3hjc3	185	12	=	=	NFP
cord-326631-7gd3hjc3	186	1	βT	βT	NNP
cord-326631-7gd3hjc3	186	2	,	,	,
cord-326631-7gd3hjc3	186	3	where	where	WRB
cord-326631-7gd3hjc3	186	4	T	T	NNP
cord-326631-7gd3hjc3	186	5	is	be	VBZ
cord-326631-7gd3hjc3	186	6	the	the	DT
cord-326631-7gd3hjc3	186	7	mean	mean	JJ
cord-326631-7gd3hjc3	186	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	186	9	period	period	NN
cord-326631-7gd3hjc3	186	10	.	.	.
cord-326631-7gd3hjc3	187	1	With	with	IN
cord-326631-7gd3hjc3	187	2	modest	modest	JJ
cord-326631-7gd3hjc3	187	3	additional	additional	JJ
cord-326631-7gd3hjc3	187	4	effort	effort	NN
cord-326631-7gd3hjc3	187	5	,	,	,
cord-326631-7gd3hjc3	187	6	we	-PRON-	PRP
cord-326631-7gd3hjc3	187	7	can	can	MD
cord-326631-7gd3hjc3	187	8	generalize	generalize	VB
cord-326631-7gd3hjc3	187	9	Theorem	Theorem	NNP
cord-326631-7gd3hjc3	187	10	6.1	6.1	CD
cord-326631-7gd3hjc3	187	11	to	to	IN
cord-326631-7gd3hjc3	187	12	the	the	DT
cord-326631-7gd3hjc3	187	13	multiple	multiple	JJ
cord-326631-7gd3hjc3	187	14	stage	stage	NN
cord-326631-7gd3hjc3	187	15	SI	SI	NNP
cord-326631-7gd3hjc3	187	16	n	n	NNP
cord-326631-7gd3hjc3	187	17	R	r	NN
cord-326631-7gd3hjc3	187	18	model	model	NN
cord-326631-7gd3hjc3	187	19	,	,	,
cord-326631-7gd3hjc3	187	20	i.e.	i.e.	FW
cord-326631-7gd3hjc3	187	21	,	,	,
cord-326631-7gd3hjc3	187	22	the	the	DT
cord-326631-7gd3hjc3	187	23	usual	usual	JJ
cord-326631-7gd3hjc3	187	24	final	final	JJ
cord-326631-7gd3hjc3	187	25	size	size	NN
cord-326631-7gd3hjc3	187	26	formula	formula	NN
cord-326631-7gd3hjc3	187	27	(	(	-LRB-
cord-326631-7gd3hjc3	187	28	5	5	LS
cord-326631-7gd3hjc3	187	29	)	)	-RRB-
cord-326631-7gd3hjc3	187	30	is	be	VBZ
cord-326631-7gd3hjc3	187	31	still	still	RB
cord-326631-7gd3hjc3	187	32	valid	valid	JJ
cord-326631-7gd3hjc3	187	33	if	if	IN
cord-326631-7gd3hjc3	187	34	there	there	EX
cord-326631-7gd3hjc3	187	35	are	be	VBP
cord-326631-7gd3hjc3	187	36	multiple	multiple	JJ
cord-326631-7gd3hjc3	187	37	infectious	infectious	JJ
cord-326631-7gd3hjc3	187	38	stages	stage	NNS
cord-326631-7gd3hjc3	187	39	and	and	CC
cord-326631-7gd3hjc3	187	40	the	the	DT
cord-326631-7gd3hjc3	187	41	durations	duration	NNS
cord-326631-7gd3hjc3	187	42	of	of	IN
cord-326631-7gd3hjc3	187	43	each	each	DT
cord-326631-7gd3hjc3	187	44	stage	stage	NN
cord-326631-7gd3hjc3	187	45	are	be	VBP
cord-326631-7gd3hjc3	187	46	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	187	47	distributed	distribute	VBN
cord-326631-7gd3hjc3	187	48	.	.	.
cord-326631-7gd3hjc3	188	1	Recall	recall	VB
cord-326631-7gd3hjc3	188	2	that	that	IN
cord-326631-7gd3hjc3	188	3	latent	latent	JJ
cord-326631-7gd3hjc3	188	4	stages	stage	NNS
cord-326631-7gd3hjc3	188	5	can	can	MD
cord-326631-7gd3hjc3	188	6	be	be	VB
cord-326631-7gd3hjc3	188	7	considered	consider	VBN
cord-326631-7gd3hjc3	188	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	188	9	stages	stage	NNS
cord-326631-7gd3hjc3	188	10	with	with	IN
cord-326631-7gd3hjc3	188	11	zero	zero	CD
cord-326631-7gd3hjc3	188	12	transmission	transmission	NN
cord-326631-7gd3hjc3	188	13	rate	rate	NN
cord-326631-7gd3hjc3	188	14	,	,	,
cord-326631-7gd3hjc3	188	15	so	so	IN
cord-326631-7gd3hjc3	188	16	we	-PRON-	PRP
cord-326631-7gd3hjc3	188	17	do	do	VBP
cord-326631-7gd3hjc3	188	18	not	not	RB
cord-326631-7gd3hjc3	188	19	make	make	VB
cord-326631-7gd3hjc3	188	20	any	any	DT
cord-326631-7gd3hjc3	188	21	explicit	explicit	JJ
cord-326631-7gd3hjc3	188	22	reference	reference	NN
cord-326631-7gd3hjc3	188	23	to	to	IN
cord-326631-7gd3hjc3	188	24	latency	latency	NNP
cord-326631-7gd3hjc3	188	25	.	.	.
cord-326631-7gd3hjc3	189	1	As	as	IN
cord-326631-7gd3hjc3	189	2	in	in	IN
cord-326631-7gd3hjc3	189	3	all	all	PDT
cord-326631-7gd3hjc3	189	4	the	the	DT
cord-326631-7gd3hjc3	189	5	situations	situation	NNS
cord-326631-7gd3hjc3	189	6	considered	consider	VBN
cord-326631-7gd3hjc3	189	7	above	above	RB
cord-326631-7gd3hjc3	189	8	,	,	,
cord-326631-7gd3hjc3	189	9	we	-PRON-	PRP
cord-326631-7gd3hjc3	189	10	assume	assume	VBP
cord-326631-7gd3hjc3	189	11	that	that	IN
cord-326631-7gd3hjc3	189	12	vital	vital	JJ
cord-326631-7gd3hjc3	189	13	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	189	14	(	(	-LRB-
cord-326631-7gd3hjc3	189	15	births	birth	NNS
cord-326631-7gd3hjc3	189	16	and	and	CC
cord-326631-7gd3hjc3	189	17	deaths	death	NNS
cord-326631-7gd3hjc3	189	18	)	)	-RRB-
cord-326631-7gd3hjc3	189	19	can	can	MD
cord-326631-7gd3hjc3	189	20	be	be	VB
cord-326631-7gd3hjc3	189	21	ignored	ignore	VBN
cord-326631-7gd3hjc3	189	22	and	and	CC
cord-326631-7gd3hjc3	189	23	that	that	IN
cord-326631-7gd3hjc3	189	24	recovery	recovery	NN
cord-326631-7gd3hjc3	189	25	entails	entail	VBZ
cord-326631-7gd3hjc3	189	26	lifelong	lifelong	JJ
cord-326631-7gd3hjc3	189	27	immunity	immunity	NN
cord-326631-7gd3hjc3	189	28	.	.	.
cord-326631-7gd3hjc3	190	1	Suppose	suppose	VB
cord-326631-7gd3hjc3	190	2	the	the	DT
cord-326631-7gd3hjc3	190	3	ith	ith	JJ
cord-326631-7gd3hjc3	190	4	infectious	infectious	JJ
cord-326631-7gd3hjc3	190	5	stage	stage	NN
cord-326631-7gd3hjc3	190	6	has	have	VBZ
cord-326631-7gd3hjc3	190	7	duration	duration	NN
cord-326631-7gd3hjc3	190	8	distribution	distribution	NN
cord-326631-7gd3hjc3	190	9	with	with	IN
cord-326631-7gd3hjc3	190	10	probability	probability	NN
cord-326631-7gd3hjc3	190	11	density	density	NN
cord-326631-7gd3hjc3	190	12	f	f	NNP
cord-326631-7gd3hjc3	190	13	i	i	NN
cord-326631-7gd3hjc3	190	14	(	(	-LRB-
cord-326631-7gd3hjc3	190	15	t	t	NN
cord-326631-7gd3hjc3	190	16	)	)	-RRB-
cord-326631-7gd3hjc3	190	17	and	and	CC
cord-326631-7gd3hjc3	191	1	mean	mean	VBP
cord-326631-7gd3hjc3	191	2	T	T	NNP
cord-326631-7gd3hjc3	191	3	i	i	PRP
cord-326631-7gd3hjc3	191	4	.	.	.
cord-326631-7gd3hjc3	192	1	Thus	thus	RB
cord-326631-7gd3hjc3	192	2	,	,	,
cord-326631-7gd3hjc3	192	3	in	in	IN
cord-326631-7gd3hjc3	192	4	the	the	DT
cord-326631-7gd3hjc3	192	5	special	special	JJ
cord-326631-7gd3hjc3	192	6	case	case	NN
cord-326631-7gd3hjc3	192	7	that	that	IN
cord-326631-7gd3hjc3	192	8	durations	duration	NNS
cord-326631-7gd3hjc3	192	9	in	in	IN
cord-326631-7gd3hjc3	192	10	each	each	DT
cord-326631-7gd3hjc3	192	11	stage	stage	NN
cord-326631-7gd3hjc3	192	12	follow	follow	VBP
cord-326631-7gd3hjc3	192	13	Gamma	gamma	NN
cord-326631-7gd3hjc3	192	14	distributions	distribution	NNS
cord-326631-7gd3hjc3	192	15	(	(	-LRB-
cord-326631-7gd3hjc3	192	16	10	10	CD
cord-326631-7gd3hjc3	192	17	)	)	-RRB-
cord-326631-7gd3hjc3	192	18	,	,	,
cord-326631-7gd3hjc3	192	19	we	-PRON-	PRP
cord-326631-7gd3hjc3	192	20	have	have	VBP
cord-326631-7gd3hjc3	192	21	f	f	XX
cord-326631-7gd3hjc3	192	22	i	i	PRP
cord-326631-7gd3hjc3	192	23	(	(	-LRB-
cord-326631-7gd3hjc3	192	24	t	t	NN
cord-326631-7gd3hjc3	192	25	)	)	-RRB-
cord-326631-7gd3hjc3	192	26	=	=	NFP
cord-326631-7gd3hjc3	193	1	g	g	NNP
cord-326631-7gd3hjc3	193	2	ki	ki	NNP
cord-326631-7gd3hjc3	193	3	φi	φi	NNP
cord-326631-7gd3hjc3	193	4	(	(	-LRB-
cord-326631-7gd3hjc3	193	5	t	t	NN
cord-326631-7gd3hjc3	193	6	)	)	-RRB-
cord-326631-7gd3hjc3	193	7	and	and	CC
cord-326631-7gd3hjc3	193	8	The	the	DT
cord-326631-7gd3hjc3	193	9	the	the	DT
cord-326631-7gd3hjc3	193	10	rate	rate	NN
cord-326631-7gd3hjc3	193	11	of	of	IN
cord-326631-7gd3hjc3	193	12	change	change	NN
cord-326631-7gd3hjc3	193	13	of	of	IN
cord-326631-7gd3hjc3	193	14	the	the	DT
cord-326631-7gd3hjc3	193	15	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	193	16	class	class	NN
cord-326631-7gd3hjc3	193	17	is	be	VBZ
cord-326631-7gd3hjc3	193	18	given	give	VBN
cord-326631-7gd3hjc3	193	19	by	by	IN
cord-326631-7gd3hjc3	193	20	Eq	Eq	NNP
cord-326631-7gd3hjc3	193	21	.	.	.
cord-326631-7gd3hjc3	194	1	(	(	-LRB-
cord-326631-7gd3hjc3	194	2	6a	6a	NNP
cord-326631-7gd3hjc3	194	3	)	)	-RRB-
cord-326631-7gd3hjc3	194	4	,	,	,
cord-326631-7gd3hjc3	194	5	as	as	IN
cord-326631-7gd3hjc3	194	6	when	when	WRB
cord-326631-7gd3hjc3	194	7	all	all	DT
cord-326631-7gd3hjc3	194	8	stage	stage	NN
cord-326631-7gd3hjc3	194	9	durations	duration	NNS
cord-326631-7gd3hjc3	194	10	are	be	VBP
cord-326631-7gd3hjc3	194	11	exponentially	exponentially	RB
cord-326631-7gd3hjc3	194	12	distributed	distribute	VBN
cord-326631-7gd3hjc3	194	13	.	.	.
cord-326631-7gd3hjc3	195	1	Similar	similar	JJ
cord-326631-7gd3hjc3	195	2	to	to	IN
cord-326631-7gd3hjc3	195	3	Section	section	NN
cord-326631-7gd3hjc3	195	4	6	6	CD
cord-326631-7gd3hjc3	195	5	,	,	,
cord-326631-7gd3hjc3	195	6	the	the	DT
cord-326631-7gd3hjc3	195	7	equation	equation	NN
cord-326631-7gd3hjc3	195	8	for	for	IN
cord-326631-7gd3hjc3	195	9	each	each	DT
cord-326631-7gd3hjc3	195	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	195	11	stage	stage	NN
cord-326631-7gd3hjc3	195	12	can	can	MD
cord-326631-7gd3hjc3	195	13	be	be	VB
cord-326631-7gd3hjc3	195	14	writteṅ	writteṅ	NN
cord-326631-7gd3hjc3	195	15	where	where	WRB
cord-326631-7gd3hjc3	195	16	U	U	NNP
cord-326631-7gd3hjc3	195	17	i	i	PRP
cord-326631-7gd3hjc3	195	18	(	(	-LRB-
cord-326631-7gd3hjc3	195	19	t	t	NN
cord-326631-7gd3hjc3	195	20	)	)	-RRB-
cord-326631-7gd3hjc3	195	21	is	be	VBZ
cord-326631-7gd3hjc3	195	22	the	the	DT
cord-326631-7gd3hjc3	195	23	number	number	NN
cord-326631-7gd3hjc3	195	24	of	of	IN
cord-326631-7gd3hjc3	195	25	individuals	individual	NNS
cord-326631-7gd3hjc3	195	26	entering	enter	VBG
cord-326631-7gd3hjc3	195	27	class	class	NN
cord-326631-7gd3hjc3	196	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	196	2	i	i	PRP
cord-326631-7gd3hjc3	196	3	at	at	IN
cord-326631-7gd3hjc3	196	4	time	time	NN
cord-326631-7gd3hjc3	196	5	t	t	NNP
cord-326631-7gd3hjc3	196	6	,	,	,
cord-326631-7gd3hjc3	196	7	and	and	CC
cord-326631-7gd3hjc3	197	1	The	the	DT
cord-326631-7gd3hjc3	197	2	initial	initial	JJ
cord-326631-7gd3hjc3	197	3	conditions	condition	NNS
cord-326631-7gd3hjc3	197	4	are	be	VBP
cord-326631-7gd3hjc3	197	5	specified	specify	VBN
cord-326631-7gd3hjc3	197	6	by	by	IN
cord-326631-7gd3hjc3	197	7	Individuals	individual	NNS
cord-326631-7gd3hjc3	197	8	who	who	WP
cord-326631-7gd3hjc3	197	9	leave	leave	VBP
cord-326631-7gd3hjc3	197	10	the	the	DT
cord-326631-7gd3hjc3	197	11	last	last	JJ
cord-326631-7gd3hjc3	197	12	infectious	infectious	JJ
cord-326631-7gd3hjc3	197	13	stage	stage	NN
cord-326631-7gd3hjc3	197	14	recover	recover	VBP
cord-326631-7gd3hjc3	197	15	(	(	-LRB-
cord-326631-7gd3hjc3	197	16	into	into	IN
cord-326631-7gd3hjc3	197	17	class	class	NN
cord-326631-7gd3hjc3	197	18	R	r	NN
cord-326631-7gd3hjc3	197	19	)	)	-RRB-
cord-326631-7gd3hjc3	197	20	,	,	,
cord-326631-7gd3hjc3	197	21	hencė	hencė	RB
cord-326631-7gd3hjc3	197	22	When	when	WRB
cord-326631-7gd3hjc3	197	23	the	the	DT
cord-326631-7gd3hjc3	197	24	infectious	infectious	JJ
cord-326631-7gd3hjc3	197	25	periods	period	NNS
cord-326631-7gd3hjc3	197	26	and	and	CC
cord-326631-7gd3hjc3	197	27	the	the	DT
cord-326631-7gd3hjc3	197	28	latent	latent	JJ
cord-326631-7gd3hjc3	197	29	period	period	NN
cord-326631-7gd3hjc3	197	30	are	be	VBP
cord-326631-7gd3hjc3	197	31	exponentially	exponentially	RB
cord-326631-7gd3hjc3	197	32	distributed	distribute	VBN
cord-326631-7gd3hjc3	197	33	,	,	,
cord-326631-7gd3hjc3	197	34	i.e.	i.e.	FW
cord-326631-7gd3hjc3	197	35	,	,	,
cord-326631-7gd3hjc3	197	36	f	f	FW
cord-326631-7gd3hjc3	197	37	i	i	PRP
cord-326631-7gd3hjc3	197	38	(	(	-LRB-
cord-326631-7gd3hjc3	197	39	t	t	NN
cord-326631-7gd3hjc3	197	40	)	)	-RRB-
cord-326631-7gd3hjc3	197	41	=	=	NFP
cord-326631-7gd3hjc3	198	1	γ	γ	NNP
cord-326631-7gd3hjc3	199	1	i	i	PRP
cord-326631-7gd3hjc3	199	2	e	e	NNP
cord-326631-7gd3hjc3	200	1	−γi	−γi	CD
cord-326631-7gd3hjc3	200	2	t	t	NNP
cord-326631-7gd3hjc3	200	3	,	,	,
cord-326631-7gd3hjc3	200	4	the	the	DT
cord-326631-7gd3hjc3	200	5	technique	technique	NN
cord-326631-7gd3hjc3	200	6	introduced	introduce	VBN
cord-326631-7gd3hjc3	200	7	in	in	IN
cord-326631-7gd3hjc3	200	8	Appendix	Appendix	NNP
cord-326631-7gd3hjc3	200	9	B	B	NNP
cord-326631-7gd3hjc3	200	10	can	can	MD
cord-326631-7gd3hjc3	200	11	be	be	VB
cord-326631-7gd3hjc3	200	12	applied	apply	VBN
cord-326631-7gd3hjc3	200	13	to	to	TO
cord-326631-7gd3hjc3	200	14	show	show	VB
cord-326631-7gd3hjc3	200	15	that	that	IN
cord-326631-7gd3hjc3	200	16	the	the	DT
cord-326631-7gd3hjc3	200	17	model	model	NN
cord-326631-7gd3hjc3	200	18	(	(	-LRB-
cord-326631-7gd3hjc3	200	19	13	13	CD
cord-326631-7gd3hjc3	200	20	)	)	-RRB-
cord-326631-7gd3hjc3	200	21	is	be	VBZ
cord-326631-7gd3hjc3	200	22	indeed	indeed	RB
cord-326631-7gd3hjc3	200	23	the	the	DT
cord-326631-7gd3hjc3	200	24	standard	standard	JJ
cord-326631-7gd3hjc3	200	25	multiple	multiple	JJ
cord-326631-7gd3hjc3	200	26	-	-	HYPH
cord-326631-7gd3hjc3	200	27	stage	stage	NN
cord-326631-7gd3hjc3	200	28	SIR	SIR	NNP
cord-326631-7gd3hjc3	200	29	model	model	NN
cord-326631-7gd3hjc3	200	30	.	.	.
cord-326631-7gd3hjc3	201	1	In	in	IN
cord-326631-7gd3hjc3	201	2	their	-PRON-	PRP$
cord-326631-7gd3hjc3	201	3	analysis	analysis	NN
cord-326631-7gd3hjc3	201	4	of	of	IN
cord-326631-7gd3hjc3	201	5	the	the	DT
cord-326631-7gd3hjc3	201	6	SI	SI	NNP
cord-326631-7gd3hjc3	201	7	n	n	NNP
cord-326631-7gd3hjc3	201	8	R	R	NNP
cord-326631-7gd3hjc3	201	9	model	model	NN
cord-326631-7gd3hjc3	201	10	with	with	IN
cord-326631-7gd3hjc3	201	11	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	201	12	distributed	distribute	VBN
cord-326631-7gd3hjc3	201	13	stage	stage	NN
cord-326631-7gd3hjc3	201	14	durations	duration	NNS
cord-326631-7gd3hjc3	201	15	(	(	-LRB-
cord-326631-7gd3hjc3	201	16	13	13	CD
cord-326631-7gd3hjc3	201	17	)	)	-RRB-
cord-326631-7gd3hjc3	201	18	,	,	,
cord-326631-7gd3hjc3	201	19	Feng	Feng	NNP
cord-326631-7gd3hjc3	201	20	and	and	CC
cord-326631-7gd3hjc3	201	21	Thieme	Thieme	NNP
cord-326631-7gd3hjc3	201	22	(	(	-LRB-
cord-326631-7gd3hjc3	201	23	2000	2000	CD
cord-326631-7gd3hjc3	201	24	)	)	-RRB-
cord-326631-7gd3hjc3	201	25	have	have	VBP
cord-326631-7gd3hjc3	201	26	shown	show	VBN
cord-326631-7gd3hjc3	201	27	that	that	IN
cord-326631-7gd3hjc3	201	28	the	the	DT
cord-326631-7gd3hjc3	201	29	basic	basic	JJ
cord-326631-7gd3hjc3	201	30	reproduction	reproduction	NN
cord-326631-7gd3hjc3	201	31	number	number	NN
cord-326631-7gd3hjc3	201	32	is	be	VBZ
cord-326631-7gd3hjc3	201	33	and	and	CC
cord-326631-7gd3hjc3	201	34	that	that	IN
cord-326631-7gd3hjc3	201	35	the	the	DT
cord-326631-7gd3hjc3	201	36	disease	disease	NN
cord-326631-7gd3hjc3	201	37	free	free	JJ
cord-326631-7gd3hjc3	201	38	equilibrium	equilibrium	NN
cord-326631-7gd3hjc3	201	39	is	be	VBZ
cord-326631-7gd3hjc3	201	40	unstable	unstable	JJ
cord-326631-7gd3hjc3	201	41	if	if	IN
cord-326631-7gd3hjc3	201	42	and	and	CC
cord-326631-7gd3hjc3	201	43	only	only	RB
cord-326631-7gd3hjc3	201	44	if	if	IN
cord-326631-7gd3hjc3	201	45	R	r	NN
cord-326631-7gd3hjc3	201	46	0	0	CD
cord-326631-7gd3hjc3	201	47	>	>	SYM
cord-326631-7gd3hjc3	201	48	1	1	CD
cord-326631-7gd3hjc3	201	49	.	.	.
cord-326631-7gd3hjc3	202	1	Similar	similar	JJ
cord-326631-7gd3hjc3	202	2	to	to	IN
cord-326631-7gd3hjc3	202	3	previous	previous	JJ
cord-326631-7gd3hjc3	202	4	sections	section	NNS
cord-326631-7gd3hjc3	202	5	,	,	,
cord-326631-7gd3hjc3	202	6	we	-PRON-	PRP
cord-326631-7gd3hjc3	202	7	find	find	VBP
cord-326631-7gd3hjc3	202	8	that	that	IN
cord-326631-7gd3hjc3	202	9	S	s	NN
cord-326631-7gd3hjc3	203	1	+	+	CC
cord-326631-7gd3hjc3	204	1	i	i	PRP
cord-326631-7gd3hjc3	205	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	206	1	i	i	PRP
cord-326631-7gd3hjc3	206	2	+	+	CC
cord-326631-7gd3hjc3	206	3	R	r	NN
cord-326631-7gd3hjc3	206	4	=	=	SYM
cord-326631-7gd3hjc3	206	5	1	1	CD
cord-326631-7gd3hjc3	206	6	is	be	VBZ
cord-326631-7gd3hjc3	206	7	invariant	invariant	JJ
cord-326631-7gd3hjc3	206	8	,	,	,
cord-326631-7gd3hjc3	206	9	S	s	NN
cord-326631-7gd3hjc3	206	10	≥	≥	NN
cord-326631-7gd3hjc3	206	11	0	0	CD
cord-326631-7gd3hjc3	206	12	,	,	,
cord-326631-7gd3hjc3	206	13	and	and	CC
cord-326631-7gd3hjc3	206	14	S(∞	S(∞	NNP
cord-326631-7gd3hjc3	206	15	)	)	-RRB-
cord-326631-7gd3hjc3	206	16	exists	exist	VBZ
cord-326631-7gd3hjc3	206	17	.	.	.
cord-326631-7gd3hjc3	207	1	Integrating	integrate	VBG
cord-326631-7gd3hjc3	207	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	207	3	.	.	.
cord-326631-7gd3hjc3	208	1	(	(	-LRB-
cord-326631-7gd3hjc3	208	2	13a	13a	NNS
cord-326631-7gd3hjc3	208	3	)	)	-RRB-
cord-326631-7gd3hjc3	208	4	from	from	IN
cord-326631-7gd3hjc3	208	5	0	0	CD
cord-326631-7gd3hjc3	208	6	to	to	IN
cord-326631-7gd3hjc3	208	7	t	t	NN
cord-326631-7gd3hjc3	208	8	and	and	CC
cord-326631-7gd3hjc3	208	9	and	and	CC
cord-326631-7gd3hjc3	208	10	switching	switch	VBG
cord-326631-7gd3hjc3	208	11	the	the	DT
cord-326631-7gd3hjc3	208	12	order	order	NN
cord-326631-7gd3hjc3	208	13	of	of	IN
cord-326631-7gd3hjc3	208	14	integrations	integration	NNS
cord-326631-7gd3hjc3	208	15	,	,	,
cord-326631-7gd3hjc3	208	16	we	-PRON-	PRP
cord-326631-7gd3hjc3	208	17	have	have	VBP
cord-326631-7gd3hjc3	208	18	I(t	I(t	NNP
cord-326631-7gd3hjc3	208	19	)	)	-RRB-
cord-326631-7gd3hjc3	208	20	≥	≥	CD
cord-326631-7gd3hjc3	208	21	0	0	CD
cord-326631-7gd3hjc3	208	22	;	;	:
cord-326631-7gd3hjc3	208	23	similarly	similarly	RB
cord-326631-7gd3hjc3	208	24	,	,	,
cord-326631-7gd3hjc3	208	25	integrating	integrate	VBG
cord-326631-7gd3hjc3	208	26	from	from	IN
cord-326631-7gd3hjc3	208	27	0	0	CD
cord-326631-7gd3hjc3	208	28	to	to	IN
cord-326631-7gd3hjc3	208	29	∞	∞	NNP
cord-326631-7gd3hjc3	208	30	,	,	,
cord-326631-7gd3hjc3	208	31	we	-PRON-	PRP
cord-326631-7gd3hjc3	208	32	have	have	VBP
cord-326631-7gd3hjc3	208	33	I(∞	i(∞	CD
cord-326631-7gd3hjc3	208	34	)	)	-RRB-
cord-326631-7gd3hjc3	209	1	=	=	SYM
cord-326631-7gd3hjc3	209	2	0	0	NFP
cord-326631-7gd3hjc3	209	3	.	.	.
cord-326631-7gd3hjc3	210	1	Thus	thus	RB
cord-326631-7gd3hjc3	210	2	,	,	,
cord-326631-7gd3hjc3	210	3	the	the	DT
cord-326631-7gd3hjc3	210	4	disease	disease	NN
cord-326631-7gd3hjc3	210	5	will	will	MD
cord-326631-7gd3hjc3	210	6	also	also	RB
cord-326631-7gd3hjc3	210	7	eventually	eventually	RB
cord-326631-7gd3hjc3	210	8	burn	burn	VB
cord-326631-7gd3hjc3	210	9	out	out	RP
cord-326631-7gd3hjc3	210	10	.	.	.
cord-326631-7gd3hjc3	211	1	Theorem	Theorem	NNP
cord-326631-7gd3hjc3	211	2	7.1	7.1	CD
cord-326631-7gd3hjc3	211	3	.	.	.
cord-326631-7gd3hjc3	212	1	Consider	consider	VB
cord-326631-7gd3hjc3	212	2	the	the	DT
cord-326631-7gd3hjc3	212	3	multiple	multiple	JJ
cord-326631-7gd3hjc3	212	4	stage	stage	NN
cord-326631-7gd3hjc3	212	5	SI	SI	NNP
cord-326631-7gd3hjc3	212	6	n	n	NNP
cord-326631-7gd3hjc3	212	7	R	r	NN
cord-326631-7gd3hjc3	212	8	epidemic	epidemic	NN
cord-326631-7gd3hjc3	212	9	model	model	NN
cord-326631-7gd3hjc3	212	10	with	with	IN
cord-326631-7gd3hjc3	212	11	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	212	12	distributed	distribute	VBN
cord-326631-7gd3hjc3	212	13	stage	stage	NN
cord-326631-7gd3hjc3	212	14	durations	duration	NNS
cord-326631-7gd3hjc3	212	15	,	,	,
cord-326631-7gd3hjc3	212	16	specified	specify	VBN
cord-326631-7gd3hjc3	212	17	by	by	IN
cord-326631-7gd3hjc3	212	18	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	212	19	.	.	.
cord-326631-7gd3hjc3	213	1	(	(	-LRB-
cord-326631-7gd3hjc3	213	2	13	13	CD
cord-326631-7gd3hjc3	213	3	)	)	-RRB-
cord-326631-7gd3hjc3	213	4	.	.	.
cord-326631-7gd3hjc3	214	1	If	if	IN
cord-326631-7gd3hjc3	214	2	the	the	DT
cord-326631-7gd3hjc3	214	3	initial	initial	JJ
cord-326631-7gd3hjc3	214	4	number	number	NN
cord-326631-7gd3hjc3	214	5	of	of	IN
cord-326631-7gd3hjc3	214	6	infectious	infectious	JJ
cord-326631-7gd3hjc3	214	7	individuals	individual	NNS
cord-326631-7gd3hjc3	214	8	is	be	VBZ
cord-326631-7gd3hjc3	214	9	suffciently	suffciently	RB
cord-326631-7gd3hjc3	214	10	small	small	JJ
cord-326631-7gd3hjc3	214	11	,	,	,
cord-326631-7gd3hjc3	214	12	i.e.	i.e.	FW
cord-326631-7gd3hjc3	214	13	,	,	,
cord-326631-7gd3hjc3	214	14	in	in	IN
cord-326631-7gd3hjc3	214	15	the	the	DT
cord-326631-7gd3hjc3	214	16	limit	limit	NN
cord-326631-7gd3hjc3	215	1	i	i	PRP
cord-326631-7gd3hjc3	216	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	216	2	i	i	PRP
cord-326631-7gd3hjc3	216	3	(	(	-LRB-
cord-326631-7gd3hjc3	216	4	0	0	NFP
cord-326631-7gd3hjc3	216	5	)	)	-RRB-
cord-326631-7gd3hjc3	217	1	→	→	SYM
cord-326631-7gd3hjc3	217	2	0	0	CD
cord-326631-7gd3hjc3	217	3	,	,	,
cord-326631-7gd3hjc3	217	4	the	the	DT
cord-326631-7gd3hjc3	217	5	final	final	JJ
cord-326631-7gd3hjc3	217	6	size	size	NN
cord-326631-7gd3hjc3	217	7	Z	Z	NNP
cord-326631-7gd3hjc3	217	8	is	be	VBZ
cord-326631-7gd3hjc3	217	9	given	give	VBN
cord-326631-7gd3hjc3	217	10	by	by	IN
cord-326631-7gd3hjc3	217	11	the	the	DT
cord-326631-7gd3hjc3	217	12	unique	unique	JJ
cord-326631-7gd3hjc3	217	13	solution	solution	NN
cord-326631-7gd3hjc3	217	14	of	of	IN
cord-326631-7gd3hjc3	217	15	Eq	Eq	NNP
cord-326631-7gd3hjc3	217	16	.	.	.
cord-326631-7gd3hjc3	218	1	(	(	-LRB-
cord-326631-7gd3hjc3	218	2	5	5	LS
cord-326631-7gd3hjc3	218	3	)	)	-RRB-
cord-326631-7gd3hjc3	218	4	,	,	,
cord-326631-7gd3hjc3	218	5	or	or	CC
cord-326631-7gd3hjc3	218	6	explicitly	explicitly	RB
cord-326631-7gd3hjc3	218	7	by	by	IN
cord-326631-7gd3hjc3	218	8	Eq	Eq	NNP
cord-326631-7gd3hjc3	218	9	.	.	.
cord-326631-7gd3hjc3	219	1	(	(	-LRB-
cord-326631-7gd3hjc3	219	2	A.2	a.2	NN
cord-326631-7gd3hjc3	219	3	)	)	-RRB-
cord-326631-7gd3hjc3	219	4	,	,	,
cord-326631-7gd3hjc3	219	5	in	in	IN
cord-326631-7gd3hjc3	219	6	which	which	WDT
cord-326631-7gd3hjc3	219	7	R	r	NN
cord-326631-7gd3hjc3	219	8	0	0	CD
cord-326631-7gd3hjc3	219	9	is	be	VBZ
cord-326631-7gd3hjc3	219	10	given	give	VBN
cord-326631-7gd3hjc3	219	11	by	by	IN
cord-326631-7gd3hjc3	219	12	Eq	Eq	NNP
cord-326631-7gd3hjc3	219	13	.	.	.
cord-326631-7gd3hjc3	220	1	(	(	-LRB-
cord-326631-7gd3hjc3	220	2	14	14	CD
cord-326631-7gd3hjc3	220	3	)	)	-RRB-
cord-326631-7gd3hjc3	220	4	.	.	.
cord-326631-7gd3hjc3	221	1	Proof	proof	NN
cord-326631-7gd3hjc3	221	2	.	.	.
cord-326631-7gd3hjc3	222	1	To	to	TO
cord-326631-7gd3hjc3	222	2	prove	prove	VB
cord-326631-7gd3hjc3	222	3	this	this	DT
cord-326631-7gd3hjc3	222	4	,	,	,
cord-326631-7gd3hjc3	222	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	222	6	divide	divide	VBP
cord-326631-7gd3hjc3	222	7	by	by	IN
cord-326631-7gd3hjc3	222	8	S	S	NNP
cord-326631-7gd3hjc3	222	9	on	on	IN
cord-326631-7gd3hjc3	222	10	both	both	DT
cord-326631-7gd3hjc3	222	11	sides	side	NNS
cord-326631-7gd3hjc3	222	12	of	of	IN
cord-326631-7gd3hjc3	222	13	(	(	-LRB-
cord-326631-7gd3hjc3	222	14	6a	6a	NN
cord-326631-7gd3hjc3	222	15	)	)	-RRB-
cord-326631-7gd3hjc3	222	16	and	and	CC
cord-326631-7gd3hjc3	222	17	integrate	integrate	VB
cord-326631-7gd3hjc3	222	18	with	with	IN
cord-326631-7gd3hjc3	222	19	respect	respect	NN
cord-326631-7gd3hjc3	222	20	to	to	IN
cord-326631-7gd3hjc3	222	21	time	time	NN
cord-326631-7gd3hjc3	222	22	,	,	,
cord-326631-7gd3hjc3	222	23	Using	use	VBG
cord-326631-7gd3hjc3	222	24	Lemma	Lemma	NNP
cord-326631-7gd3hjc3	222	25	6.1	6.1	CD
cord-326631-7gd3hjc3	222	26	,	,	,
cord-326631-7gd3hjc3	222	27	Eq	Eq	NNP
cord-326631-7gd3hjc3	222	28	.	.	.
cord-326631-7gd3hjc3	223	1	(	(	-LRB-
cord-326631-7gd3hjc3	223	2	15	15	CD
cord-326631-7gd3hjc3	223	3	)	)	-RRB-
cord-326631-7gd3hjc3	223	4	becomes	become	VBZ
cord-326631-7gd3hjc3	223	5	Suppose	suppose	NN
cord-326631-7gd3hjc3	224	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	224	2	i	i	PRP
cord-326631-7gd3hjc3	224	3	(	(	-LRB-
cord-326631-7gd3hjc3	224	4	0	0	NFP
cord-326631-7gd3hjc3	224	5	)	)	-RRB-
cord-326631-7gd3hjc3	224	6	=	=	NFP
cord-326631-7gd3hjc3	225	1	i	i	PRP
cord-326631-7gd3hjc3	225	2	1	1	CD
cord-326631-7gd3hjc3	225	3	.	.	.
cord-326631-7gd3hjc3	226	1	Switching	switch	VBG
cord-326631-7gd3hjc3	226	2	the	the	DT
cord-326631-7gd3hjc3	226	3	order	order	NN
cord-326631-7gd3hjc3	226	4	of	of	IN
cord-326631-7gd3hjc3	226	5	integration	integration	NN
cord-326631-7gd3hjc3	226	6	,	,	,
cord-326631-7gd3hjc3	226	7	Also	also	RB
cord-326631-7gd3hjc3	226	8	,	,	,
cord-326631-7gd3hjc3	226	9	integrating	integrate	VBG
cord-326631-7gd3hjc3	226	10	Eq	Eq	NNP
cord-326631-7gd3hjc3	226	11	.	.	.
cord-326631-7gd3hjc3	227	1	(	(	-LRB-
cord-326631-7gd3hjc3	227	2	13d	13d	CD
cord-326631-7gd3hjc3	227	3	)	)	-RRB-
cord-326631-7gd3hjc3	227	4	and	and	CC
cord-326631-7gd3hjc3	227	5	switching	switch	VBG
cord-326631-7gd3hjc3	227	6	the	the	DT
cord-326631-7gd3hjc3	227	7	order	order	NN
cord-326631-7gd3hjc3	227	8	of	of	IN
cord-326631-7gd3hjc3	227	9	integrations	integration	NNS
cord-326631-7gd3hjc3	227	10	,	,	,
cord-326631-7gd3hjc3	227	11	we	-PRON-	PRP
cord-326631-7gd3hjc3	227	12	have	have	VBP
cord-326631-7gd3hjc3	227	13	i.e.	i.e.	FW
cord-326631-7gd3hjc3	227	14	,	,	,
cord-326631-7gd3hjc3	227	15	summed	sum	VBN
cord-326631-7gd3hjc3	227	16	over	over	IN
cord-326631-7gd3hjc3	227	17	all	all	DT
cord-326631-7gd3hjc3	227	18	time	time	NN
cord-326631-7gd3hjc3	227	19	,	,	,
cord-326631-7gd3hjc3	227	20	the	the	DT
cord-326631-7gd3hjc3	227	21	number	number	NN
cord-326631-7gd3hjc3	227	22	of	of	IN
cord-326631-7gd3hjc3	227	23	individuals	individual	NNS
cord-326631-7gd3hjc3	227	24	who	who	WP
cord-326631-7gd3hjc3	227	25	enter	enter	VBP
cord-326631-7gd3hjc3	227	26	the	the	DT
cord-326631-7gd3hjc3	227	27	(	(	-LRB-
cord-326631-7gd3hjc3	227	28	i	i	NN
cord-326631-7gd3hjc3	227	29	+	+	SYM
cord-326631-7gd3hjc3	227	30	1)th	1)th	CD
cord-326631-7gd3hjc3	227	31	stage	stage	NN
cord-326631-7gd3hjc3	227	32	is	be	VBZ
cord-326631-7gd3hjc3	227	33	the	the	DT
cord-326631-7gd3hjc3	227	34	same	same	JJ
cord-326631-7gd3hjc3	227	35	as	as	IN
cord-326631-7gd3hjc3	227	36	the	the	DT
cord-326631-7gd3hjc3	227	37	number	number	NN
cord-326631-7gd3hjc3	227	38	who	who	WP
cord-326631-7gd3hjc3	227	39	enter	enter	VBP
cord-326631-7gd3hjc3	227	40	the	the	DT
cord-326631-7gd3hjc3	227	41	ith	ith	JJ
cord-326631-7gd3hjc3	227	42	stage	stage	NN
cord-326631-7gd3hjc3	227	43	.	.	.
cord-326631-7gd3hjc3	228	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	228	2	then	then	RB
cord-326631-7gd3hjc3	228	3	integrate	integrate	VBP
cord-326631-7gd3hjc3	228	4	Eq	Eq	NNP
cord-326631-7gd3hjc3	228	5	.	.	.
cord-326631-7gd3hjc3	229	1	(	(	-LRB-
cord-326631-7gd3hjc3	229	2	6a	6a	CD
cord-326631-7gd3hjc3	229	3	)	)	-RRB-
cord-326631-7gd3hjc3	229	4	.	.	.
cord-326631-7gd3hjc3	230	1	From	from	IN
cord-326631-7gd3hjc3	230	2	the	the	DT
cord-326631-7gd3hjc3	230	3	definition	definition	NN
cord-326631-7gd3hjc3	230	4	of	of	IN
cord-326631-7gd3hjc3	230	5	U	U	NNP
cord-326631-7gd3hjc3	230	6	1	1	CD
cord-326631-7gd3hjc3	230	7	(	(	-LRB-
cord-326631-7gd3hjc3	230	8	t	t	NN
cord-326631-7gd3hjc3	230	9	)	)	-RRB-
cord-326631-7gd3hjc3	230	10	in	in	IN
cord-326631-7gd3hjc3	230	11	Eq	Eq	NNP
cord-326631-7gd3hjc3	230	12	.	.	.
cord-326631-7gd3hjc3	231	1	(	(	-LRB-
cord-326631-7gd3hjc3	231	2	13c	13c	CD
cord-326631-7gd3hjc3	231	3	)	)	-RRB-
cord-326631-7gd3hjc3	231	4	,	,	,
cord-326631-7gd3hjc3	231	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	231	6	have	have	VBP
cord-326631-7gd3hjc3	231	7	for	for	IN
cord-326631-7gd3hjc3	231	8	all	all	DT
cord-326631-7gd3hjc3	231	9	i	i	PRP
cord-326631-7gd3hjc3	231	10	=	=	SYM
cord-326631-7gd3hjc3	231	11	1	1	CD
cord-326631-7gd3hjc3	231	12	,	,	,
cord-326631-7gd3hjc3	231	13	.	.	.
cord-326631-7gd3hjc3	231	14	.	.	.
cord-326631-7gd3hjc3	231	15	.	.	.
cord-326631-7gd3hjc3	232	1	,	,	,
cord-326631-7gd3hjc3	232	2	n.	n.	NN
cord-326631-7gd3hjc3	232	3	Notice	notice	NN
cord-326631-7gd3hjc3	232	4	that	that	IN
cord-326631-7gd3hjc3	232	5	the	the	DT
cord-326631-7gd3hjc3	232	6	final	final	JJ
cord-326631-7gd3hjc3	232	7	size	size	NN
cord-326631-7gd3hjc3	232	8	Z	z	NN
cord-326631-7gd3hjc3	232	9	=	=	NN
cord-326631-7gd3hjc3	232	10	S(0	S(0	NNP
cord-326631-7gd3hjc3	232	11	)	)	-RRB-
cord-326631-7gd3hjc3	232	12	−	−	NNP
cord-326631-7gd3hjc3	232	13	S(∞	S(∞	NNP
cord-326631-7gd3hjc3	232	14	)	)	-RRB-
cord-326631-7gd3hjc3	232	15	,	,	,
cord-326631-7gd3hjc3	232	16	so	so	RB
cord-326631-7gd3hjc3	232	17	Eq	Eq	NNP
cord-326631-7gd3hjc3	232	18	.	.	.
cord-326631-7gd3hjc3	233	1	(	(	-LRB-
cord-326631-7gd3hjc3	233	2	16	16	CD
cord-326631-7gd3hjc3	233	3	)	)	-RRB-
cord-326631-7gd3hjc3	233	4	becomes	become	VBZ
cord-326631-7gd3hjc3	233	5	During	during	IN
cord-326631-7gd3hjc3	233	6	the	the	DT
cord-326631-7gd3hjc3	233	7	epidemic	epidemic	NN
cord-326631-7gd3hjc3	233	8	of	of	IN
cord-326631-7gd3hjc3	233	9	severe	severe	JJ
cord-326631-7gd3hjc3	233	10	acute	acute	JJ
cord-326631-7gd3hjc3	233	11	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	233	12	syndrome	syndrome	NN
cord-326631-7gd3hjc3	233	13	(	(	-LRB-
cord-326631-7gd3hjc3	233	14	SARS	SARS	NNP
cord-326631-7gd3hjc3	233	15	)	)	-RRB-
cord-326631-7gd3hjc3	233	16	in	in	IN
cord-326631-7gd3hjc3	233	17	2003	2003	CD
cord-326631-7gd3hjc3	234	1	(	(	-LRB-
cord-326631-7gd3hjc3	234	2	Poutanen	Poutanen	NNP
cord-326631-7gd3hjc3	234	3	et	et	FW
cord-326631-7gd3hjc3	234	4	al	al	NNP
cord-326631-7gd3hjc3	234	5	.	.	NNP
cord-326631-7gd3hjc3	234	6	,	,	,
cord-326631-7gd3hjc3	234	7	2003	2003	CD
cord-326631-7gd3hjc3	234	8	;	;	:
cord-326631-7gd3hjc3	235	1	Low	low	JJ
cord-326631-7gd3hjc3	235	2	and	and	CC
cord-326631-7gd3hjc3	235	3	McGeer	McGeer	NNPS
cord-326631-7gd3hjc3	235	4	,	,	,
cord-326631-7gd3hjc3	235	5	2003	2003	CD
cord-326631-7gd3hjc3	235	6	)	)	-RRB-
cord-326631-7gd3hjc3	235	7	,	,	,
cord-326631-7gd3hjc3	235	8	one	one	CD
cord-326631-7gd3hjc3	235	9	aspect	aspect	NN
cord-326631-7gd3hjc3	235	10	of	of	IN
cord-326631-7gd3hjc3	235	11	observed	observed	JJ
cord-326631-7gd3hjc3	235	12	transmission	transmission	NN
cord-326631-7gd3hjc3	235	13	that	that	WDT
cord-326631-7gd3hjc3	235	14	received	receive	VBD
cord-326631-7gd3hjc3	235	15	a	a	DT
cord-326631-7gd3hjc3	235	16	great	great	JJ
cord-326631-7gd3hjc3	235	17	deal	deal	NN
cord-326631-7gd3hjc3	235	18	of	of	IN
cord-326631-7gd3hjc3	235	19	attention	attention	NN
cord-326631-7gd3hjc3	235	20	was	be	VBD
cord-326631-7gd3hjc3	235	21	the	the	DT
cord-326631-7gd3hjc3	235	22	existence	existence	NN
cord-326631-7gd3hjc3	235	23	of	of	IN
cord-326631-7gd3hjc3	235	24	super	super	JJ
cord-326631-7gd3hjc3	235	25	-	-	NNS
cord-326631-7gd3hjc3	235	26	spreaders	spreader	NNS
cord-326631-7gd3hjc3	235	27	(	(	-LRB-
cord-326631-7gd3hjc3	235	28	WHO	who	WP
cord-326631-7gd3hjc3	235	29	SARS	SARS	NNP
cord-326631-7gd3hjc3	235	30	Update	Update	NNP
cord-326631-7gd3hjc3	235	31	27	27	CD
cord-326631-7gd3hjc3	235	32	,	,	,
cord-326631-7gd3hjc3	235	33	2003	2003	CD
cord-326631-7gd3hjc3	235	34	)	)	-RRB-
cord-326631-7gd3hjc3	235	35	,	,	,
cord-326631-7gd3hjc3	235	36	i.e.	i.e.	FW
cord-326631-7gd3hjc3	235	37	,	,	,
cord-326631-7gd3hjc3	235	38	individuals	individual	NNS
cord-326631-7gd3hjc3	235	39	who	who	WP
cord-326631-7gd3hjc3	235	40	infect	infect	VBP
cord-326631-7gd3hjc3	235	41	many	many	JJ
cord-326631-7gd3hjc3	235	42	more	more	JJR
cord-326631-7gd3hjc3	235	43	people	people	NNS
cord-326631-7gd3hjc3	235	44	than	than	IN
cord-326631-7gd3hjc3	235	45	the	the	DT
cord-326631-7gd3hjc3	235	46	average	average	NN
cord-326631-7gd3hjc3	235	47	(	(	-LRB-
cord-326631-7gd3hjc3	235	48	e.g.	e.g.	RB
cord-326631-7gd3hjc3	235	49	,	,	,
cord-326631-7gd3hjc3	235	50	at	at	IN
cord-326631-7gd3hjc3	235	51	least	least	JJS
cord-326631-7gd3hjc3	235	52	an	an	DT
cord-326631-7gd3hjc3	235	53	order	order	NN
cord-326631-7gd3hjc3	235	54	of	of	IN
cord-326631-7gd3hjc3	235	55	magnitude	magnitude	NN
cord-326631-7gd3hjc3	235	56	greater	great	JJR
cord-326631-7gd3hjc3	235	57	than	than	IN
cord-326631-7gd3hjc3	235	58	R	r	NN
cord-326631-7gd3hjc3	235	59	0	0	CD
cord-326631-7gd3hjc3	235	60	)	)	-RRB-
cord-326631-7gd3hjc3	235	61	.	.	.
cord-326631-7gd3hjc3	236	1	In	in	IN
cord-326631-7gd3hjc3	236	2	this	this	DT
cord-326631-7gd3hjc3	236	3	section	section	NN
cord-326631-7gd3hjc3	236	4	,	,	,
cord-326631-7gd3hjc3	236	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	236	6	prove	prove	VBP
cord-326631-7gd3hjc3	236	7	that	that	IN
cord-326631-7gd3hjc3	236	8	the	the	DT
cord-326631-7gd3hjc3	236	9	existence	existence	NN
cord-326631-7gd3hjc3	236	10	of	of	IN
cord-326631-7gd3hjc3	236	11	the	the	DT
cord-326631-7gd3hjc3	236	12	type	type	NN
cord-326631-7gd3hjc3	236	13	of	of	IN
cord-326631-7gd3hjc3	236	14	super	super	JJ
cord-326631-7gd3hjc3	236	15	-	-	NNS
cord-326631-7gd3hjc3	236	16	spreaders	spreader	NNS
cord-326631-7gd3hjc3	236	17	that	that	WDT
cord-326631-7gd3hjc3	236	18	occurred	occur	VBD
cord-326631-7gd3hjc3	236	19	during	during	IN
cord-326631-7gd3hjc3	236	20	the	the	DT
cord-326631-7gd3hjc3	236	21	SARS	SARS	NNP
cord-326631-7gd3hjc3	236	22	outbreak	outbreak	NN
cord-326631-7gd3hjc3	236	23	in	in	IN
cord-326631-7gd3hjc3	236	24	2003	2003	CD
cord-326631-7gd3hjc3	236	25	has	have	VBZ
cord-326631-7gd3hjc3	236	26	no	no	DT
cord-326631-7gd3hjc3	236	27	effect	effect	NN
cord-326631-7gd3hjc3	236	28	on	on	IN
cord-326631-7gd3hjc3	236	29	the	the	DT
cord-326631-7gd3hjc3	236	30	final	final	JJ
cord-326631-7gd3hjc3	236	31	size	size	NN
cord-326631-7gd3hjc3	236	32	formula	formula	NN
cord-326631-7gd3hjc3	236	33	.	.	.
cord-326631-7gd3hjc3	237	1	One	one	CD
cord-326631-7gd3hjc3	237	2	mechanism	mechanism	NN
cord-326631-7gd3hjc3	237	3	for	for	IN
cord-326631-7gd3hjc3	237	4	the	the	DT
cord-326631-7gd3hjc3	237	5	generation	generation	NN
cord-326631-7gd3hjc3	237	6	of	of	IN
cord-326631-7gd3hjc3	237	7	super	super	JJ
cord-326631-7gd3hjc3	237	8	-	-	NNS
cord-326631-7gd3hjc3	237	9	spreaders	spreader	NNS
cord-326631-7gd3hjc3	237	10	is	be	VBZ
cord-326631-7gd3hjc3	237	11	that	that	IN
cord-326631-7gd3hjc3	237	12	the	the	DT
cord-326631-7gd3hjc3	237	13	infectious	infectious	JJ
cord-326631-7gd3hjc3	237	14	period	period	NN
cord-326631-7gd3hjc3	237	15	distribution	distribution	NN
cord-326631-7gd3hjc3	237	16	could	could	MD
cord-326631-7gd3hjc3	237	17	be	be	VB
cord-326631-7gd3hjc3	237	18	bimodal	bimodal	JJ
cord-326631-7gd3hjc3	237	19	,	,	,
cord-326631-7gd3hjc3	237	20	such	such	JJ
cord-326631-7gd3hjc3	237	21	that	that	IN
cord-326631-7gd3hjc3	237	22	a	a	DT
cord-326631-7gd3hjc3	237	23	small	small	JJ
cord-326631-7gd3hjc3	237	24	proportion	proportion	NN
cord-326631-7gd3hjc3	237	25	of	of	IN
cord-326631-7gd3hjc3	237	26	individuals	individual	NNS
cord-326631-7gd3hjc3	237	27	are	be	VBP
cord-326631-7gd3hjc3	237	28	infectious	infectious	JJ
cord-326631-7gd3hjc3	237	29	much	much	RB
cord-326631-7gd3hjc3	237	30	longer	long	JJR
cord-326631-7gd3hjc3	237	31	than	than	IN
cord-326631-7gd3hjc3	237	32	average	average	JJ
cord-326631-7gd3hjc3	237	33	.	.	.
cord-326631-7gd3hjc3	238	1	This	this	DT
cord-326631-7gd3hjc3	238	2	situation	situation	NN
cord-326631-7gd3hjc3	238	3	is	be	VBZ
cord-326631-7gd3hjc3	238	4	already	already	RB
cord-326631-7gd3hjc3	238	5	covered	cover	VBN
cord-326631-7gd3hjc3	238	6	by	by	IN
cord-326631-7gd3hjc3	238	7	Theorem	Theorem	NNP
cord-326631-7gd3hjc3	238	8	7.1	7.1	CD
cord-326631-7gd3hjc3	238	9	,	,	,
cord-326631-7gd3hjc3	238	10	which	which	WDT
cord-326631-7gd3hjc3	238	11	deals	deal	VBZ
cord-326631-7gd3hjc3	238	12	with	with	IN
cord-326631-7gd3hjc3	238	13	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	238	14	distributions	distribution	NNS
cord-326631-7gd3hjc3	238	15	of	of	IN
cord-326631-7gd3hjc3	238	16	stage	stage	NN
cord-326631-7gd3hjc3	238	17	durations	duration	NNS
cord-326631-7gd3hjc3	238	18	.	.	.
cord-326631-7gd3hjc3	239	1	In	in	IN
cord-326631-7gd3hjc3	239	2	this	this	DT
cord-326631-7gd3hjc3	239	3	section	section	NN
cord-326631-7gd3hjc3	239	4	,	,	,
cord-326631-7gd3hjc3	239	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	239	6	consider	consider	VBP
cord-326631-7gd3hjc3	239	7	a	a	DT
cord-326631-7gd3hjc3	239	8	different	different	JJ
cord-326631-7gd3hjc3	239	9	type	type	NN
cord-326631-7gd3hjc3	239	10	of	of	IN
cord-326631-7gd3hjc3	239	11	generalization	generalization	NN
cord-326631-7gd3hjc3	239	12	of	of	IN
cord-326631-7gd3hjc3	239	13	the	the	DT
cord-326631-7gd3hjc3	239	14	SIR	SIR	NNP
cord-326631-7gd3hjc3	239	15	model	model	NN
cord-326631-7gd3hjc3	239	16	.	.	.
cord-326631-7gd3hjc3	240	1	In	in	IN
cord-326631-7gd3hjc3	240	2	all	all	DT
cord-326631-7gd3hjc3	240	3	of	of	IN
cord-326631-7gd3hjc3	240	4	the	the	DT
cord-326631-7gd3hjc3	240	5	models	model	NNS
cord-326631-7gd3hjc3	240	6	we	-PRON-	PRP
cord-326631-7gd3hjc3	240	7	have	have	VBP
cord-326631-7gd3hjc3	240	8	considered	consider	VBN
cord-326631-7gd3hjc3	240	9	thus	thus	RB
cord-326631-7gd3hjc3	240	10	far	far	RB
cord-326631-7gd3hjc3	240	11	,	,	,
cord-326631-7gd3hjc3	240	12	it	-PRON-	PRP
cord-326631-7gd3hjc3	240	13	has	have	VBZ
cord-326631-7gd3hjc3	240	14	been	be	VBN
cord-326631-7gd3hjc3	240	15	assumed	assume	VBN
cord-326631-7gd3hjc3	240	16	implicitly	implicitly	RB
cord-326631-7gd3hjc3	240	17	that	that	IN
cord-326631-7gd3hjc3	240	18	all	all	DT
cord-326631-7gd3hjc3	240	19	infectious	infectious	JJ
cord-326631-7gd3hjc3	240	20	individuals	individual	NNS
cord-326631-7gd3hjc3	240	21	have	have	VBP
cord-326631-7gd3hjc3	240	22	the	the	DT
cord-326631-7gd3hjc3	240	23	same	same	JJ
cord-326631-7gd3hjc3	240	24	transmission	transmission	NN
cord-326631-7gd3hjc3	240	25	rate	rate	NN
cord-326631-7gd3hjc3	240	26	.	.	.
cord-326631-7gd3hjc3	241	1	If	if	IN
cord-326631-7gd3hjc3	241	2	some	some	DT
cord-326631-7gd3hjc3	241	3	individuals	individual	NNS
cord-326631-7gd3hjc3	241	4	actually	actually	RB
cord-326631-7gd3hjc3	241	5	have	have	VBP
cord-326631-7gd3hjc3	241	6	a	a	DT
cord-326631-7gd3hjc3	241	7	much	much	RB
cord-326631-7gd3hjc3	241	8	higher	high	JJR
cord-326631-7gd3hjc3	241	9	than	than	IN
cord-326631-7gd3hjc3	241	10	average	average	JJ
cord-326631-7gd3hjc3	241	11	transmission	transmission	NN
cord-326631-7gd3hjc3	241	12	rate	rate	NN
cord-326631-7gd3hjc3	241	13	then	then	RB
cord-326631-7gd3hjc3	241	14	they	-PRON-	PRP
cord-326631-7gd3hjc3	241	15	will	will	MD
cord-326631-7gd3hjc3	241	16	be	be	VB
cord-326631-7gd3hjc3	241	17	super	super	JJ
cord-326631-7gd3hjc3	241	18	-	-	NNS
cord-326631-7gd3hjc3	241	19	spreaders	spreader	NNS
cord-326631-7gd3hjc3	241	20	.	.	.
cord-326631-7gd3hjc3	242	1	This	this	DT
cord-326631-7gd3hjc3	242	2	could	could	MD
cord-326631-7gd3hjc3	242	3	arise	arise	VB
cord-326631-7gd3hjc3	242	4	,	,	,
cord-326631-7gd3hjc3	242	5	for	for	IN
cord-326631-7gd3hjc3	242	6	example	example	NN
cord-326631-7gd3hjc3	242	7	,	,	,
cord-326631-7gd3hjc3	242	8	because	because	IN
cord-326631-7gd3hjc3	242	9	of	of	IN
cord-326631-7gd3hjc3	242	10	individual	individual	JJ
cord-326631-7gd3hjc3	242	11	variation	variation	NN
cord-326631-7gd3hjc3	242	12	in	in	IN
cord-326631-7gd3hjc3	242	13	viral	viral	JJ
cord-326631-7gd3hjc3	242	14	load	load	NN
cord-326631-7gd3hjc3	242	15	(	(	-LRB-
cord-326631-7gd3hjc3	242	16	reflecting	reflect	VBG
cord-326631-7gd3hjc3	242	17	variation	variation	NN
cord-326631-7gd3hjc3	242	18	in	in	IN
cord-326631-7gd3hjc3	242	19	immune	immune	JJ
cord-326631-7gd3hjc3	242	20	response	response	NN
cord-326631-7gd3hjc3	242	21	)	)	-RRB-
cord-326631-7gd3hjc3	242	22	or	or	CC
cord-326631-7gd3hjc3	242	23	as	as	IN
cord-326631-7gd3hjc3	242	24	the	the	DT
cord-326631-7gd3hjc3	242	25	result	result	NN
cord-326631-7gd3hjc3	242	26	of	of	IN
cord-326631-7gd3hjc3	242	27	chance	chance	NN
cord-326631-7gd3hjc3	242	28	occurence	occurence	NN
cord-326631-7gd3hjc3	242	29	of	of	IN
cord-326631-7gd3hjc3	242	30	environmental	environmental	JJ
cord-326631-7gd3hjc3	242	31	circumstances	circumstance	NNS
cord-326631-7gd3hjc3	242	32	that	that	WDT
cord-326631-7gd3hjc3	242	33	promote	promote	VBP
cord-326631-7gd3hjc3	242	34	disease	disease	NN
cord-326631-7gd3hjc3	242	35	spread	spread	VB
cord-326631-7gd3hjc3	242	36	(	(	-LRB-
cord-326631-7gd3hjc3	242	37	as	as	RB
cord-326631-7gd3hjc3	242	38	apparently	apparently	RB
cord-326631-7gd3hjc3	242	39	occurred	occur	VBD
cord-326631-7gd3hjc3	242	40	during	during	IN
cord-326631-7gd3hjc3	242	41	the	the	DT
cord-326631-7gd3hjc3	242	42	SARS	SARS	NNP
cord-326631-7gd3hjc3	242	43	epidemic	epidemic	NN
cord-326631-7gd3hjc3	242	44	(	(	-LRB-
cord-326631-7gd3hjc3	242	45	WHO	who	WP
cord-326631-7gd3hjc3	242	46	SARS	SARS	NNP
cord-326631-7gd3hjc3	242	47	Update	Update	NNP
cord-326631-7gd3hjc3	242	48	33	33	CD
cord-326631-7gd3hjc3	242	49	,	,	,
cord-326631-7gd3hjc3	242	50	2003	2003	CD
cord-326631-7gd3hjc3	242	51	)	)	-RRB-
cord-326631-7gd3hjc3	242	52	)	)	-RRB-
cord-326631-7gd3hjc3	242	53	.	.	.
cord-326631-7gd3hjc3	243	1	Whatever	whatever	WDT
cord-326631-7gd3hjc3	243	2	the	the	DT
cord-326631-7gd3hjc3	243	3	origin	origin	NN
cord-326631-7gd3hjc3	243	4	,	,	,
cord-326631-7gd3hjc3	243	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	243	6	focus	focus	VBP
cord-326631-7gd3hjc3	243	7	here	here	RB
cord-326631-7gd3hjc3	243	8	on	on	IN
cord-326631-7gd3hjc3	243	9	variation	variation	NN
cord-326631-7gd3hjc3	243	10	in	in	IN
cord-326631-7gd3hjc3	243	11	transmission	transmission	NN
cord-326631-7gd3hjc3	243	12	rate	rate	NN
cord-326631-7gd3hjc3	243	13	that	that	WDT
cord-326631-7gd3hjc3	243	14	is	be	VBZ
cord-326631-7gd3hjc3	243	15	manifested	manifest	VBN
cord-326631-7gd3hjc3	243	16	only	only	RB
cord-326631-7gd3hjc3	243	17	after	after	IN
cord-326631-7gd3hjc3	243	18	an	an	DT
cord-326631-7gd3hjc3	243	19	individual	individual	NN
cord-326631-7gd3hjc3	243	20	is	be	VBZ
cord-326631-7gd3hjc3	243	21	infected	infect	VBN
cord-326631-7gd3hjc3	243	22	.	.	.
cord-326631-7gd3hjc3	244	1	In	in	IN
cord-326631-7gd3hjc3	244	2	the	the	DT
cord-326631-7gd3hjc3	244	3	following	following	JJ
cord-326631-7gd3hjc3	244	4	sections	section	NNS
cord-326631-7gd3hjc3	244	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	244	6	consider	consider	VBP
cord-326631-7gd3hjc3	244	7	the	the	DT
cord-326631-7gd3hjc3	244	8	effects	effect	NNS
cord-326631-7gd3hjc3	244	9	of	of	IN
cord-326631-7gd3hjc3	244	10	intrinsic	intrinsic	JJ
cord-326631-7gd3hjc3	244	11	variation	variation	NN
cord-326631-7gd3hjc3	244	12	in	in	IN
cord-326631-7gd3hjc3	244	13	contact	contact	NN
cord-326631-7gd3hjc3	244	14	rates	rate	NNS
cord-326631-7gd3hjc3	244	15	among	among	IN
cord-326631-7gd3hjc3	244	16	individuals	individual	NNS
cord-326631-7gd3hjc3	244	17	,	,	,
cord-326631-7gd3hjc3	244	18	which	which	WDT
cord-326631-7gd3hjc3	244	19	results	result	VBZ
cord-326631-7gd3hjc3	244	20	from	from	IN
cord-326631-7gd3hjc3	244	21	inhomogeneous	inhomogeneous	JJ
cord-326631-7gd3hjc3	244	22	contact	contact	NN
cord-326631-7gd3hjc3	244	23	network	network	NN
cord-326631-7gd3hjc3	244	24	structure	structure	NN
cord-326631-7gd3hjc3	244	25	in	in	IN
cord-326631-7gd3hjc3	244	26	the	the	DT
cord-326631-7gd3hjc3	244	27	host	host	NN
cord-326631-7gd3hjc3	244	28	population	population	NN
cord-326631-7gd3hjc3	244	29	.	.	.
cord-326631-7gd3hjc3	245	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	245	2	now	now	RB
cord-326631-7gd3hjc3	245	3	proceed	proceed	VBP
cord-326631-7gd3hjc3	245	4	to	to	TO
cord-326631-7gd3hjc3	245	5	develop	develop	VB
cord-326631-7gd3hjc3	245	6	and	and	CC
cord-326631-7gd3hjc3	245	7	analyze	analyze	VB
cord-326631-7gd3hjc3	245	8	an	an	DT
cord-326631-7gd3hjc3	245	9	SIR	SIR	NNP
cord-326631-7gd3hjc3	245	10	model	model	NN
cord-326631-7gd3hjc3	245	11	with	with	IN
cord-326631-7gd3hjc3	245	12	a	a	DT
cord-326631-7gd3hjc3	245	13	distribution	distribution	NN
cord-326631-7gd3hjc3	245	14	of	of	IN
cord-326631-7gd3hjc3	245	15	transmission	transmission	NN
cord-326631-7gd3hjc3	245	16	rates	rate	NNS
cord-326631-7gd3hjc3	245	17	and	and	CC
cord-326631-7gd3hjc3	245	18	show	show	VBP
cord-326631-7gd3hjc3	245	19	that	that	IN
cord-326631-7gd3hjc3	245	20	the	the	DT
cord-326631-7gd3hjc3	245	21	usual	usual	JJ
cord-326631-7gd3hjc3	245	22	final	final	JJ
cord-326631-7gd3hjc3	245	23	size	size	NN
cord-326631-7gd3hjc3	245	24	formula	formula	NN
cord-326631-7gd3hjc3	245	25	(	(	-LRB-
cord-326631-7gd3hjc3	245	26	5	5	LS
cord-326631-7gd3hjc3	245	27	)	)	-RRB-
cord-326631-7gd3hjc3	245	28	applies	apply	VBZ
cord-326631-7gd3hjc3	245	29	.	.	.
cord-326631-7gd3hjc3	246	1	Extension	extension	NN
cord-326631-7gd3hjc3	246	2	of	of	IN
cord-326631-7gd3hjc3	246	3	our	-PRON-	PRP$
cord-326631-7gd3hjc3	246	4	results	result	NNS
cord-326631-7gd3hjc3	246	5	to	to	IN
cord-326631-7gd3hjc3	246	6	a	a	DT
cord-326631-7gd3hjc3	246	7	multiple	multiple	JJ
cord-326631-7gd3hjc3	246	8	stage	stage	NN
cord-326631-7gd3hjc3	246	9	SI	SI	NNP
cord-326631-7gd3hjc3	246	10	n	n	NNP
cord-326631-7gd3hjc3	246	11	R	r	NN
cord-326631-7gd3hjc3	246	12	model	model	NN
cord-326631-7gd3hjc3	246	13	is	be	VBZ
cord-326631-7gd3hjc3	246	14	straightfoward	straightfoward	JJ
cord-326631-7gd3hjc3	246	15	and	and	CC
cord-326631-7gd3hjc3	246	16	similar	similar	JJ
cord-326631-7gd3hjc3	246	17	to	to	IN
cord-326631-7gd3hjc3	246	18	the	the	DT
cord-326631-7gd3hjc3	246	19	way	way	NN
cord-326631-7gd3hjc3	246	20	we	-PRON-	PRP
cord-326631-7gd3hjc3	246	21	generalized	generalize	VBD
cord-326631-7gd3hjc3	246	22	our	-PRON-	PRP$
cord-326631-7gd3hjc3	246	23	results	result	NNS
cord-326631-7gd3hjc3	246	24	for	for	IN
cord-326631-7gd3hjc3	246	25	the	the	DT
cord-326631-7gd3hjc3	246	26	SIR	SIR	NNP
cord-326631-7gd3hjc3	246	27	with	with	IN
cord-326631-7gd3hjc3	246	28	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	246	29	infectious	infectious	JJ
cord-326631-7gd3hjc3	246	30	period	period	NN
cord-326631-7gd3hjc3	246	31	distribution	distribution	NN
cord-326631-7gd3hjc3	246	32	to	to	IN
cord-326631-7gd3hjc3	246	33	an	an	DT
cord-326631-7gd3hjc3	246	34	SI	si	NN
cord-326631-7gd3hjc3	246	35	n	n	NN
cord-326631-7gd3hjc3	246	36	R	r	NN
cord-326631-7gd3hjc3	246	37	model	model	NN
cord-326631-7gd3hjc3	246	38	with	with	IN
cord-326631-7gd3hjc3	246	39	arbitrary	arbitrary	JJ
cord-326631-7gd3hjc3	246	40	stage	stage	NN
cord-326631-7gd3hjc3	246	41	duration	duration	NN
cord-326631-7gd3hjc3	246	42	distributions	distribution	NNS
cord-326631-7gd3hjc3	246	43	.	.	.
cord-326631-7gd3hjc3	247	1	Let	let	VB
cord-326631-7gd3hjc3	247	2	I(β	I(β	NNP
cord-326631-7gd3hjc3	247	3	,	,	,
cord-326631-7gd3hjc3	247	4	t	t	NN
cord-326631-7gd3hjc3	247	5	)	)	-RRB-
cord-326631-7gd3hjc3	247	6	be	be	VB
cord-326631-7gd3hjc3	247	7	the	the	DT
cord-326631-7gd3hjc3	247	8	distribution	distribution	NN
cord-326631-7gd3hjc3	247	9	(	(	-LRB-
cord-326631-7gd3hjc3	247	10	at	at	IN
cord-326631-7gd3hjc3	247	11	time	time	NN
cord-326631-7gd3hjc3	247	12	t	t	NNP
cord-326631-7gd3hjc3	247	13	)	)	-RRB-
cord-326631-7gd3hjc3	247	14	of	of	IN
cord-326631-7gd3hjc3	247	15	infectious	infectious	JJ
cord-326631-7gd3hjc3	247	16	individuals	individual	NNS
cord-326631-7gd3hjc3	247	17	that	that	WDT
cord-326631-7gd3hjc3	247	18	have	have	VBP
cord-326631-7gd3hjc3	247	19	transmission	transmission	NN
cord-326631-7gd3hjc3	247	20	rate	rate	NN
cord-326631-7gd3hjc3	247	21	β	β	NN
cord-326631-7gd3hjc3	247	22	.	.	.
cord-326631-7gd3hjc3	248	1	Note	note	VB
cord-326631-7gd3hjc3	248	2	that	that	IN
cord-326631-7gd3hjc3	248	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	248	4	assume	assume	VBP
cord-326631-7gd3hjc3	248	5	implicitly	implicitly	RB
cord-326631-7gd3hjc3	248	6	that	that	IN
cord-326631-7gd3hjc3	248	7	a	a	DT
cord-326631-7gd3hjc3	248	8	given	give	VBN
cord-326631-7gd3hjc3	248	9	individual	individual	NN
cord-326631-7gd3hjc3	248	10	retains	retain	VBZ
cord-326631-7gd3hjc3	248	11	the	the	DT
cord-326631-7gd3hjc3	248	12	same	same	JJ
cord-326631-7gd3hjc3	248	13	transmission	transmission	NN
cord-326631-7gd3hjc3	248	14	rate	rate	NN
cord-326631-7gd3hjc3	248	15	throughout	throughout	IN
cord-326631-7gd3hjc3	248	16	his	-PRON-	PRP$
cord-326631-7gd3hjc3	248	17	/	/	SYM
cord-326631-7gd3hjc3	248	18	her	-PRON-	PRP$
cord-326631-7gd3hjc3	248	19	infectious	infectious	JJ
cord-326631-7gd3hjc3	248	20	period	period	NN
cord-326631-7gd3hjc3	248	21	,	,	,
cord-326631-7gd3hjc3	248	22	and	and	CC
cord-326631-7gd3hjc3	248	23	hence	hence	RB
cord-326631-7gd3hjc3	248	24	that	that	IN
cord-326631-7gd3hjc3	248	25	this	this	DT
cord-326631-7gd3hjc3	248	26	transmission	transmission	NN
cord-326631-7gd3hjc3	248	27	rate	rate	NN
cord-326631-7gd3hjc3	248	28	is	be	VBZ
cord-326631-7gd3hjc3	248	29	determined	determine	VBN
cord-326631-7gd3hjc3	248	30	as	as	RB
cord-326631-7gd3hjc3	248	31	soon	soon	RB
cord-326631-7gd3hjc3	248	32	as	as	IN
cord-326631-7gd3hjc3	248	33	infection	infection	NN
cord-326631-7gd3hjc3	248	34	occurs	occur	VBZ
cord-326631-7gd3hjc3	248	35	.	.	.
cord-326631-7gd3hjc3	249	1	Let	let	VB
cord-326631-7gd3hjc3	249	2	q(β	q(β	NNP
cord-326631-7gd3hjc3	249	3	)	)	-RRB-
cord-326631-7gd3hjc3	249	4	be	be	VB
cord-326631-7gd3hjc3	249	5	the	the	DT
cord-326631-7gd3hjc3	249	6	probability	probability	NN
cord-326631-7gd3hjc3	249	7	that	that	IN
cord-326631-7gd3hjc3	249	8	a	a	DT
cord-326631-7gd3hjc3	249	9	newly	newly	RB
cord-326631-7gd3hjc3	249	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	249	11	individual	individual	NN
cord-326631-7gd3hjc3	249	12	has	have	VBZ
cord-326631-7gd3hjc3	249	13	transmission	transmission	NN
cord-326631-7gd3hjc3	249	14	rate	rate	NN
cord-326631-7gd3hjc3	249	15	β	β	NN
cord-326631-7gd3hjc3	249	16	.	.	.
cord-326631-7gd3hjc3	250	1	Thus	thus	RB
cord-326631-7gd3hjc3	250	2	,	,	,
cord-326631-7gd3hjc3	250	3	the	the	DT
cord-326631-7gd3hjc3	250	4	mean	mean	JJ
cord-326631-7gd3hjc3	250	5	transmission	transmission	NN
cord-326631-7gd3hjc3	250	6	rate	rate	NN
cord-326631-7gd3hjc3	250	7	is	be	VBZ
cord-326631-7gd3hjc3	250	8	The	the	DT
cord-326631-7gd3hjc3	250	9	rate	rate	NN
cord-326631-7gd3hjc3	250	10	of	of	IN
cord-326631-7gd3hjc3	250	11	change	change	NN
cord-326631-7gd3hjc3	250	12	of	of	IN
cord-326631-7gd3hjc3	250	13	the	the	DT
cord-326631-7gd3hjc3	250	14	proportion	proportion	NN
cord-326631-7gd3hjc3	250	15	of	of	IN
cord-326631-7gd3hjc3	250	16	the	the	DT
cord-326631-7gd3hjc3	250	17	population	population	NN
cord-326631-7gd3hjc3	250	18	that	that	WDT
cord-326631-7gd3hjc3	250	19	is	be	VBZ
cord-326631-7gd3hjc3	250	20	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	250	21	iṡ	iṡ	RB
cord-326631-7gd3hjc3	251	1	Upon	upon	IN
cord-326631-7gd3hjc3	251	2	infection	infection	NN
cord-326631-7gd3hjc3	251	3	,	,	,
cord-326631-7gd3hjc3	251	4	individuals	individual	NNS
cord-326631-7gd3hjc3	251	5	leave	leave	VBP
cord-326631-7gd3hjc3	251	6	the	the	DT
cord-326631-7gd3hjc3	251	7	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	251	8	class	class	NN
cord-326631-7gd3hjc3	251	9	S	s	NN
cord-326631-7gd3hjc3	251	10	and	and	CC
cord-326631-7gd3hjc3	251	11	enter	enter	VB
cord-326631-7gd3hjc3	251	12	the	the	DT
cord-326631-7gd3hjc3	251	13	infectious	infectious	JJ
cord-326631-7gd3hjc3	251	14	class	class	NN
cord-326631-7gd3hjc3	251	15	I	i	NN
cord-326631-7gd3hjc3	251	16	,	,	,
cord-326631-7gd3hjc3	251	17	a	a	DT
cord-326631-7gd3hjc3	251	18	proportion	proportion	NN
cord-326631-7gd3hjc3	251	19	q(β	q(β	NNP
cord-326631-7gd3hjc3	251	20	)	)	-RRB-
cord-326631-7gd3hjc3	251	21	of	of	IN
cord-326631-7gd3hjc3	251	22	them	-PRON-	PRP
cord-326631-7gd3hjc3	251	23	having	have	VBG
cord-326631-7gd3hjc3	251	24	a	a	DT
cord-326631-7gd3hjc3	251	25	transmission	transmission	NN
cord-326631-7gd3hjc3	251	26	rate	rate	NN
cord-326631-7gd3hjc3	251	27	β	β	NN
cord-326631-7gd3hjc3	251	28	.	.	.
cord-326631-7gd3hjc3	252	1	Upon	upon	IN
cord-326631-7gd3hjc3	252	2	recovery	recovery	NN
cord-326631-7gd3hjc3	252	3	,	,	,
cord-326631-7gd3hjc3	252	4	they	-PRON-	PRP
cord-326631-7gd3hjc3	252	5	leave	leave	VBP
cord-326631-7gd3hjc3	252	6	the	the	DT
cord-326631-7gd3hjc3	252	7	infectious	infectious	JJ
cord-326631-7gd3hjc3	252	8	class	class	NN
cord-326631-7gd3hjc3	252	9	at	at	IN
cord-326631-7gd3hjc3	252	10	rate	rate	NN
cord-326631-7gd3hjc3	252	11	γ	γ	NN
cord-326631-7gd3hjc3	252	12	.	.	.
cord-326631-7gd3hjc3	253	1	Thus	thus	RB
cord-326631-7gd3hjc3	253	2	,	,	,
cord-326631-7gd3hjc3	253	3	In	in	IN
cord-326631-7gd3hjc3	253	4	order	order	NN
cord-326631-7gd3hjc3	253	5	to	to	TO
cord-326631-7gd3hjc3	253	6	ensure	ensure	VB
cord-326631-7gd3hjc3	253	7	that	that	IN
cord-326631-7gd3hjc3	253	8	the	the	DT
cord-326631-7gd3hjc3	253	9	model	model	NN
cord-326631-7gd3hjc3	253	10	is	be	VBZ
cord-326631-7gd3hjc3	253	11	well	well	RB
cord-326631-7gd3hjc3	253	12	posed	pose	VBN
cord-326631-7gd3hjc3	253	13	,	,	,
cord-326631-7gd3hjc3	253	14	we	-PRON-	PRP
cord-326631-7gd3hjc3	253	15	must	must	MD
cord-326631-7gd3hjc3	253	16	establish	establish	VB
cord-326631-7gd3hjc3	253	17	that	that	IN
cord-326631-7gd3hjc3	253	18	if	if	IN
cord-326631-7gd3hjc3	253	19	I(β	I(β	NNP
cord-326631-7gd3hjc3	253	20	,	,	,
cord-326631-7gd3hjc3	253	21	0	0	CD
cord-326631-7gd3hjc3	253	22	)	)	-RRB-
cord-326631-7gd3hjc3	253	23	>	>	XX
cord-326631-7gd3hjc3	253	24	0	0	NFP
cord-326631-7gd3hjc3	254	1	then	then	RB
cord-326631-7gd3hjc3	254	2	I(β	I(β	NNP
cord-326631-7gd3hjc3	254	3	,	,	,
cord-326631-7gd3hjc3	254	4	t	t	NN
cord-326631-7gd3hjc3	254	5	)	)	-RRB-
cord-326631-7gd3hjc3	254	6	>	>	NFP
cord-326631-7gd3hjc3	254	7	0	0	NFP
cord-326631-7gd3hjc3	254	8	for	for	IN
cord-326631-7gd3hjc3	254	9	all	all	DT
cord-326631-7gd3hjc3	254	10	time	time	NN
cord-326631-7gd3hjc3	254	11	.	.	.
cord-326631-7gd3hjc3	255	1	Suppose	suppose	VB
cord-326631-7gd3hjc3	255	2	this	this	DT
cord-326631-7gd3hjc3	255	3	is	be	VBZ
cord-326631-7gd3hjc3	255	4	not	not	RB
cord-326631-7gd3hjc3	255	5	true	true	JJ
cord-326631-7gd3hjc3	255	6	.	.	.
cord-326631-7gd3hjc3	256	1	Then	then	RB
cord-326631-7gd3hjc3	256	2	there	there	EX
cord-326631-7gd3hjc3	256	3	existsβ	existsβ	NNS
cord-326631-7gd3hjc3	256	4	and	and	CC
cord-326631-7gd3hjc3	256	5	T	t	NN
cord-326631-7gd3hjc3	256	6	such	such	JJ
cord-326631-7gd3hjc3	256	7	that	that	DT
cord-326631-7gd3hjc3	257	1	∞	∞	NNP
cord-326631-7gd3hjc3	257	2	0	0	CD
cord-326631-7gd3hjc3	257	3	I(β	I(β	NNP
cord-326631-7gd3hjc3	257	4	,	,	,
cord-326631-7gd3hjc3	257	5	T	T	NNP
cord-326631-7gd3hjc3	257	6	)	)	-RRB-
cord-326631-7gd3hjc3	257	7	dβ	dβ	XX
cord-326631-7gd3hjc3	257	8	>	>	XX
cord-326631-7gd3hjc3	257	9	0	0	CD
cord-326631-7gd3hjc3	257	10	,	,	,
cord-326631-7gd3hjc3	257	11	I(β	I(β	NNP
cord-326631-7gd3hjc3	257	12	,	,	,
cord-326631-7gd3hjc3	257	13	t	t	NN
cord-326631-7gd3hjc3	257	14	)	)	-RRB-
cord-326631-7gd3hjc3	257	15	>	>	NFP
cord-326631-7gd3hjc3	257	16	0	0	CD
cord-326631-7gd3hjc3	257	17	for	for	IN
cord-326631-7gd3hjc3	257	18	t	t	NN
cord-326631-7gd3hjc3	257	19	<	<	XX
cord-326631-7gd3hjc3	257	20	T	T	NNP
cord-326631-7gd3hjc3	257	21	,	,	,
cord-326631-7gd3hjc3	257	22	but	but	CC
cord-326631-7gd3hjc3	257	23	I(β	I(β	NNP
cord-326631-7gd3hjc3	257	24	,	,	,
cord-326631-7gd3hjc3	257	25	T	T	NNP
cord-326631-7gd3hjc3	257	26	)	)	-RRB-
cord-326631-7gd3hjc3	257	27	=	=	SYM
cord-326631-7gd3hjc3	257	28	0	0	CD
cord-326631-7gd3hjc3	257	29	.	.	.
cord-326631-7gd3hjc3	258	1	Substituting	substitute	VBG
cord-326631-7gd3hjc3	258	2	these	these	DT
cord-326631-7gd3hjc3	258	3	conditions	condition	NNS
cord-326631-7gd3hjc3	258	4	into	into	IN
cord-326631-7gd3hjc3	258	5	Eq	Eq	NNP
cord-326631-7gd3hjc3	258	6	.	.	.
cord-326631-7gd3hjc3	259	1	(	(	-LRB-
cord-326631-7gd3hjc3	259	2	21b	21b	NNS
cord-326631-7gd3hjc3	259	3	)	)	-RRB-
cord-326631-7gd3hjc3	259	4	,	,	,
cord-326631-7gd3hjc3	259	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	259	6	obtainİ(β	obtaini̇(β	VBP
cord-326631-7gd3hjc3	259	7	,	,	,
cord-326631-7gd3hjc3	259	8	T	T	NNP
cord-326631-7gd3hjc3	259	9	)	)	-RRB-
cord-326631-7gd3hjc3	259	10	>	>	XX
cord-326631-7gd3hjc3	260	1	0	0	NFP
cord-326631-7gd3hjc3	260	2	.	.	.
cord-326631-7gd3hjc3	261	1	But	but	CC
cord-326631-7gd3hjc3	261	2	this	this	DT
cord-326631-7gd3hjc3	261	3	contradicts	contradict	VBZ
cord-326631-7gd3hjc3	261	4	the	the	DT
cord-326631-7gd3hjc3	261	5	hypothesis	hypothesis	NN
cord-326631-7gd3hjc3	261	6	that	that	IN
cord-326631-7gd3hjc3	261	7	I(β	I(β	NNP
cord-326631-7gd3hjc3	261	8	,	,	,
cord-326631-7gd3hjc3	261	9	t	t	NN
cord-326631-7gd3hjc3	261	10	)	)	-RRB-
cord-326631-7gd3hjc3	261	11	decreases	decrease	VBZ
cord-326631-7gd3hjc3	261	12	from	from	IN
cord-326631-7gd3hjc3	261	13	I(β	I(β	NNP
cord-326631-7gd3hjc3	261	14	,	,	,
cord-326631-7gd3hjc3	261	15	0	0	CD
cord-326631-7gd3hjc3	261	16	)	)	-RRB-
cord-326631-7gd3hjc3	261	17	>	>	XX
cord-326631-7gd3hjc3	262	1	0	0	CD
cord-326631-7gd3hjc3	262	2	to	to	IN
cord-326631-7gd3hjc3	262	3	I(β	I(β	NNP
cord-326631-7gd3hjc3	262	4	,	,	,
cord-326631-7gd3hjc3	262	5	T	T	NNP
cord-326631-7gd3hjc3	262	6	)	)	-RRB-
cord-326631-7gd3hjc3	263	1	=	=	SYM
cord-326631-7gd3hjc3	263	2	0	0	NFP
cord-326631-7gd3hjc3	263	3	.	.	.
cord-326631-7gd3hjc3	264	1	Hence	hence	RB
cord-326631-7gd3hjc3	264	2	I(β	I(β	NNP
cord-326631-7gd3hjc3	264	3	,	,	,
cord-326631-7gd3hjc3	264	4	t	t	NN
cord-326631-7gd3hjc3	264	5	)	)	-RRB-
cord-326631-7gd3hjc3	264	6	>	>	XX
cord-326631-7gd3hjc3	265	1	0	0	NFP
cord-326631-7gd3hjc3	265	2	for	for	IN
cord-326631-7gd3hjc3	265	3	all	all	DT
cord-326631-7gd3hjc3	265	4	t	t	NN
cord-326631-7gd3hjc3	265	5	≥	≥	CD
cord-326631-7gd3hjc3	265	6	0	0	CD
cord-326631-7gd3hjc3	265	7	.	.	.
cord-326631-7gd3hjc3	266	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	266	2	now	now	RB
cord-326631-7gd3hjc3	266	3	check	check	VBP
cord-326631-7gd3hjc3	266	4	that	that	IN
cord-326631-7gd3hjc3	266	5	the	the	DT
cord-326631-7gd3hjc3	266	6	disease	disease	NN
cord-326631-7gd3hjc3	266	7	will	will	MD
cord-326631-7gd3hjc3	266	8	always	always	RB
cord-326631-7gd3hjc3	266	9	burn	burn	VB
cord-326631-7gd3hjc3	266	10	out	out	RP
cord-326631-7gd3hjc3	266	11	in	in	IN
cord-326631-7gd3hjc3	266	12	this	this	DT
cord-326631-7gd3hjc3	266	13	model	model	NN
cord-326631-7gd3hjc3	266	14	,	,	,
cord-326631-7gd3hjc3	266	15	as	as	IN
cord-326631-7gd3hjc3	266	16	expected	expect	VBN
cord-326631-7gd3hjc3	266	17	.	.	.
cord-326631-7gd3hjc3	267	1	which	which	WDT
cord-326631-7gd3hjc3	267	2	is	be	VBZ
cord-326631-7gd3hjc3	267	3	strictly	strictly	RB
cord-326631-7gd3hjc3	267	4	negative	negative	JJ
cord-326631-7gd3hjc3	267	5	.	.	.
cord-326631-7gd3hjc3	268	1	Hence	hence	RB
cord-326631-7gd3hjc3	268	2	,	,	,
cord-326631-7gd3hjc3	268	3	S	S	NNP
cord-326631-7gd3hjc3	269	1	+	+	CC
cord-326631-7gd3hjc3	269	2	I	-PRON-	PRP
cord-326631-7gd3hjc3	269	3	tot	tot	VBP
cord-326631-7gd3hjc3	269	4	is	be	VBZ
cord-326631-7gd3hjc3	269	5	decreasing	decrease	VBG
cord-326631-7gd3hjc3	269	6	and	and	CC
cord-326631-7gd3hjc3	269	7	bounded	bound	VBN
cord-326631-7gd3hjc3	269	8	below	below	RB
cord-326631-7gd3hjc3	269	9	by	by	IN
cord-326631-7gd3hjc3	269	10	zero	zero	CD
cord-326631-7gd3hjc3	269	11	.	.	.
cord-326631-7gd3hjc3	270	1	Hence	hence	RB
cord-326631-7gd3hjc3	270	2	lim	lim	NNP
cord-326631-7gd3hjc3	270	3	t→∞	t→∞	NNP
cord-326631-7gd3hjc3	270	4	d	d	NNP
cord-326631-7gd3hjc3	270	5	dt	dt	NNP
cord-326631-7gd3hjc3	270	6	(	(	-LRB-
cord-326631-7gd3hjc3	270	7	S	S	NNP
cord-326631-7gd3hjc3	271	1	+	+	CC
cord-326631-7gd3hjc3	272	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	272	2	tot	tot	VBP
cord-326631-7gd3hjc3	272	3	)	)	-RRB-
cord-326631-7gd3hjc3	273	1	=	=	SYM
cord-326631-7gd3hjc3	273	2	0	0	CD
cord-326631-7gd3hjc3	273	3	,	,	,
cord-326631-7gd3hjc3	273	4	i.e.	i.e.	FW
cord-326631-7gd3hjc3	273	5	,	,	,
cord-326631-7gd3hjc3	273	6	I	-PRON-	PRP
cord-326631-7gd3hjc3	273	7	tot	tot	VBP
cord-326631-7gd3hjc3	273	8	(	(	-LRB-
cord-326631-7gd3hjc3	273	9	∞	∞	NNP
cord-326631-7gd3hjc3	273	10	)	)	-RRB-
cord-326631-7gd3hjc3	273	11	=	=	SYM
cord-326631-7gd3hjc3	273	12	0	0	CD
cord-326631-7gd3hjc3	273	13	.	.	.
cord-326631-7gd3hjc3	274	1	For	for	IN
cord-326631-7gd3hjc3	274	2	the	the	DT
cord-326631-7gd3hjc3	274	3	model	model	NN
cord-326631-7gd3hjc3	274	4	specified	specify	VBN
cord-326631-7gd3hjc3	274	5	by	by	IN
cord-326631-7gd3hjc3	274	6	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	274	7	.	.	.
cord-326631-7gd3hjc3	275	1	(	(	-LRB-
cord-326631-7gd3hjc3	275	2	21	21	CD
cord-326631-7gd3hjc3	275	3	)	)	-RRB-
cord-326631-7gd3hjc3	275	4	,	,	,
cord-326631-7gd3hjc3	275	5	the	the	DT
cord-326631-7gd3hjc3	275	6	basic	basic	JJ
cord-326631-7gd3hjc3	275	7	reproduction	reproduction	NN
cord-326631-7gd3hjc3	275	8	number	number	NN
cord-326631-7gd3hjc3	275	9	is	be	VBZ
cord-326631-7gd3hjc3	275	10	In	in	IN
cord-326631-7gd3hjc3	275	11	Appendix	Appendix	NNP
cord-326631-7gd3hjc3	275	12	B	B	NNP
cord-326631-7gd3hjc3	275	13	,	,	,
cord-326631-7gd3hjc3	275	14	we	-PRON-	PRP
cord-326631-7gd3hjc3	275	15	prove	prove	VBP
cord-326631-7gd3hjc3	275	16	that	that	IN
cord-326631-7gd3hjc3	275	17	the	the	DT
cord-326631-7gd3hjc3	275	18	disease	disease	NN
cord-326631-7gd3hjc3	275	19	free	free	JJ
cord-326631-7gd3hjc3	275	20	equilibrium	equilibrium	NN
cord-326631-7gd3hjc3	275	21	(	(	-LRB-
cord-326631-7gd3hjc3	275	22	DFE	DFE	NNP
cord-326631-7gd3hjc3	275	23	)	)	-RRB-
cord-326631-7gd3hjc3	275	24	is	be	VBZ
cord-326631-7gd3hjc3	275	25	unstable	unstable	JJ
cord-326631-7gd3hjc3	276	1	if	if	IN
cord-326631-7gd3hjc3	276	2	and	and	CC
cord-326631-7gd3hjc3	276	3	only	only	RB
cord-326631-7gd3hjc3	276	4	if	if	IN
cord-326631-7gd3hjc3	276	5	R	r	NN
cord-326631-7gd3hjc3	276	6	0	0	CD
cord-326631-7gd3hjc3	276	7	>	>	SYM
cord-326631-7gd3hjc3	276	8	1	1	CD
cord-326631-7gd3hjc3	276	9	.	.	.
cord-326631-7gd3hjc3	277	1	To	to	TO
cord-326631-7gd3hjc3	277	2	find	find	VB
cord-326631-7gd3hjc3	277	3	the	the	DT
cord-326631-7gd3hjc3	277	4	final	final	JJ
cord-326631-7gd3hjc3	277	5	size	size	NN
cord-326631-7gd3hjc3	277	6	,	,	,
cord-326631-7gd3hjc3	277	7	we	-PRON-	PRP
cord-326631-7gd3hjc3	277	8	divide	divide	VBP
cord-326631-7gd3hjc3	277	9	by	by	IN
cord-326631-7gd3hjc3	277	10	S	S	NNP
cord-326631-7gd3hjc3	277	11	on	on	IN
cord-326631-7gd3hjc3	277	12	both	both	DT
cord-326631-7gd3hjc3	277	13	sides	side	NNS
cord-326631-7gd3hjc3	277	14	of	of	IN
cord-326631-7gd3hjc3	277	15	(	(	-LRB-
cord-326631-7gd3hjc3	277	16	21a	21a	NNS
cord-326631-7gd3hjc3	277	17	)	)	-RRB-
cord-326631-7gd3hjc3	277	18	and	and	CC
cord-326631-7gd3hjc3	277	19	integrate	integrate	VB
cord-326631-7gd3hjc3	277	20	,	,	,
cord-326631-7gd3hjc3	277	21	Substituting	substitute	VBG
cord-326631-7gd3hjc3	277	22	Eq	Eq	NNP
cord-326631-7gd3hjc3	277	23	.	.	.
cord-326631-7gd3hjc3	278	1	(	(	-LRB-
cord-326631-7gd3hjc3	278	2	21a	21a	NNS
cord-326631-7gd3hjc3	278	3	)	)	-RRB-
cord-326631-7gd3hjc3	278	4	in	in	IN
cord-326631-7gd3hjc3	278	5	Eq	Eq	NNP
cord-326631-7gd3hjc3	278	6	.	.	.
cord-326631-7gd3hjc3	279	1	(	(	-LRB-
cord-326631-7gd3hjc3	279	2	21b	21b	NNS
cord-326631-7gd3hjc3	279	3	)	)	-RRB-
cord-326631-7gd3hjc3	279	4	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	5	can	can	MD
cord-326631-7gd3hjc3	279	6	writė	writė	VB
cord-326631-7gd3hjc3	279	7	Integrating	integrate	VBG
cord-326631-7gd3hjc3	279	8	this	this	DT
cord-326631-7gd3hjc3	279	9	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	10	obtain	obtain	VBP
cord-326631-7gd3hjc3	279	11	Since	since	IN
cord-326631-7gd3hjc3	279	12	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	13	have	have	VBP
cord-326631-7gd3hjc3	279	14	established	establish	VBN
cord-326631-7gd3hjc3	279	15	that	that	IN
cord-326631-7gd3hjc3	279	16	I(β	I(β	NNP
cord-326631-7gd3hjc3	279	17	,	,	,
cord-326631-7gd3hjc3	279	18	∞	∞	NNP
cord-326631-7gd3hjc3	279	19	)	)	-RRB-
cord-326631-7gd3hjc3	279	20	=	=	SYM
cord-326631-7gd3hjc3	279	21	0	0	NFP
cord-326631-7gd3hjc3	279	22	,	,	,
cord-326631-7gd3hjc3	279	23	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	24	can	can	MD
cord-326631-7gd3hjc3	279	25	write	write	VB
cord-326631-7gd3hjc3	279	26	Substituting	substitute	VBG
cord-326631-7gd3hjc3	279	27	(	(	-LRB-
cord-326631-7gd3hjc3	279	28	25	25	CD
cord-326631-7gd3hjc3	279	29	)	)	-RRB-
cord-326631-7gd3hjc3	279	30	into	into	IN
cord-326631-7gd3hjc3	279	31	(	(	-LRB-
cord-326631-7gd3hjc3	279	32	24	24	CD
cord-326631-7gd3hjc3	279	33	)	)	-RRB-
cord-326631-7gd3hjc3	279	34	and	and	CC
cord-326631-7gd3hjc3	279	35	using	use	VBG
cord-326631-7gd3hjc3	279	36	(	(	-LRB-
cord-326631-7gd3hjc3	279	37	23	23	CD
cord-326631-7gd3hjc3	279	38	)	)	-RRB-
cord-326631-7gd3hjc3	279	39	,	,	,
cord-326631-7gd3hjc3	279	40	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	41	obtain	obtain	VBP
cord-326631-7gd3hjc3	279	42	Hence	hence	RB
cord-326631-7gd3hjc3	279	43	,	,	,
cord-326631-7gd3hjc3	279	44	since	since	IN
cord-326631-7gd3hjc3	279	45	the	the	DT
cord-326631-7gd3hjc3	279	46	final	final	JJ
cord-326631-7gd3hjc3	279	47	size	size	NN
cord-326631-7gd3hjc3	279	48	Z	z	NN
cord-326631-7gd3hjc3	279	49	=	=	NN
cord-326631-7gd3hjc3	279	50	S(0	S(0	NNP
cord-326631-7gd3hjc3	279	51	)	)	-RRB-
cord-326631-7gd3hjc3	279	52	−	−	NNP
cord-326631-7gd3hjc3	279	53	S(∞	S(∞	NNP
cord-326631-7gd3hjc3	279	54	)	)	-RRB-
cord-326631-7gd3hjc3	279	55	,	,	,
cord-326631-7gd3hjc3	279	56	we	-PRON-	PRP
cord-326631-7gd3hjc3	279	57	have	have	VBP
cord-326631-7gd3hjc3	279	58	It	-PRON-	PRP
cord-326631-7gd3hjc3	279	59	is	be	VBZ
cord-326631-7gd3hjc3	279	60	possible	possible	JJ
cord-326631-7gd3hjc3	279	61	to	to	TO
cord-326631-7gd3hjc3	279	62	generalize	generalize	VB
cord-326631-7gd3hjc3	279	63	this	this	DT
cord-326631-7gd3hjc3	279	64	theorem	theorem	NN
cord-326631-7gd3hjc3	279	65	for	for	IN
cord-326631-7gd3hjc3	279	66	an	an	DT
cord-326631-7gd3hjc3	279	67	SI	SI	NNP
cord-326631-7gd3hjc3	279	68	n	n	NN
cord-326631-7gd3hjc3	279	69	R	r	NN
cord-326631-7gd3hjc3	279	70	model	model	NN
cord-326631-7gd3hjc3	279	71	with	with	IN
cord-326631-7gd3hjc3	279	72	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	279	73	distributed	distribute	VBN
cord-326631-7gd3hjc3	279	74	stage	stage	NN
cord-326631-7gd3hjc3	279	75	durations	duration	NNS
cord-326631-7gd3hjc3	279	76	and	and	CC
cord-326631-7gd3hjc3	279	77	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	279	78	distributed	distribute	VBN
cord-326631-7gd3hjc3	279	79	transmission	transmission	NN
cord-326631-7gd3hjc3	279	80	rates	rate	NNS
cord-326631-7gd3hjc3	279	81	in	in	IN
cord-326631-7gd3hjc3	279	82	each	each	DT
cord-326631-7gd3hjc3	279	83	stage	stage	NN
cord-326631-7gd3hjc3	279	84	.	.	.
cord-326631-7gd3hjc3	280	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	280	2	do	do	VBP
cord-326631-7gd3hjc3	280	3	not	not	RB
cord-326631-7gd3hjc3	280	4	go	go	VB
cord-326631-7gd3hjc3	280	5	through	through	IN
cord-326631-7gd3hjc3	280	6	the	the	DT
cord-326631-7gd3hjc3	280	7	details	detail	NNS
cord-326631-7gd3hjc3	280	8	because	because	IN
cord-326631-7gd3hjc3	280	9	no	no	DT
cord-326631-7gd3hjc3	280	10	new	new	JJ
cord-326631-7gd3hjc3	280	11	ideas	idea	NNS
cord-326631-7gd3hjc3	280	12	are	be	VBP
cord-326631-7gd3hjc3	280	13	required	require	VBN
cord-326631-7gd3hjc3	280	14	.	.	.
cord-326631-7gd3hjc3	281	1	With	with	IN
cord-326631-7gd3hjc3	281	2	Theorems	Theorems	NNPS
cord-326631-7gd3hjc3	281	3	7.1	7.1	CD
cord-326631-7gd3hjc3	281	4	and	and	CC
cord-326631-7gd3hjc3	281	5	8.1	8.1	CD
cord-326631-7gd3hjc3	281	6	in	in	IN
cord-326631-7gd3hjc3	281	7	hand	hand	NN
cord-326631-7gd3hjc3	281	8	,	,	,
cord-326631-7gd3hjc3	281	9	the	the	DT
cord-326631-7gd3hjc3	281	10	extra	extra	JJ
cord-326631-7gd3hjc3	281	11	effort	effort	NN
cord-326631-7gd3hjc3	281	12	required	require	VBN
cord-326631-7gd3hjc3	281	13	for	for	IN
cord-326631-7gd3hjc3	281	14	the	the	DT
cord-326631-7gd3hjc3	281	15	generalization	generalization	NN
cord-326631-7gd3hjc3	281	16	is	be	VBZ
cord-326631-7gd3hjc3	281	17	merely	merely	RB
cord-326631-7gd3hjc3	281	18	one	one	CD
cord-326631-7gd3hjc3	281	19	of	of	IN
cord-326631-7gd3hjc3	281	20	keeping	keep	VBG
cord-326631-7gd3hjc3	281	21	track	track	NN
cord-326631-7gd3hjc3	281	22	of	of	IN
cord-326631-7gd3hjc3	281	23	notation	notation	NN
cord-326631-7gd3hjc3	281	24	.	.	.
cord-326631-7gd3hjc3	282	1	In	in	IN
cord-326631-7gd3hjc3	282	2	all	all	DT
cord-326631-7gd3hjc3	282	3	of	of	IN
cord-326631-7gd3hjc3	282	4	the	the	DT
cord-326631-7gd3hjc3	282	5	models	model	NNS
cord-326631-7gd3hjc3	282	6	that	that	WDT
cord-326631-7gd3hjc3	282	7	we	-PRON-	PRP
cord-326631-7gd3hjc3	282	8	have	have	VBP
cord-326631-7gd3hjc3	282	9	discussed	discuss	VBN
cord-326631-7gd3hjc3	282	10	so	so	RB
cord-326631-7gd3hjc3	282	11	far	far	RB
cord-326631-7gd3hjc3	282	12	,	,	,
cord-326631-7gd3hjc3	282	13	we	-PRON-	PRP
cord-326631-7gd3hjc3	282	14	have	have	VBP
cord-326631-7gd3hjc3	282	15	assumed	assume	VBN
cord-326631-7gd3hjc3	282	16	that	that	IN
cord-326631-7gd3hjc3	282	17	the	the	DT
cord-326631-7gd3hjc3	282	18	population	population	NN
cord-326631-7gd3hjc3	282	19	is	be	VBZ
cord-326631-7gd3hjc3	282	20	homogeneously	homogeneously	RB
cord-326631-7gd3hjc3	282	21	mixed	mixed	JJ
cord-326631-7gd3hjc3	282	22	.	.	.
cord-326631-7gd3hjc3	283	1	In	in	IN
cord-326631-7gd3hjc3	283	2	the	the	DT
cord-326631-7gd3hjc3	283	3	remainder	remainder	NN
cord-326631-7gd3hjc3	283	4	of	of	IN
cord-326631-7gd3hjc3	283	5	this	this	DT
cord-326631-7gd3hjc3	283	6	paper	paper	NN
cord-326631-7gd3hjc3	283	7	,	,	,
cord-326631-7gd3hjc3	283	8	we	-PRON-	PRP
cord-326631-7gd3hjc3	283	9	explore	explore	VBP
cord-326631-7gd3hjc3	283	10	the	the	DT
cord-326631-7gd3hjc3	283	11	significance	significance	NN
cord-326631-7gd3hjc3	283	12	of	of	IN
cord-326631-7gd3hjc3	283	13	heterogeneous	heterogeneous	JJ
cord-326631-7gd3hjc3	283	14	mixing	mixing	NN
cord-326631-7gd3hjc3	283	15	for	for	IN
cord-326631-7gd3hjc3	283	16	the	the	DT
cord-326631-7gd3hjc3	283	17	final	final	JJ
cord-326631-7gd3hjc3	283	18	size	size	NN
cord-326631-7gd3hjc3	283	19	formula	formula	NN
cord-326631-7gd3hjc3	283	20	.	.	.
cord-326631-7gd3hjc3	284	1	In	in	IN
cord-326631-7gd3hjc3	284	2	the	the	DT
cord-326631-7gd3hjc3	284	3	present	present	JJ
cord-326631-7gd3hjc3	284	4	section	section	NN
cord-326631-7gd3hjc3	284	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	284	6	identify	identify	VBP
cord-326631-7gd3hjc3	284	7	an	an	DT
cord-326631-7gd3hjc3	284	8	important	important	JJ
cord-326631-7gd3hjc3	284	9	class	class	NN
cord-326631-7gd3hjc3	284	10	of	of	IN
cord-326631-7gd3hjc3	284	11	spatially	spatially	RB
cord-326631-7gd3hjc3	284	12	structured	structured	JJ
cord-326631-7gd3hjc3	284	13	models	model	NNS
cord-326631-7gd3hjc3	284	14	for	for	IN
cord-326631-7gd3hjc3	284	15	which	which	WDT
cord-326631-7gd3hjc3	284	16	the	the	DT
cord-326631-7gd3hjc3	284	17	standard	standard	JJ
cord-326631-7gd3hjc3	284	18	formula	formula	NN
cord-326631-7gd3hjc3	284	19	(	(	-LRB-
cord-326631-7gd3hjc3	284	20	5	5	LS
cord-326631-7gd3hjc3	284	21	)	)	-RRB-
cord-326631-7gd3hjc3	284	22	remains	remain	VBZ
cord-326631-7gd3hjc3	284	23	valid	valid	JJ
cord-326631-7gd3hjc3	284	24	.	.	.
cord-326631-7gd3hjc3	285	1	A	a	DT
cord-326631-7gd3hjc3	285	2	simple	simple	JJ
cord-326631-7gd3hjc3	285	3	but	but	CC
cord-326631-7gd3hjc3	285	4	important	important	JJ
cord-326631-7gd3hjc3	285	5	example	example	NN
cord-326631-7gd3hjc3	285	6	of	of	IN
cord-326631-7gd3hjc3	285	7	heterogenous	heterogenous	JJ
cord-326631-7gd3hjc3	285	8	mixing	mixing	NN
cord-326631-7gd3hjc3	285	9	occurs	occur	VBZ
cord-326631-7gd3hjc3	285	10	if	if	IN
cord-326631-7gd3hjc3	285	11	the	the	DT
cord-326631-7gd3hjc3	285	12	population	population	NN
cord-326631-7gd3hjc3	285	13	is	be	VBZ
cord-326631-7gd3hjc3	285	14	divided	divide	VBN
cord-326631-7gd3hjc3	285	15	into	into	IN
cord-326631-7gd3hjc3	285	16	a	a	DT
cord-326631-7gd3hjc3	285	17	number	number	NN
cord-326631-7gd3hjc3	285	18	of	of	IN
cord-326631-7gd3hjc3	285	19	spatially	spatially	RB
cord-326631-7gd3hjc3	285	20	isolated	isolate	VBN
cord-326631-7gd3hjc3	285	21	patches	patch	NNS
cord-326631-7gd3hjc3	285	22	(	(	-LRB-
cord-326631-7gd3hjc3	285	23	e.g.	e.g.	RB
cord-326631-7gd3hjc3	285	24	,	,	,
cord-326631-7gd3hjc3	285	25	cities	city	NNS
cord-326631-7gd3hjc3	285	26	)	)	-RRB-
cord-326631-7gd3hjc3	285	27	,	,	,
cord-326631-7gd3hjc3	285	28	often	often	RB
cord-326631-7gd3hjc3	285	29	called	call	VBD
cord-326631-7gd3hjc3	285	30	a	a	DT
cord-326631-7gd3hjc3	285	31	metapopulation	metapopulation	NN
cord-326631-7gd3hjc3	285	32	(	(	-LRB-
cord-326631-7gd3hjc3	285	33	Hanski	Hanski	NNP
cord-326631-7gd3hjc3	285	34	and	and	CC
cord-326631-7gd3hjc3	285	35	Gilpin	Gilpin	NNP
cord-326631-7gd3hjc3	285	36	,	,	,
cord-326631-7gd3hjc3	285	37	1997	1997	CD
cord-326631-7gd3hjc3	285	38	)	)	-RRB-
cord-326631-7gd3hjc3	285	39	.	.	.
cord-326631-7gd3hjc3	286	1	In	in	IN
cord-326631-7gd3hjc3	286	2	ecological	ecological	JJ
cord-326631-7gd3hjc3	286	3	models	model	NNS
cord-326631-7gd3hjc3	286	4	,	,	,
cord-326631-7gd3hjc3	286	5	coupling	couple	VBG
cord-326631-7gd3hjc3	286	6	among	among	IN
cord-326631-7gd3hjc3	286	7	patches	patch	NNS
cord-326631-7gd3hjc3	286	8	in	in	IN
cord-326631-7gd3hjc3	286	9	a	a	DT
cord-326631-7gd3hjc3	286	10	metapopulation	metapopulation	NN
cord-326631-7gd3hjc3	286	11	usually	usually	RB
cord-326631-7gd3hjc3	286	12	occurs	occur	VBZ
cord-326631-7gd3hjc3	286	13	as	as	IN
cord-326631-7gd3hjc3	286	14	a	a	DT
cord-326631-7gd3hjc3	286	15	result	result	NN
cord-326631-7gd3hjc3	286	16	of	of	IN
cord-326631-7gd3hjc3	286	17	migration	migration	NN
cord-326631-7gd3hjc3	286	18	(	(	-LRB-
cord-326631-7gd3hjc3	286	19	Earn	earn	VB
cord-326631-7gd3hjc3	286	20	et	et	FW
cord-326631-7gd3hjc3	286	21	al	al	NNP
cord-326631-7gd3hjc3	286	22	.	.	NNP
cord-326631-7gd3hjc3	286	23	,	,	,
cord-326631-7gd3hjc3	286	24	2000b	2000b	CD
cord-326631-7gd3hjc3	286	25	)	)	-RRB-
cord-326631-7gd3hjc3	286	26	.	.	.
cord-326631-7gd3hjc3	287	1	In	in	IN
cord-326631-7gd3hjc3	287	2	the	the	DT
cord-326631-7gd3hjc3	287	3	present	present	JJ
cord-326631-7gd3hjc3	287	4	context	context	NN
cord-326631-7gd3hjc3	287	5	,	,	,
cord-326631-7gd3hjc3	287	6	inter	inter	JJ
cord-326631-7gd3hjc3	287	7	-	-	JJ
cord-326631-7gd3hjc3	287	8	patch	patch	JJ
cord-326631-7gd3hjc3	287	9	coupling	coupling	NN
cord-326631-7gd3hjc3	287	10	occurs	occur	VBZ
cord-326631-7gd3hjc3	287	11	because	because	IN
cord-326631-7gd3hjc3	287	12	individuals	individual	NNS
cord-326631-7gd3hjc3	287	13	travel	travel	VBP
cord-326631-7gd3hjc3	287	14	temporarily	temporarily	RB
cord-326631-7gd3hjc3	287	15	from	from	IN
cord-326631-7gd3hjc3	287	16	their	-PRON-	PRP$
cord-326631-7gd3hjc3	287	17	home	home	NN
cord-326631-7gd3hjc3	287	18	patch	patch	NN
cord-326631-7gd3hjc3	287	19	to	to	IN
cord-326631-7gd3hjc3	287	20	other	other	JJ
cord-326631-7gd3hjc3	287	21	patches	patch	NNS
cord-326631-7gd3hjc3	287	22	.	.	.
cord-326631-7gd3hjc3	288	1	On	on	IN
cord-326631-7gd3hjc3	288	2	such	such	JJ
cord-326631-7gd3hjc3	288	3	journeys	journey	NNS
cord-326631-7gd3hjc3	288	4	,	,	,
cord-326631-7gd3hjc3	288	5	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	288	6	individuals	individual	NNS
cord-326631-7gd3hjc3	288	7	might	may	MD
cord-326631-7gd3hjc3	288	8	contact	contact	VB
cord-326631-7gd3hjc3	288	9	infectious	infectious	JJ
cord-326631-7gd3hjc3	288	10	individuals	individual	NNS
cord-326631-7gd3hjc3	288	11	and	and	CC
cord-326631-7gd3hjc3	288	12	become	become	VB
cord-326631-7gd3hjc3	288	13	infected	infected	JJ
cord-326631-7gd3hjc3	288	14	,	,	,
cord-326631-7gd3hjc3	288	15	and	and	CC
cord-326631-7gd3hjc3	288	16	infectious	infectious	JJ
cord-326631-7gd3hjc3	288	17	individuals	individual	NNS
cord-326631-7gd3hjc3	288	18	might	may	MD
cord-326631-7gd3hjc3	288	19	contact	contact	VB
cord-326631-7gd3hjc3	288	20	susceptibles	susceptible	NNS
cord-326631-7gd3hjc3	288	21	and	and	CC
cord-326631-7gd3hjc3	288	22	infect	infect	VB
cord-326631-7gd3hjc3	288	23	them	-PRON-	PRP
cord-326631-7gd3hjc3	288	24	.	.	.
cord-326631-7gd3hjc3	289	1	If	if	IN
cord-326631-7gd3hjc3	289	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	289	3	restrict	restrict	VBP
cord-326631-7gd3hjc3	289	4	attention	attention	NN
cord-326631-7gd3hjc3	289	5	to	to	IN
cord-326631-7gd3hjc3	289	6	a	a	DT
cord-326631-7gd3hjc3	289	7	single	single	JJ
cord-326631-7gd3hjc3	289	8	infectious	infectious	JJ
cord-326631-7gd3hjc3	289	9	stage	stage	NN
cord-326631-7gd3hjc3	289	10	with	with	IN
cord-326631-7gd3hjc3	289	11	exponentially	exponentially	RB
cord-326631-7gd3hjc3	289	12	distributed	distribute	VBN
cord-326631-7gd3hjc3	289	13	infectious	infectious	JJ
cord-326631-7gd3hjc3	289	14	period	period	NN
cord-326631-7gd3hjc3	289	15	then	then	RB
cord-326631-7gd3hjc3	289	16	the	the	DT
cord-326631-7gd3hjc3	289	17	model	model	NN
cord-326631-7gd3hjc3	289	18	is	be	VBZ
cord-326631-7gd3hjc3	289	19	specified	specify	VBN
cord-326631-7gd3hjc3	289	20	as	as	IN
cord-326631-7gd3hjc3	289	21	follows	follow	VBZ
cord-326631-7gd3hjc3	289	22	.	.	.
cord-326631-7gd3hjc3	290	1	Here	here	RB
cord-326631-7gd3hjc3	290	2	,	,	,
cord-326631-7gd3hjc3	290	3	S	S	NNP
cord-326631-7gd3hjc3	290	4	i	i	NN
cord-326631-7gd3hjc3	290	5	,	,	,
cord-326631-7gd3hjc3	290	6	I	-PRON-	PRP
cord-326631-7gd3hjc3	290	7	i	i	PRP
cord-326631-7gd3hjc3	290	8	,	,	,
cord-326631-7gd3hjc3	290	9	and	and	CC
cord-326631-7gd3hjc3	290	10	R	r	NN
cord-326631-7gd3hjc3	290	11	i	i	PRP
cord-326631-7gd3hjc3	290	12	(	(	-LRB-
cord-326631-7gd3hjc3	290	13	i	i	NN
cord-326631-7gd3hjc3	290	14	=	=	SYM
cord-326631-7gd3hjc3	290	15	1	1	CD
cord-326631-7gd3hjc3	290	16	,	,	,
cord-326631-7gd3hjc3	290	17	.	.	.
cord-326631-7gd3hjc3	290	18	.	.	.
cord-326631-7gd3hjc3	290	19	.	.	.
cord-326631-7gd3hjc3	290	20	,	,	,
cord-326631-7gd3hjc3	290	21	n	n	LS
cord-326631-7gd3hjc3	290	22	)	)	-RRB-
cord-326631-7gd3hjc3	290	23	are	be	VBP
cord-326631-7gd3hjc3	290	24	the	the	DT
cord-326631-7gd3hjc3	290	25	proportions	proportion	NNS
cord-326631-7gd3hjc3	290	26	of	of	IN
cord-326631-7gd3hjc3	290	27	the	the	DT
cord-326631-7gd3hjc3	290	28	population	population	NN
cord-326631-7gd3hjc3	290	29	in	in	IN
cord-326631-7gd3hjc3	290	30	patch	patch	NN
cord-326631-7gd3hjc3	291	1	i	i	PRP
cord-326631-7gd3hjc3	291	2	that	that	WDT
cord-326631-7gd3hjc3	291	3	are	be	VBP
cord-326631-7gd3hjc3	291	4	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	291	5	,	,	,
cord-326631-7gd3hjc3	291	6	infectious	infectious	JJ
cord-326631-7gd3hjc3	291	7	recovered	recover	VBN
cord-326631-7gd3hjc3	291	8	,	,	,
cord-326631-7gd3hjc3	291	9	respectively	respectively	RB
cord-326631-7gd3hjc3	291	10	.	.	.
cord-326631-7gd3hjc3	292	1	Summing	sum	VBG
cord-326631-7gd3hjc3	292	2	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	292	3	.	.	.
cord-326631-7gd3hjc3	293	1	(	(	-LRB-
cord-326631-7gd3hjc3	293	2	26	26	CD
cord-326631-7gd3hjc3	293	3	)	)	-RRB-
cord-326631-7gd3hjc3	293	4	,	,	,
cord-326631-7gd3hjc3	293	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	293	6	see	see	VBP
cord-326631-7gd3hjc3	293	7	that	that	IN
cord-326631-7gd3hjc3	293	8	S	s	NN
cord-326631-7gd3hjc3	293	9	i	i	PRP
cord-326631-7gd3hjc3	293	10	(	(	-LRB-
cord-326631-7gd3hjc3	293	11	t	t	NN
cord-326631-7gd3hjc3	293	12	)	)	-RRB-
cord-326631-7gd3hjc3	294	1	+	+	CC
cord-326631-7gd3hjc3	294	2	I	-PRON-	PRP
cord-326631-7gd3hjc3	294	3	i	i	PRP
cord-326631-7gd3hjc3	294	4	(	(	-LRB-
cord-326631-7gd3hjc3	294	5	t	t	NN
cord-326631-7gd3hjc3	294	6	)	)	-RRB-
cord-326631-7gd3hjc3	295	1	+	+	CC
cord-326631-7gd3hjc3	295	2	R	r	NN
cord-326631-7gd3hjc3	295	3	i	i	PRP
cord-326631-7gd3hjc3	295	4	(	(	-LRB-
cord-326631-7gd3hjc3	295	5	t	t	NN
cord-326631-7gd3hjc3	295	6	)	)	-RRB-
cord-326631-7gd3hjc3	295	7	=	=	SYM
cord-326631-7gd3hjc3	295	8	1	1	CD
cord-326631-7gd3hjc3	295	9	is	be	VBZ
cord-326631-7gd3hjc3	295	10	invariant	invariant	JJ
cord-326631-7gd3hjc3	295	11	in	in	IN
cord-326631-7gd3hjc3	295	12	all	all	DT
cord-326631-7gd3hjc3	295	13	patches	patch	NNS
cord-326631-7gd3hjc3	295	14	.	.	.
cord-326631-7gd3hjc3	296	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	296	2	denote	denote	VBP
cord-326631-7gd3hjc3	296	3	by	by	IN
cord-326631-7gd3hjc3	296	4	N	n	CD
cord-326631-7gd3hjc3	297	1	i	i	PRP
cord-326631-7gd3hjc3	298	1	the	the	DT
cord-326631-7gd3hjc3	298	2	number	number	NN
cord-326631-7gd3hjc3	298	3	of	of	IN
cord-326631-7gd3hjc3	298	4	individuals	individual	NNS
cord-326631-7gd3hjc3	298	5	in	in	IN
cord-326631-7gd3hjc3	298	6	patch	patch	NN
cord-326631-7gd3hjc3	299	1	i	i	PRP
cord-326631-7gd3hjc3	300	1	,	,	,
cord-326631-7gd3hjc3	300	2	so	so	CC
cord-326631-7gd3hjc3	300	3	the	the	DT
cord-326631-7gd3hjc3	300	4	total	total	JJ
cord-326631-7gd3hjc3	300	5	population	population	NN
cord-326631-7gd3hjc3	300	6	size	size	NN
cord-326631-7gd3hjc3	300	7	is	be	VBZ
cord-326631-7gd3hjc3	300	8	N	n	NN
cord-326631-7gd3hjc3	300	9	=	=	NN
cord-326631-7gd3hjc3	301	1	i	i	PRP
cord-326631-7gd3hjc3	302	1	N	N	NNP
cord-326631-7gd3hjc3	303	1	i	i	PRP
cord-326631-7gd3hjc3	303	2	.	.	.
cord-326631-7gd3hjc3	304	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	304	2	is	be	VBZ
cord-326631-7gd3hjc3	304	3	also	also	RB
cord-326631-7gd3hjc3	304	4	convenient	convenient	JJ
cord-326631-7gd3hjc3	304	5	to	to	TO
cord-326631-7gd3hjc3	304	6	use	use	VB
cord-326631-7gd3hjc3	304	7	B	b	NN
cord-326631-7gd3hjc3	304	8	=	=	NFP
cord-326631-7gd3hjc3	305	1	(	(	-LRB-
cord-326631-7gd3hjc3	305	2	β	β	NN
cord-326631-7gd3hjc3	305	3	i	i	NNP
cord-326631-7gd3hjc3	305	4	j	j	NNP
cord-326631-7gd3hjc3	305	5	)	)	-RRB-
cord-326631-7gd3hjc3	306	1	to	to	TO
cord-326631-7gd3hjc3	306	2	denote	denote	VB
cord-326631-7gd3hjc3	306	3	the	the	DT
cord-326631-7gd3hjc3	306	4	n	n	NNP
cord-326631-7gd3hjc3	306	5	×	×	NNP
cord-326631-7gd3hjc3	306	6	n	n	NNP
cord-326631-7gd3hjc3	306	7	transmission	transmission	NN
cord-326631-7gd3hjc3	306	8	matrix	matrix	NN
cord-326631-7gd3hjc3	306	9	.	.	.
cord-326631-7gd3hjc3	307	1	Similar	similar	JJ
cord-326631-7gd3hjc3	307	2	to	to	IN
cord-326631-7gd3hjc3	307	3	our	-PRON-	PRP$
cord-326631-7gd3hjc3	307	4	analysis	analysis	NN
cord-326631-7gd3hjc3	307	5	of	of	IN
cord-326631-7gd3hjc3	307	6	other	other	JJ
cord-326631-7gd3hjc3	307	7	models	model	NNS
cord-326631-7gd3hjc3	307	8	in	in	IN
cord-326631-7gd3hjc3	307	9	previous	previous	JJ
cord-326631-7gd3hjc3	307	10	sections	section	NNS
cord-326631-7gd3hjc3	307	11	,	,	,
cord-326631-7gd3hjc3	307	12	it	-PRON-	PRP
cord-326631-7gd3hjc3	307	13	is	be	VBZ
cord-326631-7gd3hjc3	307	14	straightforward	straightforward	JJ
cord-326631-7gd3hjc3	307	15	to	to	TO
cord-326631-7gd3hjc3	307	16	prove	prove	VB
cord-326631-7gd3hjc3	307	17	that	that	IN
cord-326631-7gd3hjc3	307	18	S	s	NN
cord-326631-7gd3hjc3	307	19	i	i	NN
cord-326631-7gd3hjc3	307	20	(	(	-LRB-
cord-326631-7gd3hjc3	307	21	∞	∞	NNP
cord-326631-7gd3hjc3	307	22	)	)	-RRB-
cord-326631-7gd3hjc3	307	23	,	,	,
cord-326631-7gd3hjc3	307	24	R	r	NN
cord-326631-7gd3hjc3	307	25	i	i	NN
cord-326631-7gd3hjc3	307	26	(	(	-LRB-
cord-326631-7gd3hjc3	307	27	∞	∞	NNP
cord-326631-7gd3hjc3	307	28	)	)	-RRB-
cord-326631-7gd3hjc3	307	29	,	,	.
cord-326631-7gd3hjc3	308	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	308	2	i	i	PRP
cord-326631-7gd3hjc3	309	1	(	(	-LRB-
cord-326631-7gd3hjc3	309	2	∞	∞	NNP
cord-326631-7gd3hjc3	309	3	)	)	-RRB-
cord-326631-7gd3hjc3	309	4	exist	exist	VBP
cord-326631-7gd3hjc3	309	5	,	,	.
cord-326631-7gd3hjc3	310	1	that	that	DT
cord-326631-7gd3hjc3	310	2	S	S	NNP
cord-326631-7gd3hjc3	310	3	i	i	NN
cord-326631-7gd3hjc3	310	4	(	(	-LRB-
cord-326631-7gd3hjc3	310	5	∞	∞	NNP
cord-326631-7gd3hjc3	310	6	)	)	-RRB-
cord-326631-7gd3hjc3	310	7	+	+	.
cord-326631-7gd3hjc3	311	1	R	r	NN
cord-326631-7gd3hjc3	311	2	i	i	NN
cord-326631-7gd3hjc3	311	3	(	(	-LRB-
cord-326631-7gd3hjc3	311	4	∞	∞	NNP
cord-326631-7gd3hjc3	311	5	)	)	-RRB-
cord-326631-7gd3hjc3	311	6	=	=	SYM
cord-326631-7gd3hjc3	311	7	1	1	CD
cord-326631-7gd3hjc3	311	8	and	and	CC
cord-326631-7gd3hjc3	311	9	that	that	IN
cord-326631-7gd3hjc3	311	10	I	-PRON-	PRP
cord-326631-7gd3hjc3	311	11	i	i	PRP
cord-326631-7gd3hjc3	311	12	(	(	-LRB-
cord-326631-7gd3hjc3	311	13	∞	∞	NNP
cord-326631-7gd3hjc3	311	14	)	)	-RRB-
cord-326631-7gd3hjc3	311	15	=	=	SYM
cord-326631-7gd3hjc3	311	16	0	0	CD
cord-326631-7gd3hjc3	311	17	.	.	.
cord-326631-7gd3hjc3	312	1	Since	since	IN
cord-326631-7gd3hjc3	312	2	β	β	NN
cord-326631-7gd3hjc3	313	1	i	i	PRP
cord-326631-7gd3hjc3	313	2	j	j	NNP
cord-326631-7gd3hjc3	313	3	≥	≥	NNP
cord-326631-7gd3hjc3	313	4	0	0	NNP
cord-326631-7gd3hjc3	313	5	,	,	,
cord-326631-7gd3hjc3	313	6	the	the	DT
cord-326631-7gd3hjc3	313	7	dominant	dominant	JJ
cord-326631-7gd3hjc3	313	8	eigenvalue	eigenvalue	NN
cord-326631-7gd3hjc3	313	9	λ	λ	NN
cord-326631-7gd3hjc3	313	10	of	of	IN
cord-326631-7gd3hjc3	313	11	B	B	NNP
cord-326631-7gd3hjc3	313	12	is	be	VBZ
cord-326631-7gd3hjc3	313	13	real	real	JJ
cord-326631-7gd3hjc3	313	14	and	and	CC
cord-326631-7gd3hjc3	313	15	positive	positive	JJ
cord-326631-7gd3hjc3	313	16	(	(	-LRB-
cord-326631-7gd3hjc3	313	17	Horn	Horn	NNP
cord-326631-7gd3hjc3	313	18	and	and	CC
cord-326631-7gd3hjc3	313	19	Johnson	Johnson	NNP
cord-326631-7gd3hjc3	313	20	,	,	,
cord-326631-7gd3hjc3	313	21	1985	1985	CD
cord-326631-7gd3hjc3	313	22	)	)	-RRB-
cord-326631-7gd3hjc3	313	23	.	.	.
cord-326631-7gd3hjc3	314	1	If	if	IN
cord-326631-7gd3hjc3	314	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	314	3	linearize	linearize	VBP
cord-326631-7gd3hjc3	314	4	the	the	DT
cord-326631-7gd3hjc3	314	5	model	model	NN
cord-326631-7gd3hjc3	314	6	(	(	-LRB-
cord-326631-7gd3hjc3	314	7	26	26	CD
cord-326631-7gd3hjc3	314	8	)	)	-RRB-
cord-326631-7gd3hjc3	314	9	at	at	IN
cord-326631-7gd3hjc3	314	10	the	the	DT
cord-326631-7gd3hjc3	314	11	disease	disease	NN
cord-326631-7gd3hjc3	314	12	free	free	JJ
cord-326631-7gd3hjc3	314	13	equilibrium	equilibrium	NN
cord-326631-7gd3hjc3	314	14	(	(	-LRB-
cord-326631-7gd3hjc3	314	15	DFE	DFE	NNP
cord-326631-7gd3hjc3	314	16	)	)	-RRB-
cord-326631-7gd3hjc3	315	1	(	(	-LRB-
cord-326631-7gd3hjc3	315	2	S	S	NNP
cord-326631-7gd3hjc3	316	1	i	i	PRP
cord-326631-7gd3hjc3	317	1	=	=	SYM
cord-326631-7gd3hjc3	317	2	1	1	CD
cord-326631-7gd3hjc3	317	3	,	,	,
cord-326631-7gd3hjc3	318	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	319	1	i	i	PRP
cord-326631-7gd3hjc3	319	2	=	=	SYM
cord-326631-7gd3hjc3	319	3	0	0	NFP
cord-326631-7gd3hjc3	319	4	,	,	,
cord-326631-7gd3hjc3	319	5	R	r	NN
cord-326631-7gd3hjc3	319	6	i	i	NN
cord-326631-7gd3hjc3	319	7	=	=	NN
cord-326631-7gd3hjc3	319	8	0	0	CD
cord-326631-7gd3hjc3	319	9	)	)	-RRB-
cord-326631-7gd3hjc3	319	10	,	,	,
cord-326631-7gd3hjc3	319	11	we	-PRON-	PRP
cord-326631-7gd3hjc3	319	12	see	see	VBP
cord-326631-7gd3hjc3	319	13	that	that	IN
cord-326631-7gd3hjc3	319	14	the	the	DT
cord-326631-7gd3hjc3	319	15	stability	stability	NN
cord-326631-7gd3hjc3	319	16	of	of	IN
cord-326631-7gd3hjc3	319	17	the	the	DT
cord-326631-7gd3hjc3	319	18	DFE	DFE	NNP
cord-326631-7gd3hjc3	319	19	is	be	VBZ
cord-326631-7gd3hjc3	319	20	determined	determine	VBN
cord-326631-7gd3hjc3	319	21	by	by	IN
cord-326631-7gd3hjc3	319	22	λ	λ	NNP
cord-326631-7gd3hjc3	319	23	.	.	.
cord-326631-7gd3hjc3	320	1	If	if	IN
cord-326631-7gd3hjc3	320	2	λ	λ	NN
cord-326631-7gd3hjc3	320	3	/	/	SYM
cord-326631-7gd3hjc3	320	4	γ	γ	NN
cord-326631-7gd3hjc3	320	5	>	>	XX
cord-326631-7gd3hjc3	320	6	1	1	CD
cord-326631-7gd3hjc3	320	7	,	,	,
cord-326631-7gd3hjc3	320	8	then	then	RB
cord-326631-7gd3hjc3	320	9	the	the	DT
cord-326631-7gd3hjc3	320	10	DFE	DFE	NNP
cord-326631-7gd3hjc3	320	11	is	be	VBZ
cord-326631-7gd3hjc3	320	12	unstable	unstable	JJ
cord-326631-7gd3hjc3	320	13	,	,	,
cord-326631-7gd3hjc3	320	14	otherwise	otherwise	RB
cord-326631-7gd3hjc3	320	15	it	-PRON-	PRP
cord-326631-7gd3hjc3	320	16	is	be	VBZ
cord-326631-7gd3hjc3	320	17	stable	stable	JJ
cord-326631-7gd3hjc3	320	18	.	.	.
cord-326631-7gd3hjc3	321	1	Thus	thus	RB
cord-326631-7gd3hjc3	321	2	,	,	,
cord-326631-7gd3hjc3	321	3	the	the	DT
cord-326631-7gd3hjc3	321	4	threshold	threshold	NN
cord-326631-7gd3hjc3	321	5	for	for	IN
cord-326631-7gd3hjc3	321	6	exponential	exponential	JJ
cord-326631-7gd3hjc3	321	7	growth	growth	NN
cord-326631-7gd3hjc3	321	8	of	of	IN
cord-326631-7gd3hjc3	321	9	cases	case	NNS
cord-326631-7gd3hjc3	321	10	(	(	-LRB-
cord-326631-7gd3hjc3	321	11	an	an	DT
cord-326631-7gd3hjc3	321	12	epidemic	epidemic	NN
cord-326631-7gd3hjc3	321	13	)	)	-RRB-
cord-326631-7gd3hjc3	321	14	is	be	VBZ
cord-326631-7gd3hjc3	321	15	determined	determine	VBN
cord-326631-7gd3hjc3	321	16	by	by	IN
cord-326631-7gd3hjc3	321	17	the	the	DT
cord-326631-7gd3hjc3	321	18	value	value	NN
cord-326631-7gd3hjc3	321	19	of	of	IN
cord-326631-7gd3hjc3	321	20	R	r	NN
cord-326631-7gd3hjc3	321	21	0	0	CD
cord-326631-7gd3hjc3	321	22	=	=	NFP
cord-326631-7gd3hjc3	322	1	λ	λ	NNP
cord-326631-7gd3hjc3	322	2	/	/	SYM
cord-326631-7gd3hjc3	322	3	γ	γ	NNP
cord-326631-7gd3hjc3	322	4	,	,	,
cord-326631-7gd3hjc3	322	5	which	which	WDT
cord-326631-7gd3hjc3	322	6	can	can	MD
cord-326631-7gd3hjc3	322	7	be	be	VB
cord-326631-7gd3hjc3	322	8	interpreted	interpret	VBN
cord-326631-7gd3hjc3	322	9	as	as	IN
cord-326631-7gd3hjc3	322	10	the	the	DT
cord-326631-7gd3hjc3	322	11	basic	basic	JJ
cord-326631-7gd3hjc3	322	12	reproduction	reproduction	NN
cord-326631-7gd3hjc3	322	13	number	number	NN
cord-326631-7gd3hjc3	322	14	(	(	-LRB-
cord-326631-7gd3hjc3	322	15	van	van	NNP
cord-326631-7gd3hjc3	322	16	den	den	NNP
cord-326631-7gd3hjc3	322	17	Driessche	Driessche	NNP
cord-326631-7gd3hjc3	322	18	and	and	CC
cord-326631-7gd3hjc3	322	19	Watmough	Watmough	NNP
cord-326631-7gd3hjc3	322	20	,	,	,
cord-326631-7gd3hjc3	322	21	2002	2002	CD
cord-326631-7gd3hjc3	322	22	)	)	-RRB-
cord-326631-7gd3hjc3	322	23	.	.	.
cord-326631-7gd3hjc3	323	1	The	the	DT
cord-326631-7gd3hjc3	323	2	final	final	JJ
cord-326631-7gd3hjc3	323	3	size	size	NN
cord-326631-7gd3hjc3	323	4	in	in	IN
cord-326631-7gd3hjc3	323	5	patch	patch	NN
cord-326631-7gd3hjc3	324	1	i	i	PRP
cord-326631-7gd3hjc3	324	2	is	be	VBZ
cord-326631-7gd3hjc3	325	1	Z	Z	NNP
cord-326631-7gd3hjc3	325	2	i	i	NN
cord-326631-7gd3hjc3	325	3	=	=	NFP
cord-326631-7gd3hjc3	326	1	S	S	NNP
cord-326631-7gd3hjc3	326	2	i	i	NN
cord-326631-7gd3hjc3	326	3	(	(	-LRB-
cord-326631-7gd3hjc3	326	4	0	0	NFP
cord-326631-7gd3hjc3	326	5	)	)	-RRB-
cord-326631-7gd3hjc3	327	1	−	−	NNP
cord-326631-7gd3hjc3	327	2	S	S	NNP
cord-326631-7gd3hjc3	327	3	i	i	NN
cord-326631-7gd3hjc3	327	4	(	(	-LRB-
cord-326631-7gd3hjc3	327	5	∞	∞	NNP
cord-326631-7gd3hjc3	327	6	)	)	-RRB-
cord-326631-7gd3hjc3	327	7	.	.	.
cord-326631-7gd3hjc3	328	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	328	2	can	can	MD
cord-326631-7gd3hjc3	328	3	obtain	obtain	VB
cord-326631-7gd3hjc3	328	4	a	a	DT
cord-326631-7gd3hjc3	328	5	system	system	NN
cord-326631-7gd3hjc3	328	6	of	of	IN
cord-326631-7gd3hjc3	328	7	n	n	CC
cord-326631-7gd3hjc3	328	8	coupled	couple	VBN
cord-326631-7gd3hjc3	328	9	algebraic	algebraic	JJ
cord-326631-7gd3hjc3	328	10	equations	equation	NNS
cord-326631-7gd3hjc3	328	11	for	for	IN
cord-326631-7gd3hjc3	328	12	the	the	DT
cord-326631-7gd3hjc3	328	13	Z	z	NN
cord-326631-7gd3hjc3	328	14	i	i	PRP
cord-326631-7gd3hjc3	328	15	if	if	IN
cord-326631-7gd3hjc3	328	16	we	-PRON-	PRP
cord-326631-7gd3hjc3	328	17	divide	divide	VBP
cord-326631-7gd3hjc3	328	18	by	by	IN
cord-326631-7gd3hjc3	328	19	S	s	NN
cord-326631-7gd3hjc3	328	20	i	i	PRP
cord-326631-7gd3hjc3	328	21	on	on	IN
cord-326631-7gd3hjc3	328	22	both	both	DT
cord-326631-7gd3hjc3	328	23	sides	side	NNS
cord-326631-7gd3hjc3	328	24	of	of	IN
cord-326631-7gd3hjc3	328	25	Eq	Eq	NNP
cord-326631-7gd3hjc3	328	26	.	.	.
cord-326631-7gd3hjc3	329	1	(	(	-LRB-
cord-326631-7gd3hjc3	329	2	26a	26a	NNS
cord-326631-7gd3hjc3	329	3	)	)	-RRB-
cord-326631-7gd3hjc3	329	4	and	and	CC
cord-326631-7gd3hjc3	329	5	integrate	integrate	VB
cord-326631-7gd3hjc3	329	6	from	from	IN
cord-326631-7gd3hjc3	329	7	0	0	CD
cord-326631-7gd3hjc3	329	8	to	to	IN
cord-326631-7gd3hjc3	329	9	∞.	∞.	NNP
cord-326631-7gd3hjc3	330	1	These	these	DT
cord-326631-7gd3hjc3	330	2	algebraic	algebraic	JJ
cord-326631-7gd3hjc3	330	3	equations	equation	NNS
cord-326631-7gd3hjc3	330	4	contain	contain	VBP
cord-326631-7gd3hjc3	330	5	∞	∞	NNP
cord-326631-7gd3hjc3	330	6	0	0	NFP
cord-326631-7gd3hjc3	330	7	I	i	NN
cord-326631-7gd3hjc3	330	8	i	i	PRP
cord-326631-7gd3hjc3	330	9	dt	dt	NN
cord-326631-7gd3hjc3	330	10	,	,	,
cord-326631-7gd3hjc3	330	11	which	which	WDT
cord-326631-7gd3hjc3	330	12	can	can	MD
cord-326631-7gd3hjc3	330	13	be	be	VB
cord-326631-7gd3hjc3	330	14	eliminated	eliminate	VBN
cord-326631-7gd3hjc3	330	15	by	by	IN
cord-326631-7gd3hjc3	330	16	integrating	integrate	VBG
cord-326631-7gd3hjc3	330	17	Eq	Eq	NNP
cord-326631-7gd3hjc3	330	18	.	.	.
cord-326631-7gd3hjc3	331	1	(	(	-LRB-
cord-326631-7gd3hjc3	331	2	26c	26c	NNS
cord-326631-7gd3hjc3	331	3	)	)	-RRB-
cord-326631-7gd3hjc3	332	1	and	and	CC
cord-326631-7gd3hjc3	332	2	noting	note	VBG
cord-326631-7gd3hjc3	332	3	that	that	IN
cord-326631-7gd3hjc3	332	4	Z	z	NN
cord-326631-7gd3hjc3	332	5	i	i	NN
cord-326631-7gd3hjc3	332	6	=	=	NFP
cord-326631-7gd3hjc3	333	1	R	r	NN
cord-326631-7gd3hjc3	333	2	i	i	NN
cord-326631-7gd3hjc3	333	3	(	(	-LRB-
cord-326631-7gd3hjc3	333	4	∞	∞	NNP
cord-326631-7gd3hjc3	333	5	)	)	-RRB-
cord-326631-7gd3hjc3	333	6	−	−	NNP
cord-326631-7gd3hjc3	334	1	R	r	NN
cord-326631-7gd3hjc3	334	2	i	i	NN
cord-326631-7gd3hjc3	334	3	(	(	-LRB-
cord-326631-7gd3hjc3	334	4	0	0	NFP
cord-326631-7gd3hjc3	334	5	)	)	-RRB-
cord-326631-7gd3hjc3	334	6	.	.	.
cord-326631-7gd3hjc3	335	1	In	in	IN
cord-326631-7gd3hjc3	335	2	the	the	DT
cord-326631-7gd3hjc3	335	3	limit	limit	NN
cord-326631-7gd3hjc3	335	4	I	-PRON-	PRP
cord-326631-7gd3hjc3	335	5	i	i	PRP
cord-326631-7gd3hjc3	335	6	(	(	-LRB-
cord-326631-7gd3hjc3	335	7	0	0	NFP
cord-326631-7gd3hjc3	335	8	)	)	-RRB-
cord-326631-7gd3hjc3	335	9	→	→	SYM
cord-326631-7gd3hjc3	335	10	0	0	NFP
cord-326631-7gd3hjc3	335	11	,	,	,
cord-326631-7gd3hjc3	335	12	S	S	NNP
cord-326631-7gd3hjc3	335	13	i	i	NN
cord-326631-7gd3hjc3	335	14	(	(	-LRB-
cord-326631-7gd3hjc3	335	15	0	0	NFP
cord-326631-7gd3hjc3	335	16	)	)	-RRB-
cord-326631-7gd3hjc3	335	17	→	→	SYM
cord-326631-7gd3hjc3	335	18	1	1	CD
cord-326631-7gd3hjc3	335	19	,	,	,
cord-326631-7gd3hjc3	335	20	we	-PRON-	PRP
cord-326631-7gd3hjc3	335	21	obtain	obtain	VBP
cord-326631-7gd3hjc3	335	22	These	these	DT
cord-326631-7gd3hjc3	335	23	equations	equation	NNS
cord-326631-7gd3hjc3	335	24	form	form	VBP
cord-326631-7gd3hjc3	335	25	a	a	DT
cord-326631-7gd3hjc3	335	26	special	special	JJ
cord-326631-7gd3hjc3	335	27	case	case	NN
cord-326631-7gd3hjc3	335	28	of	of	IN
cord-326631-7gd3hjc3	335	29	a	a	DT
cord-326631-7gd3hjc3	335	30	more	more	RBR
cord-326631-7gd3hjc3	335	31	general	general	JJ
cord-326631-7gd3hjc3	335	32	final	final	JJ
cord-326631-7gd3hjc3	335	33	size	size	NN
cord-326631-7gd3hjc3	335	34	formula	formula	NN
cord-326631-7gd3hjc3	335	35	discussed	discuss	VBN
cord-326631-7gd3hjc3	335	36	by	by	IN
cord-326631-7gd3hjc3	335	37	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	335	38	and	and	CC
cord-326631-7gd3hjc3	335	39	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	335	40	(	(	-LRB-
cord-326631-7gd3hjc3	335	41	2000	2000	CD
cord-326631-7gd3hjc3	335	42	)	)	-RRB-
cord-326631-7gd3hjc3	336	1	(	(	-LRB-
cord-326631-7gd3hjc3	336	2	exercises	exercise	NNS
cord-326631-7gd3hjc3	336	3	6.17	6.17	CD
cord-326631-7gd3hjc3	336	4	and	and	CC
cord-326631-7gd3hjc3	336	5	6.19	6.19	CD
cord-326631-7gd3hjc3	336	6	)	)	-RRB-
cord-326631-7gd3hjc3	336	7	.	.	.
cord-326631-7gd3hjc3	337	1	In	in	IN
cord-326631-7gd3hjc3	337	2	their	-PRON-	PRP$
cord-326631-7gd3hjc3	337	3	solution	solution	NN
cord-326631-7gd3hjc3	337	4	to	to	TO
cord-326631-7gd3hjc3	337	5	exercise	exercise	VB
cord-326631-7gd3hjc3	337	6	6.19	6.19	CD
cord-326631-7gd3hjc3	337	7	,	,	,
cord-326631-7gd3hjc3	337	8	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	337	9	and	and	CC
cord-326631-7gd3hjc3	337	10	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	337	11	(	(	-LRB-
cord-326631-7gd3hjc3	337	12	2000	2000	CD
cord-326631-7gd3hjc3	337	13	)	)	-RRB-
cord-326631-7gd3hjc3	337	14	sketch	sketch	VB
cord-326631-7gd3hjc3	337	15	an	an	DT
cord-326631-7gd3hjc3	337	16	argument	argument	NN
cord-326631-7gd3hjc3	337	17	that	that	WDT
cord-326631-7gd3hjc3	337	18	implies	imply	VBZ
cord-326631-7gd3hjc3	337	19	that	that	IN
cord-326631-7gd3hjc3	337	20	if	if	IN
cord-326631-7gd3hjc3	337	21	R	r	NN
cord-326631-7gd3hjc3	337	22	0	0	CD
cord-326631-7gd3hjc3	337	23	>	>	SYM
cord-326631-7gd3hjc3	337	24	1	1	CD
cord-326631-7gd3hjc3	337	25	then	then	RB
cord-326631-7gd3hjc3	337	26	there	there	EX
cord-326631-7gd3hjc3	337	27	is	be	VBZ
cord-326631-7gd3hjc3	337	28	a	a	DT
cord-326631-7gd3hjc3	337	29	unique	unique	JJ
cord-326631-7gd3hjc3	337	30	non	non	JJ
cord-326631-7gd3hjc3	337	31	-	-	JJ
cord-326631-7gd3hjc3	337	32	trivial	trivial	JJ
cord-326631-7gd3hjc3	337	33	(	(	-LRB-
cord-326631-7gd3hjc3	337	34	i.e.	i.e.	FW
cord-326631-7gd3hjc3	337	35	,	,	,
cord-326631-7gd3hjc3	337	36	non	non	JJ
cord-326631-7gd3hjc3	337	37	-	-	JJ
cord-326631-7gd3hjc3	337	38	zero	zero	JJ
cord-326631-7gd3hjc3	337	39	)	)	-RRB-
cord-326631-7gd3hjc3	337	40	solution	solution	NN
cord-326631-7gd3hjc3	337	41	to	to	IN
cord-326631-7gd3hjc3	337	42	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	337	43	.	.	.
cord-326631-7gd3hjc3	338	1	(	(	-LRB-
cord-326631-7gd3hjc3	338	2	27	27	CD
cord-326631-7gd3hjc3	338	3	)	)	-RRB-
cord-326631-7gd3hjc3	338	4	.	.	.
cord-326631-7gd3hjc3	339	1	The	the	DT
cord-326631-7gd3hjc3	339	2	final	final	JJ
cord-326631-7gd3hjc3	339	3	size	size	NN
cord-326631-7gd3hjc3	339	4	for	for	IN
cord-326631-7gd3hjc3	339	5	the	the	DT
cord-326631-7gd3hjc3	339	6	whole	whole	JJ
cord-326631-7gd3hjc3	339	7	metapopulation	metapopulation	NN
cord-326631-7gd3hjc3	339	8	,	,	,
cord-326631-7gd3hjc3	339	9	Z	Z	NNP
cord-326631-7gd3hjc3	339	10	,	,	,
cord-326631-7gd3hjc3	339	11	is	be	VBZ
cord-326631-7gd3hjc3	339	12	not	not	RB
cord-326631-7gd3hjc3	339	13	in	in	IN
cord-326631-7gd3hjc3	339	14	general	general	JJ
cord-326631-7gd3hjc3	339	15	the	the	DT
cord-326631-7gd3hjc3	339	16	simple	simple	JJ
cord-326631-7gd3hjc3	339	17	average	average	NN
cord-326631-7gd3hjc3	339	18	of	of	IN
cord-326631-7gd3hjc3	339	19	the	the	DT
cord-326631-7gd3hjc3	339	20	Z	z	NN
cord-326631-7gd3hjc3	340	1	i	i	PRP
cord-326631-7gd3hjc3	340	2	's	be	VBZ
cord-326631-7gd3hjc3	340	3	in	in	IN
cord-326631-7gd3hjc3	340	4	Eq	Eq	NNP
cord-326631-7gd3hjc3	340	5	.	.	.
cord-326631-7gd3hjc3	341	1	(	(	-LRB-
cord-326631-7gd3hjc3	341	2	27	27	CD
cord-326631-7gd3hjc3	341	3	)	)	-RRB-
cord-326631-7gd3hjc3	341	4	.	.	.
cord-326631-7gd3hjc3	342	1	Rather	rather	RB
cord-326631-7gd3hjc3	342	2	,	,	,
cord-326631-7gd3hjc3	342	3	each	each	DT
cord-326631-7gd3hjc3	342	4	Z	z	NN
cord-326631-7gd3hjc3	342	5	i	i	PRP
cord-326631-7gd3hjc3	342	6	must	must	MD
cord-326631-7gd3hjc3	342	7	be	be	VB
cord-326631-7gd3hjc3	342	8	weighted	weight	VBN
cord-326631-7gd3hjc3	342	9	by	by	IN
cord-326631-7gd3hjc3	342	10	the	the	DT
cord-326631-7gd3hjc3	342	11	population	population	NN
cord-326631-7gd3hjc3	342	12	size	size	NN
cord-326631-7gd3hjc3	342	13	N	N	NNP
cord-326631-7gd3hjc3	342	14	i	i	PRP
cord-326631-7gd3hjc3	342	15	of	of	IN
cord-326631-7gd3hjc3	342	16	patch	patch	NN
cord-326631-7gd3hjc3	343	1	i	i	PRP
cord-326631-7gd3hjc3	343	2	,	,	,
cord-326631-7gd3hjc3	343	3	i.e.	i.e.	FW
cord-326631-7gd3hjc3	343	4	,	,	,
cord-326631-7gd3hjc3	343	5	Consequently	consequently	RB
cord-326631-7gd3hjc3	343	6	,	,	,
cord-326631-7gd3hjc3	343	7	there	there	EX
cord-326631-7gd3hjc3	343	8	will	will	MD
cord-326631-7gd3hjc3	343	9	always	always	RB
cord-326631-7gd3hjc3	343	10	be	be	VB
cord-326631-7gd3hjc3	343	11	particular	particular	JJ
cord-326631-7gd3hjc3	343	12	values	value	NNS
cord-326631-7gd3hjc3	343	13	of	of	IN
cord-326631-7gd3hjc3	343	14	the	the	DT
cord-326631-7gd3hjc3	343	15	N	n	NN
cord-326631-7gd3hjc3	343	16	i	i	PRP
cord-326631-7gd3hjc3	343	17	that	that	WDT
cord-326631-7gd3hjc3	343	18	make	make	VBP
cord-326631-7gd3hjc3	343	19	Z	z	NN
cord-326631-7gd3hjc3	343	20	in	in	IN
cord-326631-7gd3hjc3	343	21	Eq	Eq	NNP
cord-326631-7gd3hjc3	343	22	.	.	.
cord-326631-7gd3hjc3	344	1	(	(	-LRB-
cord-326631-7gd3hjc3	344	2	28	28	CD
cord-326631-7gd3hjc3	344	3	)	)	-RRB-
cord-326631-7gd3hjc3	344	4	equal	equal	JJ
cord-326631-7gd3hjc3	344	5	to	to	IN
cord-326631-7gd3hjc3	344	6	the	the	DT
cord-326631-7gd3hjc3	344	7	solution	solution	NN
cord-326631-7gd3hjc3	344	8	of	of	IN
cord-326631-7gd3hjc3	344	9	the	the	DT
cord-326631-7gd3hjc3	344	10	standard	standard	JJ
cord-326631-7gd3hjc3	344	11	formula	formula	NN
cord-326631-7gd3hjc3	344	12	(	(	-LRB-
cord-326631-7gd3hjc3	344	13	5	5	CD
cord-326631-7gd3hjc3	344	14	)	)	-RRB-
cord-326631-7gd3hjc3	344	15	.	.	.
cord-326631-7gd3hjc3	345	1	However	however	RB
cord-326631-7gd3hjc3	345	2	,	,	,
cord-326631-7gd3hjc3	345	3	since	since	IN
cord-326631-7gd3hjc3	345	4	population	population	NN
cord-326631-7gd3hjc3	345	5	sizes	size	NNS
cord-326631-7gd3hjc3	345	6	are	be	VBP
cord-326631-7gd3hjc3	345	7	given	give	VBN
cord-326631-7gd3hjc3	345	8	a	a	DT
cord-326631-7gd3hjc3	345	9	priori	priori	FW
cord-326631-7gd3hjc3	345	10	,	,	,
cord-326631-7gd3hjc3	345	11	the	the	DT
cord-326631-7gd3hjc3	345	12	problem	problem	NN
cord-326631-7gd3hjc3	345	13	of	of	IN
cord-326631-7gd3hjc3	345	14	interest	interest	NN
cord-326631-7gd3hjc3	345	15	is	be	VBZ
cord-326631-7gd3hjc3	345	16	to	to	TO
cord-326631-7gd3hjc3	345	17	find	find	VB
cord-326631-7gd3hjc3	345	18	necessary	necessary	JJ
cord-326631-7gd3hjc3	345	19	and	and	CC
cord-326631-7gd3hjc3	345	20	sufficient	sufficient	JJ
cord-326631-7gd3hjc3	345	21	conditions	condition	NNS
cord-326631-7gd3hjc3	345	22	on	on	IN
cord-326631-7gd3hjc3	345	23	the	the	DT
cord-326631-7gd3hjc3	345	24	transmission	transmission	NN
cord-326631-7gd3hjc3	345	25	matrix	matrix	NN
cord-326631-7gd3hjc3	345	26	(	(	-LRB-
cord-326631-7gd3hjc3	345	27	B	b	NN
cord-326631-7gd3hjc3	345	28	)	)	-RRB-
cord-326631-7gd3hjc3	345	29	that	that	WDT
cord-326631-7gd3hjc3	345	30	ensure	ensure	VBP
cord-326631-7gd3hjc3	345	31	that	that	IN
cord-326631-7gd3hjc3	345	32	the	the	DT
cord-326631-7gd3hjc3	345	33	sum	sum	NN
cord-326631-7gd3hjc3	345	34	in	in	IN
cord-326631-7gd3hjc3	345	35	Eq	Eq	NNP
cord-326631-7gd3hjc3	345	36	.	.	.
cord-326631-7gd3hjc3	346	1	(	(	-LRB-
cord-326631-7gd3hjc3	346	2	28	28	CD
cord-326631-7gd3hjc3	346	3	)	)	-RRB-
cord-326631-7gd3hjc3	346	4	is	be	VBZ
cord-326631-7gd3hjc3	346	5	equal	equal	JJ
cord-326631-7gd3hjc3	346	6	to	to	IN
cord-326631-7gd3hjc3	346	7	the	the	DT
cord-326631-7gd3hjc3	346	8	final	final	JJ
cord-326631-7gd3hjc3	346	9	size	size	NN
cord-326631-7gd3hjc3	346	10	obtained	obtain	VBN
cord-326631-7gd3hjc3	346	11	from	from	IN
cord-326631-7gd3hjc3	346	12	the	the	DT
cord-326631-7gd3hjc3	346	13	standard	standard	JJ
cord-326631-7gd3hjc3	346	14	formula	formula	NN
cord-326631-7gd3hjc3	346	15	(	(	-LRB-
cord-326631-7gd3hjc3	346	16	5	5	CD
cord-326631-7gd3hjc3	346	17	)	)	-RRB-
cord-326631-7gd3hjc3	346	18	,	,	,
cord-326631-7gd3hjc3	346	19	regardless	regardless	RB
cord-326631-7gd3hjc3	346	20	of	of	IN
cord-326631-7gd3hjc3	346	21	the	the	DT
cord-326631-7gd3hjc3	346	22	values	value	NNS
cord-326631-7gd3hjc3	346	23	of	of	IN
cord-326631-7gd3hjc3	346	24	the	the	DT
cord-326631-7gd3hjc3	346	25	N	N	NNP
cord-326631-7gd3hjc3	346	26	i	i	NNP
cord-326631-7gd3hjc3	346	27	.	.	.
cord-326631-7gd3hjc3	347	1	In	in	IN
cord-326631-7gd3hjc3	347	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	347	3	.	.	.
cord-326631-7gd3hjc3	348	1	(	(	-LRB-
cord-326631-7gd3hjc3	348	2	28	28	CD
cord-326631-7gd3hjc3	348	3	)	)	-RRB-
cord-326631-7gd3hjc3	348	4	,	,	,
cord-326631-7gd3hjc3	348	5	Z	Z	NNP
cord-326631-7gd3hjc3	348	6	will	will	MD
cord-326631-7gd3hjc3	348	7	have	have	VB
cord-326631-7gd3hjc3	348	8	no	no	DT
cord-326631-7gd3hjc3	348	9	dependence	dependence	NN
cord-326631-7gd3hjc3	348	10	on	on	IN
cord-326631-7gd3hjc3	348	11	the	the	DT
cord-326631-7gd3hjc3	348	12	patch	patch	NN
cord-326631-7gd3hjc3	348	13	population	population	NN
cord-326631-7gd3hjc3	348	14	sizes	size	NNS
cord-326631-7gd3hjc3	348	15	if	if	IN
cord-326631-7gd3hjc3	348	16	and	and	CC
cord-326631-7gd3hjc3	348	17	and	and	CC
cord-326631-7gd3hjc3	348	18	only	only	RB
cord-326631-7gd3hjc3	348	19	if	if	IN
cord-326631-7gd3hjc3	348	20	Given	give	VBN
cord-326631-7gd3hjc3	348	21	this	this	DT
cord-326631-7gd3hjc3	348	22	,	,	,
cord-326631-7gd3hjc3	348	23	Eq	Eq	NNP
cord-326631-7gd3hjc3	348	24	.	.	.
cord-326631-7gd3hjc3	349	1	(	(	-LRB-
cord-326631-7gd3hjc3	349	2	27	27	CD
cord-326631-7gd3hjc3	349	3	)	)	-RRB-
cord-326631-7gd3hjc3	349	4	implies	imply	VBZ
cord-326631-7gd3hjc3	349	5	i.e.	i.e.	FW
cord-326631-7gd3hjc3	349	6	,	,	,
cord-326631-7gd3hjc3	349	7	the	the	DT
cord-326631-7gd3hjc3	349	8	transmission	transmission	NN
cord-326631-7gd3hjc3	349	9	rate	rate	NN
cord-326631-7gd3hjc3	349	10	is	be	VBZ
cord-326631-7gd3hjc3	349	11	the	the	DT
cord-326631-7gd3hjc3	349	12	same	same	JJ
cord-326631-7gd3hjc3	349	13	in	in	IN
cord-326631-7gd3hjc3	349	14	all	all	DT
cord-326631-7gd3hjc3	349	15	patches	patch	NNS
cord-326631-7gd3hjc3	349	16	.	.	.
cord-326631-7gd3hjc3	350	1	If	if	IN
cord-326631-7gd3hjc3	350	2	,	,	,
cord-326631-7gd3hjc3	350	3	on	on	IN
cord-326631-7gd3hjc3	350	4	the	the	DT
cord-326631-7gd3hjc3	350	5	other	other	JJ
cord-326631-7gd3hjc3	350	6	hand	hand	NN
cord-326631-7gd3hjc3	350	7	,	,	,
cord-326631-7gd3hjc3	350	8	we	-PRON-	PRP
cord-326631-7gd3hjc3	350	9	start	start	VBP
cord-326631-7gd3hjc3	350	10	with	with	IN
cord-326631-7gd3hjc3	350	11	Eq	Eq	NNP
cord-326631-7gd3hjc3	350	12	.	.	.
cord-326631-7gd3hjc3	351	1	(	(	-LRB-
cord-326631-7gd3hjc3	351	2	30	30	CD
cord-326631-7gd3hjc3	351	3	)	)	-RRB-
cord-326631-7gd3hjc3	351	4	as	as	IN
cord-326631-7gd3hjc3	351	5	an	an	DT
cord-326631-7gd3hjc3	351	6	assumption	assumption	NN
cord-326631-7gd3hjc3	351	7	,	,	,
cord-326631-7gd3hjc3	351	8	then	then	RB
cord-326631-7gd3hjc3	351	9	inserting	insert	VBG
cord-326631-7gd3hjc3	351	10	Eq	Eq	NNP
cord-326631-7gd3hjc3	351	11	.	.	.
cord-326631-7gd3hjc3	352	1	(	(	-LRB-
cord-326631-7gd3hjc3	352	2	29	29	CD
cord-326631-7gd3hjc3	352	3	)	)	-RRB-
cord-326631-7gd3hjc3	352	4	in	in	IN
cord-326631-7gd3hjc3	352	5	Eq	Eq	NNP
cord-326631-7gd3hjc3	352	6	.	.	.
cord-326631-7gd3hjc3	353	1	(	(	-LRB-
cord-326631-7gd3hjc3	353	2	27	27	CD
cord-326631-7gd3hjc3	353	3	)	)	-RRB-
cord-326631-7gd3hjc3	353	4	Restricting	restrict	VBG
cord-326631-7gd3hjc3	353	5	attention	attention	NN
cord-326631-7gd3hjc3	353	6	to	to	IN
cord-326631-7gd3hjc3	353	7	situations	situation	NNS
cord-326631-7gd3hjc3	353	8	in	in	IN
cord-326631-7gd3hjc3	353	9	which	which	WDT
cord-326631-7gd3hjc3	353	10	the	the	DT
cord-326631-7gd3hjc3	353	11	transmission	transmission	NN
cord-326631-7gd3hjc3	353	12	rate	rate	NN
cord-326631-7gd3hjc3	353	13	is	be	VBZ
cord-326631-7gd3hjc3	353	14	the	the	DT
cord-326631-7gd3hjc3	353	15	same	same	JJ
cord-326631-7gd3hjc3	353	16	in	in	IN
cord-326631-7gd3hjc3	353	17	every	every	DT
cord-326631-7gd3hjc3	353	18	patch	patch	NN
cord-326631-7gd3hjc3	353	19	may	may	MD
cord-326631-7gd3hjc3	353	20	seem	seem	VB
cord-326631-7gd3hjc3	353	21	to	to	TO
cord-326631-7gd3hjc3	353	22	be	be	VB
cord-326631-7gd3hjc3	353	23	an	an	DT
cord-326631-7gd3hjc3	353	24	extremely	extremely	RB
cord-326631-7gd3hjc3	353	25	stringent	stringent	JJ
cord-326631-7gd3hjc3	353	26	constraint	constraint	NN
cord-326631-7gd3hjc3	353	27	.	.	.
cord-326631-7gd3hjc3	354	1	In	in	IN
cord-326631-7gd3hjc3	354	2	fact	fact	NN
cord-326631-7gd3hjc3	354	3	,	,	,
cord-326631-7gd3hjc3	354	4	this	this	DT
cord-326631-7gd3hjc3	354	5	is	be	VBZ
cord-326631-7gd3hjc3	354	6	often	often	RB
cord-326631-7gd3hjc3	354	7	the	the	DT
cord-326631-7gd3hjc3	354	8	situation	situation	NN
cord-326631-7gd3hjc3	354	9	of	of	IN
cord-326631-7gd3hjc3	354	10	interest	interest	NN
cord-326631-7gd3hjc3	354	11	.	.	.
cord-326631-7gd3hjc3	355	1	For	for	IN
cord-326631-7gd3hjc3	355	2	example	example	NN
cord-326631-7gd3hjc3	355	3	,	,	,
cord-326631-7gd3hjc3	355	4	individuals	individual	NNS
cord-326631-7gd3hjc3	355	5	who	who	WP
cord-326631-7gd3hjc3	355	6	normally	normally	RB
cord-326631-7gd3hjc3	355	7	reside	reside	VBP
cord-326631-7gd3hjc3	355	8	in	in	IN
cord-326631-7gd3hjc3	355	9	Boston	Boston	NNP
cord-326631-7gd3hjc3	355	10	,	,	,
cord-326631-7gd3hjc3	355	11	Philadelphia	Philadelphia	NNP
cord-326631-7gd3hjc3	355	12	or	or	CC
cord-326631-7gd3hjc3	355	13	New	New	NNP
cord-326631-7gd3hjc3	355	14	York	York	NNP
cord-326631-7gd3hjc3	355	15	can	can	MD
cord-326631-7gd3hjc3	355	16	expect	expect	VB
cord-326631-7gd3hjc3	355	17	to	to	TO
cord-326631-7gd3hjc3	355	18	contact	contact	VB
cord-326631-7gd3hjc3	355	19	similar	similar	JJ
cord-326631-7gd3hjc3	355	20	numbers	number	NNS
cord-326631-7gd3hjc3	355	21	of	of	IN
cord-326631-7gd3hjc3	355	22	people	people	NNS
cord-326631-7gd3hjc3	355	23	each	each	DT
cord-326631-7gd3hjc3	355	24	day	day	NN
cord-326631-7gd3hjc3	355	25	,	,	,
cord-326631-7gd3hjc3	355	26	even	even	RB
cord-326631-7gd3hjc3	355	27	though	though	IN
cord-326631-7gd3hjc3	355	28	the	the	DT
cord-326631-7gd3hjc3	355	29	New	New	NNP
cord-326631-7gd3hjc3	355	30	York	York	NNP
cord-326631-7gd3hjc3	355	31	metropolitan	metropolitan	JJ
cord-326631-7gd3hjc3	355	32	area	area	NN
cord-326631-7gd3hjc3	355	33	has	have	VBZ
cord-326631-7gd3hjc3	355	34	a	a	DT
cord-326631-7gd3hjc3	355	35	population	population	NN
cord-326631-7gd3hjc3	355	36	that	that	WDT
cord-326631-7gd3hjc3	355	37	is	be	VBZ
cord-326631-7gd3hjc3	355	38	several	several	JJ
cord-326631-7gd3hjc3	355	39	times	time	NNS
cord-326631-7gd3hjc3	355	40	larger	large	JJR
cord-326631-7gd3hjc3	355	41	than	than	IN
cord-326631-7gd3hjc3	355	42	the	the	DT
cord-326631-7gd3hjc3	355	43	other	other	JJ
cord-326631-7gd3hjc3	355	44	two	two	CD
cord-326631-7gd3hjc3	355	45	.	.	.
cord-326631-7gd3hjc3	356	1	More	more	RBR
cord-326631-7gd3hjc3	356	2	generally	generally	RB
cord-326631-7gd3hjc3	356	3	,	,	,
cord-326631-7gd3hjc3	356	4	if	if	IN
cord-326631-7gd3hjc3	356	5	patches	patch	NNS
cord-326631-7gd3hjc3	356	6	represent	represent	VBP
cord-326631-7gd3hjc3	356	7	large	large	JJ
cord-326631-7gd3hjc3	356	8	cities	city	NNS
cord-326631-7gd3hjc3	356	9	in	in	IN
cord-326631-7gd3hjc3	356	10	a	a	DT
cord-326631-7gd3hjc3	356	11	given	give	VBN
cord-326631-7gd3hjc3	356	12	country	country	NN
cord-326631-7gd3hjc3	356	13	,	,	,
cord-326631-7gd3hjc3	356	14	then	then	RB
cord-326631-7gd3hjc3	356	15	it	-PRON-	PRP
cord-326631-7gd3hjc3	356	16	is	be	VBZ
cord-326631-7gd3hjc3	356	17	reasonable	reasonable	JJ
cord-326631-7gd3hjc3	356	18	to	to	TO
cord-326631-7gd3hjc3	356	19	expect	expect	VB
cord-326631-7gd3hjc3	356	20	that	that	IN
cord-326631-7gd3hjc3	356	21	the	the	DT
cord-326631-7gd3hjc3	356	22	number	number	NN
cord-326631-7gd3hjc3	356	23	of	of	IN
cord-326631-7gd3hjc3	356	24	contacts	contact	NNS
cord-326631-7gd3hjc3	356	25	an	an	DT
cord-326631-7gd3hjc3	356	26	individual	individual	NN
cord-326631-7gd3hjc3	356	27	has	have	VBZ
cord-326631-7gd3hjc3	356	28	will	will	MD
cord-326631-7gd3hjc3	356	29	not	not	RB
cord-326631-7gd3hjc3	356	30	depend	depend	VB
cord-326631-7gd3hjc3	356	31	strongly	strongly	RB
cord-326631-7gd3hjc3	356	32	on	on	IN
cord-326631-7gd3hjc3	356	33	the	the	DT
cord-326631-7gd3hjc3	356	34	size	size	NN
cord-326631-7gd3hjc3	356	35	of	of	IN
cord-326631-7gd3hjc3	356	36	the	the	DT
cord-326631-7gd3hjc3	356	37	city	city	NN
cord-326631-7gd3hjc3	356	38	.	.	.
cord-326631-7gd3hjc3	357	1	Given	give	VBN
cord-326631-7gd3hjc3	357	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	357	3	.	.	.
cord-326631-7gd3hjc3	358	1	(	(	-LRB-
cord-326631-7gd3hjc3	358	2	30	30	CD
cord-326631-7gd3hjc3	358	3	)	)	-RRB-
cord-326631-7gd3hjc3	358	4	,	,	,
cord-326631-7gd3hjc3	358	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	358	6	can	can	MD
cord-326631-7gd3hjc3	358	7	write	write	VB
cord-326631-7gd3hjc3	358	8	where	where	WRB
cord-326631-7gd3hjc3	358	9	P	p	NN
cord-326631-7gd3hjc3	358	10	i	i	PRP
cord-326631-7gd3hjc3	358	11	j	j	NNP
cord-326631-7gd3hjc3	358	12	is	be	VBZ
cord-326631-7gd3hjc3	358	13	the	the	DT
cord-326631-7gd3hjc3	358	14	probability	probability	NN
cord-326631-7gd3hjc3	358	15	,	,	,
cord-326631-7gd3hjc3	358	16	for	for	IN
cord-326631-7gd3hjc3	358	17	an	an	DT
cord-326631-7gd3hjc3	358	18	individual	individual	NN
cord-326631-7gd3hjc3	358	19	in	in	IN
cord-326631-7gd3hjc3	358	20	patch	patch	NN
cord-326631-7gd3hjc3	359	1	i	i	PRP
cord-326631-7gd3hjc3	359	2	,	,	,
cord-326631-7gd3hjc3	359	3	that	that	IN
cord-326631-7gd3hjc3	359	4	a	a	DT
cord-326631-7gd3hjc3	359	5	given	give	VBN
cord-326631-7gd3hjc3	359	6	contact	contact	NN
cord-326631-7gd3hjc3	359	7	is	be	VBZ
cord-326631-7gd3hjc3	359	8	with	with	IN
cord-326631-7gd3hjc3	359	9	an	an	DT
cord-326631-7gd3hjc3	359	10	individual	individual	NN
cord-326631-7gd3hjc3	359	11	in	in	IN
cord-326631-7gd3hjc3	359	12	patch	patch	NN
cord-326631-7gd3hjc3	359	13	j	j	NNP
cord-326631-7gd3hjc3	359	14	,	,	,
cord-326631-7gd3hjc3	359	15	and	and	CC
cord-326631-7gd3hjc3	359	16	β	β	NN
cord-326631-7gd3hjc3	359	17	is	be	VBZ
cord-326631-7gd3hjc3	359	18	the	the	DT
cord-326631-7gd3hjc3	359	19	transmission	transmission	NN
cord-326631-7gd3hjc3	359	20	rate	rate	NN
cord-326631-7gd3hjc3	359	21	(	(	-LRB-
cord-326631-7gd3hjc3	359	22	the	the	DT
cord-326631-7gd3hjc3	359	23	product	product	NN
cord-326631-7gd3hjc3	359	24	of	of	IN
cord-326631-7gd3hjc3	359	25	the	the	DT
cord-326631-7gd3hjc3	359	26	number	number	NN
cord-326631-7gd3hjc3	359	27	of	of	IN
cord-326631-7gd3hjc3	359	28	contacts	contact	NNS
cord-326631-7gd3hjc3	359	29	per	per	IN
cord-326631-7gd3hjc3	359	30	unit	unit	NN
cord-326631-7gd3hjc3	359	31	time	time	NN
cord-326631-7gd3hjc3	359	32	and	and	CC
cord-326631-7gd3hjc3	359	33	the	the	DT
cord-326631-7gd3hjc3	359	34	probability	probability	NN
cord-326631-7gd3hjc3	359	35	that	that	IN
cord-326631-7gd3hjc3	359	36	a	a	DT
cord-326631-7gd3hjc3	359	37	contact	contact	NN
cord-326631-7gd3hjc3	359	38	between	between	IN
cord-326631-7gd3hjc3	359	39	a	a	DT
cord-326631-7gd3hjc3	359	40	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	359	41	and	and	CC
cord-326631-7gd3hjc3	359	42	an	an	DT
cord-326631-7gd3hjc3	359	43	infectious	infectious	JJ
cord-326631-7gd3hjc3	359	44	individual	individual	JJ
cord-326631-7gd3hjc3	359	45	leads	lead	VBZ
cord-326631-7gd3hjc3	359	46	to	to	IN
cord-326631-7gd3hjc3	359	47	transmission	transmission	NN
cord-326631-7gd3hjc3	359	48	)	)	-RRB-
cord-326631-7gd3hjc3	359	49	.	.	.
cord-326631-7gd3hjc3	360	1	Note	note	VB
cord-326631-7gd3hjc3	360	2	that	that	IN
cord-326631-7gd3hjc3	360	3	since	since	IN
cord-326631-7gd3hjc3	360	4	the	the	DT
cord-326631-7gd3hjc3	360	5	rows	row	NNS
cord-326631-7gd3hjc3	360	6	of	of	IN
cord-326631-7gd3hjc3	360	7	the	the	DT
cord-326631-7gd3hjc3	360	8	matrix	matrix	NN
cord-326631-7gd3hjc3	360	9	P	p	NN
cord-326631-7gd3hjc3	360	10	are	be	VBP
cord-326631-7gd3hjc3	360	11	probability	probability	NN
cord-326631-7gd3hjc3	360	12	distributions	distribution	NNS
cord-326631-7gd3hjc3	360	13	,	,	,
cord-326631-7gd3hjc3	360	14	it	-PRON-	PRP
cord-326631-7gd3hjc3	360	15	follows	follow	VBZ
cord-326631-7gd3hjc3	360	16	that	that	IN
cord-326631-7gd3hjc3	360	17	n	n	NN
cord-326631-7gd3hjc3	360	18	j=1	j=1	NNP
cord-326631-7gd3hjc3	360	19	P	P	NNP
cord-326631-7gd3hjc3	360	20	i	i	NN
cord-326631-7gd3hjc3	360	21	j	j	NN
cord-326631-7gd3hjc3	360	22	=	=	SYM
cord-326631-7gd3hjc3	360	23	1	1	CD
cord-326631-7gd3hjc3	360	24	,	,	,
cord-326631-7gd3hjc3	360	25	i	i	PRP
cord-326631-7gd3hjc3	360	26	=	=	SYM
cord-326631-7gd3hjc3	360	27	1	1	CD
cord-326631-7gd3hjc3	360	28	,	,	,
cord-326631-7gd3hjc3	360	29	.	.	.
cord-326631-7gd3hjc3	360	30	.	.	.
cord-326631-7gd3hjc3	360	31	.	.	.
cord-326631-7gd3hjc3	361	1	,	,	,
cord-326631-7gd3hjc3	361	2	n	n	JJ
cord-326631-7gd3hjc3	361	3	,	,	,
cord-326631-7gd3hjc3	361	4	i.e.	i.e.	FW
cord-326631-7gd3hjc3	361	5	,	,	,
cord-326631-7gd3hjc3	361	6	P	p	NN
cord-326631-7gd3hjc3	361	7	is	be	VBZ
cord-326631-7gd3hjc3	361	8	a	a	DT
cord-326631-7gd3hjc3	361	9	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	361	10	matrix	matrix	NN
cord-326631-7gd3hjc3	361	11	(	(	-LRB-
cord-326631-7gd3hjc3	361	12	Horn	Horn	NNP
cord-326631-7gd3hjc3	361	13	and	and	CC
cord-326631-7gd3hjc3	361	14	Johnson	Johnson	NNP
cord-326631-7gd3hjc3	361	15	,	,	,
cord-326631-7gd3hjc3	361	16	1985	1985	CD
cord-326631-7gd3hjc3	361	17	)	)	-RRB-
cord-326631-7gd3hjc3	361	18	.	.	.
cord-326631-7gd3hjc3	362	1	For	for	IN
cord-326631-7gd3hjc3	362	2	convenience	convenience	NN
cord-326631-7gd3hjc3	362	3	,	,	,
cord-326631-7gd3hjc3	362	4	we	-PRON-	PRP
cord-326631-7gd3hjc3	362	5	make	make	VBP
cord-326631-7gd3hjc3	362	6	the	the	DT
cord-326631-7gd3hjc3	362	7	mild	mild	JJ
cord-326631-7gd3hjc3	362	8	assumption	assumption	NN
cord-326631-7gd3hjc3	362	9	that	that	IN
cord-326631-7gd3hjc3	362	10	P	p	NN
cord-326631-7gd3hjc3	362	11	i	i	NN
cord-326631-7gd3hjc3	362	12	j	j	NN
cord-326631-7gd3hjc3	362	13	>	>	XX
cord-326631-7gd3hjc3	363	1	0	0	NFP
cord-326631-7gd3hjc3	364	1	for	for	IN
cord-326631-7gd3hjc3	364	2	all	all	DT
cord-326631-7gd3hjc3	364	3	i	i	PRP
cord-326631-7gd3hjc3	364	4	and	and	CC
cord-326631-7gd3hjc3	364	5	j	j	NNP
cord-326631-7gd3hjc3	364	6	,	,	,
cord-326631-7gd3hjc3	364	7	i.e.	i.e.	FW
cord-326631-7gd3hjc3	364	8	,	,	,
cord-326631-7gd3hjc3	364	9	for	for	IN
cord-326631-7gd3hjc3	364	10	any	any	DT
cord-326631-7gd3hjc3	364	11	pair	pair	NN
cord-326631-7gd3hjc3	364	12	of	of	IN
cord-326631-7gd3hjc3	364	13	patches	patch	NNS
cord-326631-7gd3hjc3	364	14	,	,	,
cord-326631-7gd3hjc3	364	15	there	there	EX
cord-326631-7gd3hjc3	364	16	is	be	VBZ
cord-326631-7gd3hjc3	364	17	a	a	DT
cord-326631-7gd3hjc3	364	18	non	non	JJ
cord-326631-7gd3hjc3	364	19	-	-	JJ
cord-326631-7gd3hjc3	364	20	zero	zero	JJ
cord-326631-7gd3hjc3	364	21	probability	probability	NN
cord-326631-7gd3hjc3	364	22	that	that	IN
cord-326631-7gd3hjc3	364	23	residents	resident	NNS
cord-326631-7gd3hjc3	364	24	of	of	IN
cord-326631-7gd3hjc3	364	25	the	the	DT
cord-326631-7gd3hjc3	364	26	two	two	CD
cord-326631-7gd3hjc3	364	27	patches	patch	NNS
cord-326631-7gd3hjc3	364	28	will	will	MD
cord-326631-7gd3hjc3	364	29	come	come	VB
cord-326631-7gd3hjc3	364	30	into	into	IN
cord-326631-7gd3hjc3	364	31	contact	contact	NN
cord-326631-7gd3hjc3	364	32	.	.	.
cord-326631-7gd3hjc3	365	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	365	2	then	then	RB
cord-326631-7gd3hjc3	365	3	follows	follow	VBZ
cord-326631-7gd3hjc3	365	4	that	that	IN
cord-326631-7gd3hjc3	365	5	if	if	IN
cord-326631-7gd3hjc3	365	6	the	the	DT
cord-326631-7gd3hjc3	365	7	final	final	JJ
cord-326631-7gd3hjc3	365	8	size	size	NN
cord-326631-7gd3hjc3	365	9	Z	Z	NNP
cord-326631-7gd3hjc3	365	10	is	be	VBZ
cord-326631-7gd3hjc3	365	11	positive	positive	JJ
cord-326631-7gd3hjc3	365	12	then	then	RB
cord-326631-7gd3hjc3	365	13	the	the	DT
cord-326631-7gd3hjc3	365	14	final	final	JJ
cord-326631-7gd3hjc3	365	15	size	size	NN
cord-326631-7gd3hjc3	365	16	Z	Z	NNP
cord-326631-7gd3hjc3	365	17	i	i	PRP
cord-326631-7gd3hjc3	365	18	is	be	VBZ
cord-326631-7gd3hjc3	365	19	strictly	strictly	RB
cord-326631-7gd3hjc3	365	20	positive	positive	JJ
cord-326631-7gd3hjc3	365	21	in	in	IN
cord-326631-7gd3hjc3	365	22	every	every	DT
cord-326631-7gd3hjc3	365	23	patch	patch	NN
cord-326631-7gd3hjc3	365	24	.	.	.
cord-326631-7gd3hjc3	366	1	To	to	TO
cord-326631-7gd3hjc3	366	2	see	see	VB
cord-326631-7gd3hjc3	366	3	this	this	DT
cord-326631-7gd3hjc3	366	4	,	,	,
cord-326631-7gd3hjc3	366	5	note	note	VB
cord-326631-7gd3hjc3	366	6	that	that	IN
cord-326631-7gd3hjc3	366	7	if	if	IN
cord-326631-7gd3hjc3	366	8	Z	z	NN
cord-326631-7gd3hjc3	366	9	i	i	NN
cord-326631-7gd3hjc3	366	10	=	=	SYM
cord-326631-7gd3hjc3	366	11	0	0	NFP
cord-326631-7gd3hjc3	366	12	for	for	IN
cord-326631-7gd3hjc3	366	13	some	some	DT
cord-326631-7gd3hjc3	366	14	i	i	PRP
cord-326631-7gd3hjc3	366	15	then	then	RB
cord-326631-7gd3hjc3	366	16	Eq	Eq	NNP
cord-326631-7gd3hjc3	366	17	.	.	.
cord-326631-7gd3hjc3	367	1	(	(	-LRB-
cord-326631-7gd3hjc3	367	2	27	27	CD
cord-326631-7gd3hjc3	367	3	)	)	-RRB-
cord-326631-7gd3hjc3	367	4	 	 	_SP
cord-326631-7gd3hjc3	368	1	Since	since	IN
cord-326631-7gd3hjc3	368	2	P	p	NN
cord-326631-7gd3hjc3	368	3	i	i	NN
cord-326631-7gd3hjc3	368	4	j	j	NN
cord-326631-7gd3hjc3	368	5	>	>	XX
cord-326631-7gd3hjc3	368	6	0	0	NFP
cord-326631-7gd3hjc3	368	7	implies	imply	VBZ
cord-326631-7gd3hjc3	369	1	β	β	NNP
cord-326631-7gd3hjc3	369	2	i	i	NN
cord-326631-7gd3hjc3	369	3	j	j	NNP
cord-326631-7gd3hjc3	369	4	>	>	XX
cord-326631-7gd3hjc3	370	1	0	0	NFP
cord-326631-7gd3hjc3	371	1	,	,	,
cord-326631-7gd3hjc3	371	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	371	3	.	.	.
cord-326631-7gd3hjc3	372	1	(	(	-LRB-
cord-326631-7gd3hjc3	372	2	33	33	CD
cord-326631-7gd3hjc3	372	3	)	)	-RRB-
cord-326631-7gd3hjc3	372	4	implies	imply	VBZ
cord-326631-7gd3hjc3	372	5	Z	Z	NNP
cord-326631-7gd3hjc3	372	6	j	j	NN
cord-326631-7gd3hjc3	372	7	=	=	SYM
cord-326631-7gd3hjc3	372	8	0	0	NFP
cord-326631-7gd3hjc3	372	9	for	for	IN
cord-326631-7gd3hjc3	372	10	all	all	DT
cord-326631-7gd3hjc3	372	11	j.	j.	NNP
cord-326631-7gd3hjc3	373	1	Since	since	IN
cord-326631-7gd3hjc3	373	2	P	p	NN
cord-326631-7gd3hjc3	373	3	is	be	VBZ
cord-326631-7gd3hjc3	373	4	a	a	DT
cord-326631-7gd3hjc3	373	5	positive	positive	JJ
cord-326631-7gd3hjc3	373	6	,	,	,
cord-326631-7gd3hjc3	373	7	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	373	8	matrix	matrix	NN
cord-326631-7gd3hjc3	373	9	,	,	,
cord-326631-7gd3hjc3	373	10	its	-PRON-	PRP$
cord-326631-7gd3hjc3	373	11	largest	large	JJS
cord-326631-7gd3hjc3	373	12	eigenvalue	eigenvalue	NN
cord-326631-7gd3hjc3	373	13	is	be	VBZ
cord-326631-7gd3hjc3	373	14	1	1	CD
cord-326631-7gd3hjc3	373	15	(	(	-LRB-
cord-326631-7gd3hjc3	373	16	Horn	Horn	NNP
cord-326631-7gd3hjc3	373	17	and	and	CC
cord-326631-7gd3hjc3	373	18	Johnson	Johnson	NNP
cord-326631-7gd3hjc3	373	19	,	,	,
cord-326631-7gd3hjc3	373	20	1985	1985	CD
cord-326631-7gd3hjc3	373	21	)	)	-RRB-
cord-326631-7gd3hjc3	373	22	.	.	.
cord-326631-7gd3hjc3	374	1	Consequently	consequently	RB
cord-326631-7gd3hjc3	374	2	,	,	,
cord-326631-7gd3hjc3	374	3	the	the	DT
cord-326631-7gd3hjc3	374	4	largest	large	JJS
cord-326631-7gd3hjc3	374	5	eigenvalue	eigenvalue	NN
cord-326631-7gd3hjc3	374	6	of	of	IN
cord-326631-7gd3hjc3	374	7	B	b	NN
cord-326631-7gd3hjc3	374	8	=	=	SYM
cord-326631-7gd3hjc3	374	9	β	β	NN
cord-326631-7gd3hjc3	374	10	P	p	NN
cord-326631-7gd3hjc3	374	11	is	be	VBZ
cord-326631-7gd3hjc3	374	12	β	β	NN
cord-326631-7gd3hjc3	374	13	and	and	CC
cord-326631-7gd3hjc3	374	14	the	the	DT
cord-326631-7gd3hjc3	374	15	basic	basic	JJ
cord-326631-7gd3hjc3	374	16	reproduction	reproduction	NN
cord-326631-7gd3hjc3	374	17	number	number	NN
cord-326631-7gd3hjc3	374	18	is	be	VBZ
cord-326631-7gd3hjc3	374	19	R	r	NN
cord-326631-7gd3hjc3	374	20	0	0	CD
cord-326631-7gd3hjc3	374	21	=	=	NFP
cord-326631-7gd3hjc3	375	1	β	β	NN
cord-326631-7gd3hjc3	375	2	γ	γ	NNP
cord-326631-7gd3hjc3	375	3	.	.	.
cord-326631-7gd3hjc3	376	1	Therefore	therefore	RB
cord-326631-7gd3hjc3	376	2	,	,	,
cord-326631-7gd3hjc3	376	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	376	4	have	have	VBP
cord-326631-7gd3hjc3	376	5	Theorem	theorem	NN
cord-326631-7gd3hjc3	376	6	9.1	9.1	CD
cord-326631-7gd3hjc3	376	7	.	.	.
cord-326631-7gd3hjc3	377	1	Consider	consider	VB
cord-326631-7gd3hjc3	377	2	the	the	DT
cord-326631-7gd3hjc3	377	3	multi	multi	JJ
cord-326631-7gd3hjc3	377	4	-	-	JJ
cord-326631-7gd3hjc3	377	5	patch	patch	JJ
cord-326631-7gd3hjc3	377	6	SIR	SIR	NNP
cord-326631-7gd3hjc3	377	7	epidemic	epidemic	NN
cord-326631-7gd3hjc3	377	8	model	model	NN
cord-326631-7gd3hjc3	377	9	specified	specify	VBN
cord-326631-7gd3hjc3	377	10	by	by	IN
cord-326631-7gd3hjc3	377	11	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	377	12	.	.	.
cord-326631-7gd3hjc3	378	1	(	(	-LRB-
cord-326631-7gd3hjc3	378	2	26	26	CD
cord-326631-7gd3hjc3	378	3	)	)	-RRB-
cord-326631-7gd3hjc3	378	4	.	.	.
cord-326631-7gd3hjc3	379	1	Suppose	suppose	VB
cord-326631-7gd3hjc3	379	2	the	the	DT
cord-326631-7gd3hjc3	379	3	transmission	transmission	NN
cord-326631-7gd3hjc3	379	4	rate	rate	NN
cord-326631-7gd3hjc3	379	5	in	in	IN
cord-326631-7gd3hjc3	379	6	each	each	DT
cord-326631-7gd3hjc3	379	7	patch	patch	NN
cord-326631-7gd3hjc3	379	8	is	be	VBZ
cord-326631-7gd3hjc3	379	9	the	the	DT
cord-326631-7gd3hjc3	379	10	same	same	JJ
cord-326631-7gd3hjc3	379	11	,	,	,
cord-326631-7gd3hjc3	379	12	i.e.	i.e.	FW
cord-326631-7gd3hjc3	379	13	,	,	,
cord-326631-7gd3hjc3	379	14	n	n	NN
cord-326631-7gd3hjc3	379	15	j=1	j=1	NNP
cord-326631-7gd3hjc3	379	16	β	β	XX
cord-326631-7gd3hjc3	380	1	i	i	PRP
cord-326631-7gd3hjc3	380	2	j	j	NNP
cord-326631-7gd3hjc3	380	3	=	=	SYM
cord-326631-7gd3hjc3	380	4	β	β	NNP
cord-326631-7gd3hjc3	380	5	,	,	,
cord-326631-7gd3hjc3	380	6	for	for	IN
cord-326631-7gd3hjc3	380	7	each	each	DT
cord-326631-7gd3hjc3	380	8	i.	i.	NN
cord-326631-7gd3hjc3	381	1	Then	then	RB
cord-326631-7gd3hjc3	381	2	,	,	,
cord-326631-7gd3hjc3	381	3	in	in	IN
cord-326631-7gd3hjc3	381	4	the	the	DT
cord-326631-7gd3hjc3	381	5	limit	limit	NN
cord-326631-7gd3hjc3	381	6	that	that	IN
cord-326631-7gd3hjc3	381	7	the	the	DT
cord-326631-7gd3hjc3	381	8	initial	initial	JJ
cord-326631-7gd3hjc3	381	9	proportion	proportion	NN
cord-326631-7gd3hjc3	381	10	of	of	IN
cord-326631-7gd3hjc3	381	11	individuals	individual	NNS
cord-326631-7gd3hjc3	381	12	that	that	WDT
cord-326631-7gd3hjc3	381	13	are	be	VBP
cord-326631-7gd3hjc3	381	14	infectious	infectious	JJ
cord-326631-7gd3hjc3	381	15	is	be	VBZ
cord-326631-7gd3hjc3	382	1	small	small	JJ
cord-326631-7gd3hjc3	382	2	,	,	,
cord-326631-7gd3hjc3	382	3	i.e.	i.e.	FW
cord-326631-7gd3hjc3	382	4	,	,	,
cord-326631-7gd3hjc3	382	5	I	-PRON-	PRP
cord-326631-7gd3hjc3	383	1	i	i	PRP
cord-326631-7gd3hjc3	383	2	(	(	-LRB-
cord-326631-7gd3hjc3	383	3	0	0	NFP
cord-326631-7gd3hjc3	383	4	)	)	-RRB-
cord-326631-7gd3hjc3	384	1	→	→	SYM
cord-326631-7gd3hjc3	384	2	0	0	CD
cord-326631-7gd3hjc3	384	3	for	for	IN
cord-326631-7gd3hjc3	384	4	each	each	DT
cord-326631-7gd3hjc3	384	5	i	i	PRP
cord-326631-7gd3hjc3	384	6	,	,	,
cord-326631-7gd3hjc3	384	7	the	the	DT
cord-326631-7gd3hjc3	384	8	final	final	JJ
cord-326631-7gd3hjc3	384	9	size	size	NN
cord-326631-7gd3hjc3	384	10	Z	z	NN
cord-326631-7gd3hjc3	384	11	of	of	IN
cord-326631-7gd3hjc3	384	12	an	an	DT
cord-326631-7gd3hjc3	384	13	epidemic	epidemic	NN
cord-326631-7gd3hjc3	384	14	is	be	VBZ
cord-326631-7gd3hjc3	384	15	given	give	VBN
cord-326631-7gd3hjc3	384	16	implicitly	implicitly	RB
cord-326631-7gd3hjc3	384	17	by	by	IN
cord-326631-7gd3hjc3	384	18	Eq	Eq	NNP
cord-326631-7gd3hjc3	384	19	.	.	.
cord-326631-7gd3hjc3	385	1	(	(	-LRB-
cord-326631-7gd3hjc3	385	2	5	5	LS
cord-326631-7gd3hjc3	385	3	)	)	-RRB-
cord-326631-7gd3hjc3	385	4	,	,	,
cord-326631-7gd3hjc3	385	5	or	or	CC
cord-326631-7gd3hjc3	385	6	explicitly	explicitly	RB
cord-326631-7gd3hjc3	385	7	by	by	IN
cord-326631-7gd3hjc3	385	8	Eq	Eq	NNP
cord-326631-7gd3hjc3	385	9	.	.	.
cord-326631-7gd3hjc3	386	1	(	(	-LRB-
cord-326631-7gd3hjc3	386	2	A.2	a.2	NN
cord-326631-7gd3hjc3	386	3	)	)	-RRB-
cord-326631-7gd3hjc3	386	4	,	,	,
cord-326631-7gd3hjc3	386	5	where	where	WRB
cord-326631-7gd3hjc3	386	6	R	r	NN
cord-326631-7gd3hjc3	386	7	0	0	CD
cord-326631-7gd3hjc3	386	8	=	=	NFP
cord-326631-7gd3hjc3	387	1	β	β	NN
cord-326631-7gd3hjc3	387	2	γ	γ	NNP
cord-326631-7gd3hjc3	387	3	.	.	.
cord-326631-7gd3hjc3	388	1	At	at	IN
cord-326631-7gd3hjc3	388	2	this	this	DT
cord-326631-7gd3hjc3	388	3	point	point	NN
cord-326631-7gd3hjc3	388	4	,	,	,
cord-326631-7gd3hjc3	388	5	it	-PRON-	PRP
cord-326631-7gd3hjc3	388	6	will	will	MD
cord-326631-7gd3hjc3	388	7	come	come	VB
cord-326631-7gd3hjc3	388	8	as	as	IN
cord-326631-7gd3hjc3	388	9	no	no	DT
cord-326631-7gd3hjc3	388	10	surprise	surprise	NN
cord-326631-7gd3hjc3	388	11	that	that	IN
cord-326631-7gd3hjc3	388	12	with	with	IN
cord-326631-7gd3hjc3	388	13	some	some	DT
cord-326631-7gd3hjc3	388	14	effort	effort	NN
cord-326631-7gd3hjc3	388	15	in	in	IN
cord-326631-7gd3hjc3	388	16	keeping	keep	VBG
cord-326631-7gd3hjc3	388	17	track	track	NN
cord-326631-7gd3hjc3	388	18	of	of	IN
cord-326631-7gd3hjc3	388	19	notation	notation	NN
cord-326631-7gd3hjc3	388	20	,	,	,
cord-326631-7gd3hjc3	388	21	Theorem	theorem	NN
cord-326631-7gd3hjc3	388	22	9.1	9.1	CD
cord-326631-7gd3hjc3	388	23	can	can	MD
cord-326631-7gd3hjc3	388	24	be	be	VB
cord-326631-7gd3hjc3	388	25	generalized	generalize	VBN
cord-326631-7gd3hjc3	388	26	to	to	IN
cord-326631-7gd3hjc3	388	27	a	a	DT
cord-326631-7gd3hjc3	388	28	multi	multi	JJ
cord-326631-7gd3hjc3	388	29	-	-	JJ
cord-326631-7gd3hjc3	388	30	patch	patch	NN
cord-326631-7gd3hjc3	388	31	SI	si	NN
cord-326631-7gd3hjc3	388	32	n	n	NNP
cord-326631-7gd3hjc3	388	33	R	r	NN
cord-326631-7gd3hjc3	388	34	model	model	NN
cord-326631-7gd3hjc3	388	35	with	with	IN
cord-326631-7gd3hjc3	388	36	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	388	37	distributed	distribute	VBN
cord-326631-7gd3hjc3	388	38	stage	stage	NN
cord-326631-7gd3hjc3	388	39	durations	duration	NNS
cord-326631-7gd3hjc3	388	40	and	and	CC
cord-326631-7gd3hjc3	388	41	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	388	42	distributed	distribute	VBN
cord-326631-7gd3hjc3	388	43	transmission	transmission	NN
cord-326631-7gd3hjc3	388	44	rates	rate	NNS
cord-326631-7gd3hjc3	388	45	.	.	.
cord-326631-7gd3hjc3	388	46	 	 	_SP
cord-326631-7gd3hjc3	389	1	Equations	equation	NNS
cord-326631-7gd3hjc3	389	2	(	(	-LRB-
cord-326631-7gd3hjc3	389	3	26	26	CD
cord-326631-7gd3hjc3	389	4	)	)	-RRB-
cord-326631-7gd3hjc3	389	5	,	,	,
cord-326631-7gd3hjc3	389	6	which	which	WDT
cord-326631-7gd3hjc3	389	7	specify	specify	VBP
cord-326631-7gd3hjc3	389	8	the	the	DT
cord-326631-7gd3hjc3	389	9	spatially	spatially	RB
cord-326631-7gd3hjc3	389	10	heterogeneous	heterogeneous	JJ
cord-326631-7gd3hjc3	389	11	model	model	NN
cord-326631-7gd3hjc3	389	12	we	-PRON-	PRP
cord-326631-7gd3hjc3	389	13	analyzed	analyze	VBD
cord-326631-7gd3hjc3	389	14	in	in	IN
cord-326631-7gd3hjc3	389	15	the	the	DT
cord-326631-7gd3hjc3	389	16	previous	previous	JJ
cord-326631-7gd3hjc3	389	17	section	section	NN
cord-326631-7gd3hjc3	389	18	,	,	,
cord-326631-7gd3hjc3	389	19	can	can	MD
cord-326631-7gd3hjc3	389	20	be	be	VB
cord-326631-7gd3hjc3	389	21	interpretted	interprette	VBN
cord-326631-7gd3hjc3	389	22	as	as	IN
cord-326631-7gd3hjc3	389	23	representing	represent	VBG
cord-326631-7gd3hjc3	389	24	other	other	JJ
cord-326631-7gd3hjc3	389	25	types	type	NNS
cord-326631-7gd3hjc3	389	26	of	of	IN
cord-326631-7gd3hjc3	389	27	social	social	JJ
cord-326631-7gd3hjc3	389	28	heterogeneities	heterogeneity	NNS
cord-326631-7gd3hjc3	389	29	,	,	,
cord-326631-7gd3hjc3	389	30	which	which	WDT
cord-326631-7gd3hjc3	389	31	are	be	VBP
cord-326631-7gd3hjc3	389	32	known	know	VBN
cord-326631-7gd3hjc3	389	33	to	to	TO
cord-326631-7gd3hjc3	389	34	yield	yield	VB
cord-326631-7gd3hjc3	389	35	different	different	JJ
cord-326631-7gd3hjc3	389	36	final	final	JJ
cord-326631-7gd3hjc3	389	37	size	size	NN
cord-326631-7gd3hjc3	389	38	formulae	formula	NNS
cord-326631-7gd3hjc3	389	39	(	(	-LRB-
cord-326631-7gd3hjc3	389	40	Gart	Gart	NNP
cord-326631-7gd3hjc3	389	41	,	,	,
cord-326631-7gd3hjc3	389	42	1968	1968	CD
cord-326631-7gd3hjc3	389	43	;	;	:
cord-326631-7gd3hjc3	389	44	Dwyer	Dwyer	NNP
cord-326631-7gd3hjc3	389	45	et	et	NNP
cord-326631-7gd3hjc3	389	46	al	al	NNP
cord-326631-7gd3hjc3	389	47	.	.	NNP
cord-326631-7gd3hjc3	389	48	,	,	,
cord-326631-7gd3hjc3	389	49	2000	2000	CD
cord-326631-7gd3hjc3	389	50	;	;	:
cord-326631-7gd3hjc3	389	51	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	389	52	and	and	CC
cord-326631-7gd3hjc3	389	53	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	389	54	,	,	,
cord-326631-7gd3hjc3	389	55	2000	2000	CD
cord-326631-7gd3hjc3	389	56	;	;	:
cord-326631-7gd3hjc3	389	57	Andreasen	Andreasen	NNP
cord-326631-7gd3hjc3	389	58	,	,	,
cord-326631-7gd3hjc3	389	59	2003	2003	CD
cord-326631-7gd3hjc3	389	60	)	)	-RRB-
cord-326631-7gd3hjc3	389	61	.	.	.
cord-326631-7gd3hjc3	390	1	In	in	IN
cord-326631-7gd3hjc3	390	2	this	this	DT
cord-326631-7gd3hjc3	390	3	section	section	NN
cord-326631-7gd3hjc3	390	4	,	,	,
cord-326631-7gd3hjc3	390	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	390	6	briefly	briefly	RB
cord-326631-7gd3hjc3	390	7	discuss	discuss	VBP
cord-326631-7gd3hjc3	390	8	two	two	CD
cord-326631-7gd3hjc3	390	9	other	other	JJ
cord-326631-7gd3hjc3	390	10	interpretations	interpretation	NNS
cord-326631-7gd3hjc3	390	11	,	,	,
cord-326631-7gd3hjc3	390	12	which	which	WDT
cord-326631-7gd3hjc3	390	13	lead	lead	VBP
cord-326631-7gd3hjc3	390	14	to	to	IN
cord-326631-7gd3hjc3	390	15	a	a	DT
cord-326631-7gd3hjc3	390	16	transmision	transmision	NN
cord-326631-7gd3hjc3	390	17	matrix	matrix	NN
cord-326631-7gd3hjc3	390	18	that	that	WDT
cord-326631-7gd3hjc3	390	19	is	be	VBZ
cord-326631-7gd3hjc3	390	20	not	not	RB
cord-326631-7gd3hjc3	390	21	proportional	proportional	JJ
cord-326631-7gd3hjc3	390	22	to	to	IN
cord-326631-7gd3hjc3	390	23	a	a	DT
cord-326631-7gd3hjc3	390	24	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	390	25	matrix	matrix	NN
cord-326631-7gd3hjc3	390	26	and	and	CC
cord-326631-7gd3hjc3	390	27	will	will	MD
cord-326631-7gd3hjc3	390	28	not	not	RB
cord-326631-7gd3hjc3	390	29	yield	yield	VB
cord-326631-7gd3hjc3	390	30	the	the	DT
cord-326631-7gd3hjc3	390	31	usual	usual	JJ
cord-326631-7gd3hjc3	390	32	final	final	JJ
cord-326631-7gd3hjc3	390	33	size	size	NN
cord-326631-7gd3hjc3	390	34	formula	formula	NN
cord-326631-7gd3hjc3	390	35	(	(	-LRB-
cord-326631-7gd3hjc3	390	36	5	5	CD
cord-326631-7gd3hjc3	390	37	)	)	-RRB-
cord-326631-7gd3hjc3	390	38	.	.	.
cord-326631-7gd3hjc3	391	1	Rather	rather	RB
cord-326631-7gd3hjc3	391	2	than	than	IN
cord-326631-7gd3hjc3	391	3	specifying	specify	VBG
cord-326631-7gd3hjc3	391	4	heterogeneities	heterogeneity	NNS
cord-326631-7gd3hjc3	391	5	of	of	IN
cord-326631-7gd3hjc3	391	6	transmission	transmission	NN
cord-326631-7gd3hjc3	391	7	resulting	result	VBG
cord-326631-7gd3hjc3	391	8	from	from	IN
cord-326631-7gd3hjc3	391	9	spatial	spatial	JJ
cord-326631-7gd3hjc3	391	10	structure	structure	NN
cord-326631-7gd3hjc3	391	11	,	,	,
cord-326631-7gd3hjc3	391	12	as	as	IN
cord-326631-7gd3hjc3	391	13	in	in	IN
cord-326631-7gd3hjc3	391	14	the	the	DT
cord-326631-7gd3hjc3	391	15	previous	previous	JJ
cord-326631-7gd3hjc3	391	16	section	section	NN
cord-326631-7gd3hjc3	391	17	,	,	,
cord-326631-7gd3hjc3	391	18	suppose	suppose	VB
cord-326631-7gd3hjc3	391	19	that	that	IN
cord-326631-7gd3hjc3	391	20	heterogeneities	heterogeneity	NNS
cord-326631-7gd3hjc3	391	21	arise	arise	VBP
cord-326631-7gd3hjc3	391	22	from	from	IN
cord-326631-7gd3hjc3	391	23	age	age	NN
cord-326631-7gd3hjc3	391	24	-	-	HYPH
cord-326631-7gd3hjc3	391	25	structured	structure	VBN
cord-326631-7gd3hjc3	391	26	mixing	mixing	NN
cord-326631-7gd3hjc3	391	27	patterns	pattern	NNS
cord-326631-7gd3hjc3	391	28	.	.	.
cord-326631-7gd3hjc3	392	1	One	one	CD
cord-326631-7gd3hjc3	392	2	possible	possible	JJ
cord-326631-7gd3hjc3	392	3	formulation	formulation	NN
cord-326631-7gd3hjc3	392	4	is	be	VBZ
cord-326631-7gd3hjc3	392	5	to	to	TO
cord-326631-7gd3hjc3	392	6	categorize	categorize	VB
cord-326631-7gd3hjc3	392	7	the	the	DT
cord-326631-7gd3hjc3	392	8	population	population	NN
cord-326631-7gd3hjc3	392	9	by	by	IN
cord-326631-7gd3hjc3	392	10	discrete	discrete	JJ
cord-326631-7gd3hjc3	392	11	age	age	NN
cord-326631-7gd3hjc3	392	12	cohorts	cohort	NNS
cord-326631-7gd3hjc3	392	13	,	,	,
cord-326631-7gd3hjc3	392	14	which	which	WDT
cord-326631-7gd3hjc3	392	15	is	be	VBZ
cord-326631-7gd3hjc3	392	16	typically	typically	RB
cord-326631-7gd3hjc3	392	17	motivated	motivate	VBN
cord-326631-7gd3hjc3	392	18	by	by	IN
cord-326631-7gd3hjc3	392	19	mixing	mix	VBG
cord-326631-7gd3hjc3	392	20	patterns	pattern	NNS
cord-326631-7gd3hjc3	392	21	of	of	IN
cord-326631-7gd3hjc3	392	22	children	child	NNS
cord-326631-7gd3hjc3	392	23	in	in	IN
cord-326631-7gd3hjc3	392	24	schools	school	NNS
cord-326631-7gd3hjc3	392	25	.	.	.
cord-326631-7gd3hjc3	393	1	If	if	IN
cord-326631-7gd3hjc3	393	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	393	3	consider	consider	VBP
cord-326631-7gd3hjc3	393	4	a	a	DT
cord-326631-7gd3hjc3	393	5	time	time	NN
cord-326631-7gd3hjc3	393	6	-	-	HYPH
cord-326631-7gd3hjc3	393	7	scale	scale	NN
cord-326631-7gd3hjc3	393	8	short	short	JJ
cord-326631-7gd3hjc3	393	9	enough	enough	RB
cord-326631-7gd3hjc3	393	10	that	that	DT
cord-326631-7gd3hjc3	393	11	transfer	transfer	NN
cord-326631-7gd3hjc3	393	12	from	from	IN
cord-326631-7gd3hjc3	393	13	one	one	CD
cord-326631-7gd3hjc3	393	14	cohort	cohort	NN
cord-326631-7gd3hjc3	393	15	to	to	IN
cord-326631-7gd3hjc3	393	16	the	the	DT
cord-326631-7gd3hjc3	393	17	next	next	JJ
cord-326631-7gd3hjc3	393	18	can	can	MD
cord-326631-7gd3hjc3	393	19	be	be	VB
cord-326631-7gd3hjc3	393	20	ignored	ignore	VBN
cord-326631-7gd3hjc3	393	21	,	,	,
cord-326631-7gd3hjc3	393	22	then	then	RB
cord-326631-7gd3hjc3	393	23	the	the	DT
cord-326631-7gd3hjc3	393	24	standard	standard	JJ
cord-326631-7gd3hjc3	393	25	"	"	``
cord-326631-7gd3hjc3	393	26	realistic	realistic	JJ
cord-326631-7gd3hjc3	393	27	agestructured	agestructured	JJ
cord-326631-7gd3hjc3	393	28	model	model	NN
cord-326631-7gd3hjc3	393	29	"	"	''
cord-326631-7gd3hjc3	393	30	(	(	-LRB-
cord-326631-7gd3hjc3	393	31	Schenzle	Schenzle	NNP
cord-326631-7gd3hjc3	393	32	,	,	,
cord-326631-7gd3hjc3	393	33	1984	1984	CD
cord-326631-7gd3hjc3	393	34	)	)	-RRB-
cord-326631-7gd3hjc3	393	35	reduces	reduce	VBZ
cord-326631-7gd3hjc3	393	36	to	to	IN
cord-326631-7gd3hjc3	393	37	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	393	38	.	.	.
cord-326631-7gd3hjc3	394	1	(	(	-LRB-
cord-326631-7gd3hjc3	394	2	26	26	CD
cord-326631-7gd3hjc3	394	3	)	)	-RRB-
cord-326631-7gd3hjc3	394	4	,	,	,
cord-326631-7gd3hjc3	394	5	where	where	WRB
cord-326631-7gd3hjc3	394	6	the	the	DT
cord-326631-7gd3hjc3	394	7	transmission	transmission	NN
cord-326631-7gd3hjc3	394	8	matrix	matrix	NN
cord-326631-7gd3hjc3	394	9	B	B	NNP
cord-326631-7gd3hjc3	394	10	now	now	RB
cord-326631-7gd3hjc3	394	11	refers	refer	VBZ
cord-326631-7gd3hjc3	394	12	to	to	TO
cord-326631-7gd3hjc3	394	13	contact	contact	VB
cord-326631-7gd3hjc3	394	14	patterns	pattern	NNS
cord-326631-7gd3hjc3	394	15	among	among	IN
cord-326631-7gd3hjc3	394	16	different	different	JJ
cord-326631-7gd3hjc3	394	17	age	age	NN
cord-326631-7gd3hjc3	394	18	cohorts	cohort	NNS
cord-326631-7gd3hjc3	394	19	.	.	.
cord-326631-7gd3hjc3	395	1	As	as	IN
cord-326631-7gd3hjc3	395	2	in	in	IN
cord-326631-7gd3hjc3	395	3	the	the	DT
cord-326631-7gd3hjc3	395	4	case	case	NN
cord-326631-7gd3hjc3	395	5	of	of	IN
cord-326631-7gd3hjc3	395	6	the	the	DT
cord-326631-7gd3hjc3	395	7	spatial	spatial	JJ
cord-326631-7gd3hjc3	395	8	patch	patch	NN
cord-326631-7gd3hjc3	395	9	interpretation	interpretation	NN
cord-326631-7gd3hjc3	395	10	,	,	,
cord-326631-7gd3hjc3	395	11	it	-PRON-	PRP
cord-326631-7gd3hjc3	395	12	might	may	MD
cord-326631-7gd3hjc3	395	13	be	be	VB
cord-326631-7gd3hjc3	395	14	reasonable	reasonable	JJ
cord-326631-7gd3hjc3	395	15	to	to	TO
cord-326631-7gd3hjc3	395	16	assume	assume	VB
cord-326631-7gd3hjc3	395	17	that	that	IN
cord-326631-7gd3hjc3	395	18	there	there	EX
cord-326631-7gd3hjc3	395	19	is	be	VBZ
cord-326631-7gd3hjc3	395	20	a	a	DT
cord-326631-7gd3hjc3	395	21	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	395	22	matrix	matrix	NN
cord-326631-7gd3hjc3	395	23	P	p	NN
cord-326631-7gd3hjc3	395	24	such	such	JJ
cord-326631-7gd3hjc3	395	25	that	that	DT
cord-326631-7gd3hjc3	396	1	where	where	WRB
cord-326631-7gd3hjc3	396	2	the	the	DT
cord-326631-7gd3hjc3	396	3	interpretation	interpretation	NN
cord-326631-7gd3hjc3	396	4	is	be	VBZ
cord-326631-7gd3hjc3	396	5	that	that	IN
cord-326631-7gd3hjc3	396	6	individuals	individual	NNS
cord-326631-7gd3hjc3	396	7	in	in	IN
cord-326631-7gd3hjc3	396	8	cohort	cohort	NN
cord-326631-7gd3hjc3	396	9	i	i	PRP
cord-326631-7gd3hjc3	396	10	have	have	VBP
cord-326631-7gd3hjc3	396	11	a	a	DT
cord-326631-7gd3hjc3	396	12	proportion	proportion	NN
cord-326631-7gd3hjc3	396	13	P	p	NN
cord-326631-7gd3hjc3	396	14	i	i	NNP
cord-326631-7gd3hjc3	396	15	j	j	NNP
cord-326631-7gd3hjc3	396	16	of	of	IN
cord-326631-7gd3hjc3	396	17	their	-PRON-	PRP$
cord-326631-7gd3hjc3	396	18	contacts	contact	NNS
cord-326631-7gd3hjc3	396	19	with	with	IN
cord-326631-7gd3hjc3	396	20	individuals	individual	NNS
cord-326631-7gd3hjc3	396	21	in	in	IN
cord-326631-7gd3hjc3	396	22	cohort	cohort	NN
cord-326631-7gd3hjc3	396	23	j	j	NNP
cord-326631-7gd3hjc3	396	24	,	,	,
cord-326631-7gd3hjc3	396	25	and	and	CC
cord-326631-7gd3hjc3	396	26	β	β	NN
cord-326631-7gd3hjc3	396	27	i	i	PRP
cord-326631-7gd3hjc3	396	28	is	be	VBZ
cord-326631-7gd3hjc3	396	29	the	the	DT
cord-326631-7gd3hjc3	396	30	transmission	transmission	NN
cord-326631-7gd3hjc3	396	31	rate	rate	NN
cord-326631-7gd3hjc3	396	32	for	for	IN
cord-326631-7gd3hjc3	396	33	individuals	individual	NNS
cord-326631-7gd3hjc3	396	34	in	in	IN
cord-326631-7gd3hjc3	396	35	cohort	cohort	NN
cord-326631-7gd3hjc3	396	36	i.	i.	NN
cord-326631-7gd3hjc3	397	1	Unlike	unlike	IN
cord-326631-7gd3hjc3	397	2	the	the	DT
cord-326631-7gd3hjc3	397	3	spatial	spatial	JJ
cord-326631-7gd3hjc3	397	4	interpretation	interpretation	NN
cord-326631-7gd3hjc3	397	5	,	,	,
cord-326631-7gd3hjc3	397	6	however	however	RB
cord-326631-7gd3hjc3	397	7	,	,	,
cord-326631-7gd3hjc3	397	8	it	-PRON-	PRP
cord-326631-7gd3hjc3	397	9	would	would	MD
cord-326631-7gd3hjc3	397	10	be	be	VB
cord-326631-7gd3hjc3	397	11	hard	hard	JJ
cord-326631-7gd3hjc3	397	12	to	to	TO
cord-326631-7gd3hjc3	397	13	justify	justify	VB
cord-326631-7gd3hjc3	397	14	taking	take	VBG
cord-326631-7gd3hjc3	397	15	β	β	NN
cord-326631-7gd3hjc3	397	16	i	i	PRP
cord-326631-7gd3hjc3	397	17	to	to	TO
cord-326631-7gd3hjc3	397	18	be	be	VB
cord-326631-7gd3hjc3	397	19	the	the	DT
cord-326631-7gd3hjc3	397	20	same	same	JJ
cord-326631-7gd3hjc3	397	21	for	for	IN
cord-326631-7gd3hjc3	397	22	each	each	DT
cord-326631-7gd3hjc3	397	23	i.	i.	NN
cord-326631-7gd3hjc3	398	1	In	in	IN
cord-326631-7gd3hjc3	398	2	particular	particular	JJ
cord-326631-7gd3hjc3	398	3	,	,	,
cord-326631-7gd3hjc3	398	4	young	young	JJ
cord-326631-7gd3hjc3	398	5	children	child	NNS
cord-326631-7gd3hjc3	398	6	tend	tend	VBP
cord-326631-7gd3hjc3	398	7	to	to	TO
cord-326631-7gd3hjc3	398	8	come	come	VB
cord-326631-7gd3hjc3	398	9	into	into	IN
cord-326631-7gd3hjc3	398	10	much	much	RB
cord-326631-7gd3hjc3	398	11	closer	close	JJR
cord-326631-7gd3hjc3	398	12	contact	contact	NN
cord-326631-7gd3hjc3	398	13	with	with	IN
cord-326631-7gd3hjc3	398	14	their	-PRON-	PRP$
cord-326631-7gd3hjc3	398	15	classmates	classmate	NNS
cord-326631-7gd3hjc3	398	16	than	than	IN
cord-326631-7gd3hjc3	398	17	teenagers	teenager	NNS
cord-326631-7gd3hjc3	398	18	or	or	CC
cord-326631-7gd3hjc3	398	19	adults	adult	NNS
cord-326631-7gd3hjc3	398	20	do	do	VBP
cord-326631-7gd3hjc3	398	21	with	with	IN
cord-326631-7gd3hjc3	398	22	members	member	NNS
cord-326631-7gd3hjc3	398	23	of	of	IN
cord-326631-7gd3hjc3	398	24	their	-PRON-	PRP$
cord-326631-7gd3hjc3	398	25	cohorts	cohort	NNS
cord-326631-7gd3hjc3	398	26	.	.	.
cord-326631-7gd3hjc3	399	1	As	as	IN
cord-326631-7gd3hjc3	399	2	a	a	DT
cord-326631-7gd3hjc3	399	3	result	result	NN
cord-326631-7gd3hjc3	399	4	,	,	,
cord-326631-7gd3hjc3	399	5	Theorem	theorem	NN
cord-326631-7gd3hjc3	399	6	9.1	9.1	CD
cord-326631-7gd3hjc3	399	7	will	will	MD
cord-326631-7gd3hjc3	399	8	not	not	RB
cord-326631-7gd3hjc3	399	9	apply	apply	VB
cord-326631-7gd3hjc3	399	10	and	and	CC
cord-326631-7gd3hjc3	399	11	the	the	DT
cord-326631-7gd3hjc3	399	12	final	final	JJ
cord-326631-7gd3hjc3	399	13	size	size	NN
cord-326631-7gd3hjc3	399	14	will	will	MD
cord-326631-7gd3hjc3	399	15	not	not	RB
cord-326631-7gd3hjc3	399	16	be	be	VB
cord-326631-7gd3hjc3	399	17	given	give	VBN
cord-326631-7gd3hjc3	399	18	by	by	IN
cord-326631-7gd3hjc3	399	19	the	the	DT
cord-326631-7gd3hjc3	399	20	usual	usual	JJ
cord-326631-7gd3hjc3	399	21	formula	formula	NN
cord-326631-7gd3hjc3	399	22	(	(	-LRB-
cord-326631-7gd3hjc3	399	23	5	5	CD
cord-326631-7gd3hjc3	399	24	)	)	-RRB-
cord-326631-7gd3hjc3	399	25	.	.	.
cord-326631-7gd3hjc3	400	1	In	in	IN
cord-326631-7gd3hjc3	400	2	Section	section	NN
cord-326631-7gd3hjc3	400	3	8	8	CD
cord-326631-7gd3hjc3	400	4	where	where	WRB
cord-326631-7gd3hjc3	400	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	400	6	discussed	discuss	VBD
cord-326631-7gd3hjc3	400	7	super	super	JJ
cord-326631-7gd3hjc3	400	8	-	-	NNS
cord-326631-7gd3hjc3	400	9	spreaders	spreader	NNS
cord-326631-7gd3hjc3	400	10	,	,	,
cord-326631-7gd3hjc3	400	11	we	-PRON-	PRP
cord-326631-7gd3hjc3	400	12	specifically	specifically	RB
cord-326631-7gd3hjc3	400	13	excluded	exclude	VBD
cord-326631-7gd3hjc3	400	14	the	the	DT
cord-326631-7gd3hjc3	400	15	types	type	NNS
cord-326631-7gd3hjc3	400	16	of	of	IN
cord-326631-7gd3hjc3	400	17	super	super	JJ
cord-326631-7gd3hjc3	400	18	-	-	NNS
cord-326631-7gd3hjc3	400	19	spreaders	spreader	NNS
cord-326631-7gd3hjc3	400	20	that	that	WDT
cord-326631-7gd3hjc3	400	21	occur	occur	VBP
cord-326631-7gd3hjc3	400	22	for	for	IN
cord-326631-7gd3hjc3	400	23	sexually	sexually	RB
cord-326631-7gd3hjc3	400	24	transmitted	transmit	VBN
cord-326631-7gd3hjc3	400	25	diseases	disease	NNS
cord-326631-7gd3hjc3	400	26	,	,	,
cord-326631-7gd3hjc3	400	27	namely	namely	RB
cord-326631-7gd3hjc3	400	28	individuals	individual	NNS
cord-326631-7gd3hjc3	400	29	who	who	WP
cord-326631-7gd3hjc3	400	30	always	always	RB
cord-326631-7gd3hjc3	400	31	have	have	VBP
cord-326631-7gd3hjc3	400	32	a	a	DT
cord-326631-7gd3hjc3	400	33	higher	high	JJR
cord-326631-7gd3hjc3	400	34	rate	rate	NN
cord-326631-7gd3hjc3	400	35	of	of	IN
cord-326631-7gd3hjc3	400	36	contact	contact	NN
cord-326631-7gd3hjc3	400	37	with	with	IN
cord-326631-7gd3hjc3	400	38	others	other	NNS
cord-326631-7gd3hjc3	400	39	,	,	,
cord-326631-7gd3hjc3	400	40	regardless	regardless	RB
cord-326631-7gd3hjc3	400	41	of	of	IN
cord-326631-7gd3hjc3	400	42	whether	whether	IN
cord-326631-7gd3hjc3	400	43	they	-PRON-	PRP
cord-326631-7gd3hjc3	400	44	happen	happen	VBP
cord-326631-7gd3hjc3	400	45	to	to	TO
cord-326631-7gd3hjc3	400	46	be	be	VB
cord-326631-7gd3hjc3	400	47	infected	infect	VBN
cord-326631-7gd3hjc3	400	48	.	.	.
cord-326631-7gd3hjc3	401	1	When	when	WRB
cord-326631-7gd3hjc3	401	2	such	such	JJ
cord-326631-7gd3hjc3	401	3	"	"	``
cord-326631-7gd3hjc3	401	4	core	core	NN
cord-326631-7gd3hjc3	401	5	groups	group	NNS
cord-326631-7gd3hjc3	401	6	"	"	''
cord-326631-7gd3hjc3	401	7	(	(	-LRB-
cord-326631-7gd3hjc3	401	8	Yorke	Yorke	NNP
cord-326631-7gd3hjc3	401	9	and	and	CC
cord-326631-7gd3hjc3	401	10	Hethcote	Hethcote	NNP
cord-326631-7gd3hjc3	401	11	,	,	,
cord-326631-7gd3hjc3	401	12	1984	1984	CD
cord-326631-7gd3hjc3	401	13	;	;	:
cord-326631-7gd3hjc3	401	14	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	401	15	et	et	NNP
cord-326631-7gd3hjc3	401	16	al	al	NNP
cord-326631-7gd3hjc3	401	17	.	.	NNP
cord-326631-7gd3hjc3	401	18	,	,	,
cord-326631-7gd3hjc3	401	19	1986	1986	CD
cord-326631-7gd3hjc3	401	20	)	)	-RRB-
cord-326631-7gd3hjc3	401	21	exist	exist	VBP
cord-326631-7gd3hjc3	401	22	,	,	,
cord-326631-7gd3hjc3	401	23	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	401	24	.	.	.
cord-326631-7gd3hjc3	402	1	(	(	-LRB-
cord-326631-7gd3hjc3	402	2	26	26	CD
cord-326631-7gd3hjc3	402	3	)	)	-RRB-
cord-326631-7gd3hjc3	402	4	can	can	MD
cord-326631-7gd3hjc3	402	5	still	still	RB
cord-326631-7gd3hjc3	402	6	be	be	VB
cord-326631-7gd3hjc3	402	7	used	use	VBN
cord-326631-7gd3hjc3	402	8	,	,	,
cord-326631-7gd3hjc3	402	9	with	with	IN
cord-326631-7gd3hjc3	402	10	the	the	DT
cord-326631-7gd3hjc3	402	11	interpretation	interpretation	NN
cord-326631-7gd3hjc3	402	12	that	that	IN
cord-326631-7gd3hjc3	402	13	the	the	DT
cord-326631-7gd3hjc3	402	14	stratification	stratification	NN
cord-326631-7gd3hjc3	402	15	of	of	IN
cord-326631-7gd3hjc3	402	16	the	the	DT
cord-326631-7gd3hjc3	402	17	population	population	NN
cord-326631-7gd3hjc3	402	18	is	be	VBZ
cord-326631-7gd3hjc3	402	19	by	by	IN
cord-326631-7gd3hjc3	402	20	social	social	JJ
cord-326631-7gd3hjc3	402	21	group	group	NN
cord-326631-7gd3hjc3	402	22	rather	rather	RB
cord-326631-7gd3hjc3	402	23	than	than	IN
cord-326631-7gd3hjc3	402	24	spatial	spatial	JJ
cord-326631-7gd3hjc3	402	25	region	region	NN
cord-326631-7gd3hjc3	402	26	or	or	CC
cord-326631-7gd3hjc3	402	27	age	age	NN
cord-326631-7gd3hjc3	402	28	cohort	cohort	NN
cord-326631-7gd3hjc3	402	29	.	.	.
cord-326631-7gd3hjc3	403	1	Like	like	IN
cord-326631-7gd3hjc3	403	2	the	the	DT
cord-326631-7gd3hjc3	403	3	age	age	NN
cord-326631-7gd3hjc3	403	4	-	-	HYPH
cord-326631-7gd3hjc3	403	5	structured	structure	VBN
cord-326631-7gd3hjc3	403	6	situation	situation	NN
cord-326631-7gd3hjc3	403	7	,	,	,
cord-326631-7gd3hjc3	403	8	we	-PRON-	PRP
cord-326631-7gd3hjc3	403	9	can	can	MD
cord-326631-7gd3hjc3	403	10	safely	safely	RB
cord-326631-7gd3hjc3	403	11	assume	assume	VB
cord-326631-7gd3hjc3	403	12	that	that	IN
cord-326631-7gd3hjc3	403	13	Eq	Eq	NNP
cord-326631-7gd3hjc3	403	14	.	.	.
cord-326631-7gd3hjc3	404	1	(	(	-LRB-
cord-326631-7gd3hjc3	404	2	34	34	CD
cord-326631-7gd3hjc3	404	3	)	)	-RRB-
cord-326631-7gd3hjc3	404	4	holds	hold	VBZ
cord-326631-7gd3hjc3	404	5	but	but	CC
cord-326631-7gd3hjc3	404	6	not	not	RB
cord-326631-7gd3hjc3	404	7	that	that	DT
cord-326631-7gd3hjc3	405	1	β	β	NN
cord-326631-7gd3hjc3	406	1	i	i	PRP
cord-326631-7gd3hjc3	406	2	is	be	VBZ
cord-326631-7gd3hjc3	406	3	the	the	DT
cord-326631-7gd3hjc3	406	4	same	same	JJ
cord-326631-7gd3hjc3	406	5	for	for	IN
cord-326631-7gd3hjc3	406	6	every	every	DT
cord-326631-7gd3hjc3	406	7	i	i	PRP
cord-326631-7gd3hjc3	406	8	as	as	IN
cord-326631-7gd3hjc3	406	9	in	in	IN
cord-326631-7gd3hjc3	406	10	Eq	Eq	NNP
cord-326631-7gd3hjc3	406	11	.	.	.
cord-326631-7gd3hjc3	407	1	(	(	-LRB-
cord-326631-7gd3hjc3	407	2	30	30	CD
cord-326631-7gd3hjc3	407	3	)	)	-RRB-
cord-326631-7gd3hjc3	407	4	.	.	.
cord-326631-7gd3hjc3	408	1	Indeed	indeed	RB
cord-326631-7gd3hjc3	408	2	,	,	,
cord-326631-7gd3hjc3	408	3	a	a	DT
cord-326631-7gd3hjc3	408	4	large	large	JJ
cord-326631-7gd3hjc3	408	5	difference	difference	NN
cord-326631-7gd3hjc3	408	6	in	in	IN
cord-326631-7gd3hjc3	408	7	β	β	NN
cord-326631-7gd3hjc3	408	8	i	i	PRP
cord-326631-7gd3hjc3	408	9	is	be	VBZ
cord-326631-7gd3hjc3	408	10	precisely	precisely	RB
cord-326631-7gd3hjc3	408	11	what	what	WP
cord-326631-7gd3hjc3	408	12	defines	define	VBZ
cord-326631-7gd3hjc3	408	13	the	the	DT
cord-326631-7gd3hjc3	408	14	core	core	NN
cord-326631-7gd3hjc3	408	15	groups	group	NNS
cord-326631-7gd3hjc3	408	16	.	.	.
cord-326631-7gd3hjc3	409	1	Again	again	RB
cord-326631-7gd3hjc3	409	2	,	,	,
cord-326631-7gd3hjc3	409	3	we	-PRON-	PRP
cord-326631-7gd3hjc3	409	4	have	have	VBP
cord-326631-7gd3hjc3	409	5	a	a	DT
cord-326631-7gd3hjc3	409	6	situation	situation	NN
cord-326631-7gd3hjc3	409	7	where	where	WRB
cord-326631-7gd3hjc3	409	8	the	the	DT
cord-326631-7gd3hjc3	409	9	usual	usual	JJ
cord-326631-7gd3hjc3	409	10	final	final	JJ
cord-326631-7gd3hjc3	409	11	size	size	NN
cord-326631-7gd3hjc3	409	12	formula	formula	NN
cord-326631-7gd3hjc3	409	13	will	will	MD
cord-326631-7gd3hjc3	409	14	not	not	RB
cord-326631-7gd3hjc3	409	15	apply	apply	VB
cord-326631-7gd3hjc3	409	16	.	.	.
cord-326631-7gd3hjc3	410	1	Core	core	NN
cord-326631-7gd3hjc3	410	2	groups	group	NNS
cord-326631-7gd3hjc3	410	3	are	be	VBP
cord-326631-7gd3hjc3	410	4	well	well	RB
cord-326631-7gd3hjc3	410	5	known	know	VBN
cord-326631-7gd3hjc3	410	6	to	to	TO
cord-326631-7gd3hjc3	410	7	have	have	VB
cord-326631-7gd3hjc3	410	8	a	a	DT
cord-326631-7gd3hjc3	410	9	critical	critical	JJ
cord-326631-7gd3hjc3	410	10	role	role	NN
cord-326631-7gd3hjc3	410	11	in	in	IN
cord-326631-7gd3hjc3	410	12	the	the	DT
cord-326631-7gd3hjc3	410	13	transmission	transmission	NN
cord-326631-7gd3hjc3	410	14	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	410	15	of	of	IN
cord-326631-7gd3hjc3	410	16	sexually	sexually	RB
cord-326631-7gd3hjc3	410	17	transmitted	transmit	VBN
cord-326631-7gd3hjc3	410	18	diseases	disease	NNS
cord-326631-7gd3hjc3	410	19	,	,	,
cord-326631-7gd3hjc3	410	20	so	so	CC
cord-326631-7gd3hjc3	410	21	it	-PRON-	PRP
cord-326631-7gd3hjc3	410	22	is	be	VBZ
cord-326631-7gd3hjc3	410	23	not	not	RB
cord-326631-7gd3hjc3	410	24	surprising	surprising	JJ
cord-326631-7gd3hjc3	410	25	that	that	IN
cord-326631-7gd3hjc3	410	26	they	-PRON-	PRP
cord-326631-7gd3hjc3	410	27	will	will	MD
cord-326631-7gd3hjc3	410	28	affect	affect	VB
cord-326631-7gd3hjc3	410	29	the	the	DT
cord-326631-7gd3hjc3	410	30	final	final	JJ
cord-326631-7gd3hjc3	410	31	size	size	NN
cord-326631-7gd3hjc3	410	32	of	of	IN
cord-326631-7gd3hjc3	410	33	epidemics	epidemic	NNS
cord-326631-7gd3hjc3	410	34	.	.	.
cord-326631-7gd3hjc3	411	1	The	the	DT
cord-326631-7gd3hjc3	411	2	well	well	RB
cord-326631-7gd3hjc3	411	3	-	-	HYPH
cord-326631-7gd3hjc3	411	4	known	know	VBN
cord-326631-7gd3hjc3	411	5	formula	formula	NN
cord-326631-7gd3hjc3	411	6	(	(	-LRB-
cord-326631-7gd3hjc3	411	7	5	5	CD
cord-326631-7gd3hjc3	411	8	)	)	-RRB-
cord-326631-7gd3hjc3	411	9	for	for	IN
cord-326631-7gd3hjc3	411	10	the	the	DT
cord-326631-7gd3hjc3	411	11	expected	expect	VBN
cord-326631-7gd3hjc3	411	12	final	final	JJ
cord-326631-7gd3hjc3	411	13	size	size	NN
cord-326631-7gd3hjc3	411	14	of	of	IN
cord-326631-7gd3hjc3	411	15	an	an	DT
cord-326631-7gd3hjc3	411	16	epidemic	epidemic	NN
cord-326631-7gd3hjc3	411	17	is	be	VBZ
cord-326631-7gd3hjc3	411	18	valid	valid	JJ
cord-326631-7gd3hjc3	411	19	in	in	IN
cord-326631-7gd3hjc3	411	20	remarkably	remarkably	RB
cord-326631-7gd3hjc3	411	21	general	general	JJ
cord-326631-7gd3hjc3	411	22	circumstances	circumstance	NNS
cord-326631-7gd3hjc3	411	23	.	.	.
cord-326631-7gd3hjc3	412	1	Previous	previous	JJ
cord-326631-7gd3hjc3	412	2	work	work	NN
cord-326631-7gd3hjc3	412	3	(	(	-LRB-
cord-326631-7gd3hjc3	412	4	e.g.	e.g.	RB
cord-326631-7gd3hjc3	412	5	,	,	,
cord-326631-7gd3hjc3	412	6	Kermack	Kermack	NNP
cord-326631-7gd3hjc3	412	7	and	and	CC
cord-326631-7gd3hjc3	412	8	McKendrick	McKendrick	NNP
cord-326631-7gd3hjc3	412	9	(	(	-LRB-
cord-326631-7gd3hjc3	412	10	1927	1927	CD
cord-326631-7gd3hjc3	412	11	)	)	-RRB-
cord-326631-7gd3hjc3	412	12	;	;	:
cord-326631-7gd3hjc3	412	13	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	412	14	and	and	CC
cord-326631-7gd3hjc3	412	15	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	412	16	(	(	-LRB-
cord-326631-7gd3hjc3	412	17	1980	1980	CD
cord-326631-7gd3hjc3	412	18	)	)	-RRB-
cord-326631-7gd3hjc3	412	19	;	;	:
cord-326631-7gd3hjc3	412	20	Diekmann	Diekmann	NNP
cord-326631-7gd3hjc3	412	21	and	and	CC
cord-326631-7gd3hjc3	412	22	Heesterbeek	Heesterbeek	NNP
cord-326631-7gd3hjc3	412	23	(	(	-LRB-
cord-326631-7gd3hjc3	412	24	2000	2000	CD
cord-326631-7gd3hjc3	412	25	)	)	-RRB-
cord-326631-7gd3hjc3	412	26	)	)	-RRB-
cord-326631-7gd3hjc3	412	27	established	establish	VBD
cord-326631-7gd3hjc3	412	28	that	that	IN
cord-326631-7gd3hjc3	412	29	the	the	DT
cord-326631-7gd3hjc3	412	30	formula	formula	NN
cord-326631-7gd3hjc3	412	31	is	be	VBZ
cord-326631-7gd3hjc3	412	32	valid	valid	JJ
cord-326631-7gd3hjc3	412	33	in	in	IN
cord-326631-7gd3hjc3	412	34	an	an	DT
cord-326631-7gd3hjc3	412	35	SIR	SIR	NNP
cord-326631-7gd3hjc3	412	36	model	model	NN
cord-326631-7gd3hjc3	412	37	with	with	IN
cord-326631-7gd3hjc3	412	38	an	an	DT
cord-326631-7gd3hjc3	412	39	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	412	40	distributed	distribute	VBN
cord-326631-7gd3hjc3	412	41	infectious	infectious	JJ
cord-326631-7gd3hjc3	412	42	period	period	NN
cord-326631-7gd3hjc3	412	43	(	(	-LRB-
cord-326631-7gd3hjc3	412	44	Theorem	Theorem	NNP
cord-326631-7gd3hjc3	412	45	6.1	6.1	CD
cord-326631-7gd3hjc3	412	46	)	)	-RRB-
cord-326631-7gd3hjc3	412	47	.	.	.
cord-326631-7gd3hjc3	413	1	Here	here	RB
cord-326631-7gd3hjc3	413	2	we	-PRON-	PRP
cord-326631-7gd3hjc3	413	3	have	have	VBP
cord-326631-7gd3hjc3	413	4	shown	show	VBN
cord-326631-7gd3hjc3	413	5	,	,	,
cord-326631-7gd3hjc3	413	6	in	in	IN
cord-326631-7gd3hjc3	413	7	addition	addition	NN
cord-326631-7gd3hjc3	413	8	,	,	,
cord-326631-7gd3hjc3	413	9	that	that	IN
cord-326631-7gd3hjc3	413	10	the	the	DT
cord-326631-7gd3hjc3	413	11	standard	standard	JJ
cord-326631-7gd3hjc3	413	12	formula	formula	NN
cord-326631-7gd3hjc3	413	13	(	(	-LRB-
cord-326631-7gd3hjc3	413	14	5	5	LS
cord-326631-7gd3hjc3	413	15	)	)	-RRB-
cord-326631-7gd3hjc3	413	16	is	be	VBZ
cord-326631-7gd3hjc3	413	17	invariant	invariant	JJ
cord-326631-7gd3hjc3	413	18	to	to	IN
cord-326631-7gd3hjc3	413	19	the	the	DT
cord-326631-7gd3hjc3	413	20	number	number	NN
cord-326631-7gd3hjc3	413	21	of	of	IN
cord-326631-7gd3hjc3	413	22	latent	latent	JJ
cord-326631-7gd3hjc3	413	23	and	and	CC
cord-326631-7gd3hjc3	413	24	infectious	infectious	JJ
cord-326631-7gd3hjc3	413	25	stages	stage	NNS
cord-326631-7gd3hjc3	413	26	of	of	IN
cord-326631-7gd3hjc3	413	27	disease	disease	NN
cord-326631-7gd3hjc3	413	28	(	(	-LRB-
cord-326631-7gd3hjc3	413	29	Theorem	Theorem	NNP
cord-326631-7gd3hjc3	413	30	7.1	7.1	CD
cord-326631-7gd3hjc3	413	31	)	)	-RRB-
cord-326631-7gd3hjc3	413	32	,	,	,
cord-326631-7gd3hjc3	413	33	the	the	DT
cord-326631-7gd3hjc3	413	34	distributions	distribution	NNS
cord-326631-7gd3hjc3	413	35	of	of	IN
cord-326631-7gd3hjc3	413	36	transmission	transmission	NN
cord-326631-7gd3hjc3	413	37	rates	rate	NNS
cord-326631-7gd3hjc3	413	38	within	within	IN
cord-326631-7gd3hjc3	413	39	stages	stage	NNS
cord-326631-7gd3hjc3	413	40	(	(	-LRB-
cord-326631-7gd3hjc3	413	41	Theorem	theorem	NN
cord-326631-7gd3hjc3	413	42	8.1	8.1	CD
cord-326631-7gd3hjc3	413	43	)	)	-RRB-
cord-326631-7gd3hjc3	413	44	,	,	,
cord-326631-7gd3hjc3	413	45	and	and	CC
cord-326631-7gd3hjc3	413	46	even	even	RB
cord-326631-7gd3hjc3	413	47	to	to	IN
cord-326631-7gd3hjc3	413	48	common	common	JJ
cord-326631-7gd3hjc3	413	49	spatial	spatial	JJ
cord-326631-7gd3hjc3	413	50	contact	contact	NN
cord-326631-7gd3hjc3	413	51	heterogeneities	heterogeneity	NNS
cord-326631-7gd3hjc3	413	52	(	(	-LRB-
cord-326631-7gd3hjc3	413	53	Theorem	theorem	NN
cord-326631-7gd3hjc3	413	54	9.1	9.1	CD
cord-326631-7gd3hjc3	413	55	)	)	-RRB-
cord-326631-7gd3hjc3	413	56	.	.	.
cord-326631-7gd3hjc3	414	1	The	the	DT
cord-326631-7gd3hjc3	414	2	invariance	invariance	NN
cord-326631-7gd3hjc3	414	3	of	of	IN
cord-326631-7gd3hjc3	414	4	the	the	DT
cord-326631-7gd3hjc3	414	5	final	final	JJ
cord-326631-7gd3hjc3	414	6	size	size	NN
cord-326631-7gd3hjc3	414	7	formula	formula	NN
cord-326631-7gd3hjc3	414	8	has	have	VBZ
cord-326631-7gd3hjc3	414	9	important	important	JJ
cord-326631-7gd3hjc3	414	10	practical	practical	JJ
cord-326631-7gd3hjc3	414	11	implications	implication	NNS
cord-326631-7gd3hjc3	414	12	.	.	.
cord-326631-7gd3hjc3	415	1	Typically	typically	RB
cord-326631-7gd3hjc3	415	2	,	,	,
cord-326631-7gd3hjc3	415	3	the	the	DT
cord-326631-7gd3hjc3	415	4	time	time	NN
cord-326631-7gd3hjc3	415	5	at	at	IN
cord-326631-7gd3hjc3	415	6	which	which	WDT
cord-326631-7gd3hjc3	415	7	one	one	PRP
cord-326631-7gd3hjc3	415	8	wishes	wish	VBZ
cord-326631-7gd3hjc3	415	9	to	to	TO
cord-326631-7gd3hjc3	415	10	estimate	estimate	VB
cord-326631-7gd3hjc3	415	11	the	the	DT
cord-326631-7gd3hjc3	415	12	expected	expect	VBN
cord-326631-7gd3hjc3	415	13	final	final	JJ
cord-326631-7gd3hjc3	415	14	size	size	NN
cord-326631-7gd3hjc3	415	15	of	of	IN
cord-326631-7gd3hjc3	415	16	an	an	DT
cord-326631-7gd3hjc3	415	17	epidemic	epidemic	NN
cord-326631-7gd3hjc3	415	18	is	be	VBZ
cord-326631-7gd3hjc3	415	19	long	long	RB
cord-326631-7gd3hjc3	415	20	before	before	IN
cord-326631-7gd3hjc3	415	21	enough	enough	JJ
cord-326631-7gd3hjc3	415	22	information	information	NN
cord-326631-7gd3hjc3	415	23	has	have	VBZ
cord-326631-7gd3hjc3	415	24	been	be	VBN
cord-326631-7gd3hjc3	415	25	gathered	gather	VBN
cord-326631-7gd3hjc3	415	26	to	to	TO
cord-326631-7gd3hjc3	415	27	estimate	estimate	VB
cord-326631-7gd3hjc3	415	28	the	the	DT
cord-326631-7gd3hjc3	415	29	distributions	distribution	NNS
cord-326631-7gd3hjc3	415	30	of	of	IN
cord-326631-7gd3hjc3	415	31	latent	latent	JJ
cord-326631-7gd3hjc3	415	32	and	and	CC
cord-326631-7gd3hjc3	415	33	infectious	infectious	JJ
cord-326631-7gd3hjc3	415	34	periods	period	NNS
cord-326631-7gd3hjc3	415	35	or	or	CC
cord-326631-7gd3hjc3	415	36	other	other	JJ
cord-326631-7gd3hjc3	415	37	epidemiological	epidemiological	JJ
cord-326631-7gd3hjc3	415	38	details	detail	NNS
cord-326631-7gd3hjc3	415	39	.	.	.
cord-326631-7gd3hjc3	416	1	Our	-PRON-	PRP$
cord-326631-7gd3hjc3	416	2	theorems	theorem	NNS
cord-326631-7gd3hjc3	416	3	provide	provide	VBP
cord-326631-7gd3hjc3	416	4	rigorous	rigorous	JJ
cord-326631-7gd3hjc3	416	5	support	support	NN
cord-326631-7gd3hjc3	416	6	for	for	IN
cord-326631-7gd3hjc3	416	7	estimates	estimate	NNS
cord-326631-7gd3hjc3	416	8	of	of	IN
cord-326631-7gd3hjc3	416	9	the	the	DT
cord-326631-7gd3hjc3	416	10	expected	expect	VBN
cord-326631-7gd3hjc3	416	11	magnitude	magnitude	NN
cord-326631-7gd3hjc3	416	12	of	of	IN
cord-326631-7gd3hjc3	416	13	epidemics	epidemic	NNS
cord-326631-7gd3hjc3	416	14	based	base	VBN
cord-326631-7gd3hjc3	416	15	solely	solely	RB
cord-326631-7gd3hjc3	416	16	on	on	IN
cord-326631-7gd3hjc3	416	17	estimates	estimate	NNS
cord-326631-7gd3hjc3	416	18	of	of	IN
cord-326631-7gd3hjc3	416	19	the	the	DT
cord-326631-7gd3hjc3	416	20	basic	basic	JJ
cord-326631-7gd3hjc3	416	21	reproduction	reproduction	NN
cord-326631-7gd3hjc3	416	22	number	number	NN
cord-326631-7gd3hjc3	416	23	R	r	NN
cord-326631-7gd3hjc3	416	24	0	0	CD
cord-326631-7gd3hjc3	416	25	,	,	,
cord-326631-7gd3hjc3	416	26	which	which	WDT
cord-326631-7gd3hjc3	416	27	is	be	VBZ
cord-326631-7gd3hjc3	416	28	the	the	DT
cord-326631-7gd3hjc3	416	29	only	only	JJ
cord-326631-7gd3hjc3	416	30	parameter	parameter	NN
cord-326631-7gd3hjc3	416	31	that	that	WDT
cord-326631-7gd3hjc3	416	32	appears	appear	VBZ
cord-326631-7gd3hjc3	416	33	in	in	IN
cord-326631-7gd3hjc3	416	34	the	the	DT
cord-326631-7gd3hjc3	416	35	final	final	JJ
cord-326631-7gd3hjc3	416	36	size	size	NN
cord-326631-7gd3hjc3	416	37	formula	formula	NN
cord-326631-7gd3hjc3	416	38	(	(	-LRB-
cord-326631-7gd3hjc3	416	39	5	5	CD
cord-326631-7gd3hjc3	416	40	)	)	-RRB-
cord-326631-7gd3hjc3	416	41	.	.	.
cord-326631-7gd3hjc3	417	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	417	2	should	should	MD
cord-326631-7gd3hjc3	417	3	be	be	VB
cord-326631-7gd3hjc3	417	4	noted	note	VBN
cord-326631-7gd3hjc3	417	5	that	that	IN
cord-326631-7gd3hjc3	417	6	the	the	DT
cord-326631-7gd3hjc3	417	7	final	final	JJ
cord-326631-7gd3hjc3	417	8	size	size	NN
cord-326631-7gd3hjc3	417	9	formula	formula	NN
cord-326631-7gd3hjc3	417	10	refers	refer	VBZ
cord-326631-7gd3hjc3	417	11	only	only	RB
cord-326631-7gd3hjc3	417	12	to	to	IN
cord-326631-7gd3hjc3	417	13	the	the	DT
cord-326631-7gd3hjc3	417	14	ensemble	ensemble	JJ
cord-326631-7gd3hjc3	417	15	average	average	JJ
cord-326631-7gd3hjc3	417	16	size	size	NN
cord-326631-7gd3hjc3	417	17	of	of	IN
cord-326631-7gd3hjc3	417	18	an	an	DT
cord-326631-7gd3hjc3	417	19	epidemic	epidemic	NN
cord-326631-7gd3hjc3	417	20	for	for	IN
cord-326631-7gd3hjc3	417	21	a	a	DT
cord-326631-7gd3hjc3	417	22	disease	disease	NN
cord-326631-7gd3hjc3	417	23	with	with	IN
cord-326631-7gd3hjc3	417	24	a	a	DT
cord-326631-7gd3hjc3	417	25	given	give	VBN
cord-326631-7gd3hjc3	417	26	R	r	NN
cord-326631-7gd3hjc3	417	27	0	0	CD
cord-326631-7gd3hjc3	417	28	.	.	.
cord-326631-7gd3hjc3	418	1	Different	different	JJ
cord-326631-7gd3hjc3	418	2	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	418	3	realizations	realization	NNS
cord-326631-7gd3hjc3	418	4	of	of	IN
cord-326631-7gd3hjc3	418	5	the	the	DT
cord-326631-7gd3hjc3	418	6	same	same	JJ
cord-326631-7gd3hjc3	418	7	process	process	NN
cord-326631-7gd3hjc3	418	8	will	will	MD
cord-326631-7gd3hjc3	418	9	lead	lead	VB
cord-326631-7gd3hjc3	418	10	to	to	IN
cord-326631-7gd3hjc3	418	11	different	different	JJ
cord-326631-7gd3hjc3	418	12	final	final	JJ
cord-326631-7gd3hjc3	418	13	sizes	size	NNS
cord-326631-7gd3hjc3	418	14	and	and	CC
cord-326631-7gd3hjc3	418	15	our	-PRON-	PRP$
cord-326631-7gd3hjc3	418	16	analysis	analysis	NN
cord-326631-7gd3hjc3	418	17	says	say	VBZ
cord-326631-7gd3hjc3	418	18	nothing	nothing	NN
cord-326631-7gd3hjc3	418	19	about	about	IN
cord-326631-7gd3hjc3	418	20	the	the	DT
cord-326631-7gd3hjc3	418	21	variance	variance	NN
cord-326631-7gd3hjc3	418	22	or	or	CC
cord-326631-7gd3hjc3	418	23	higher	high	JJR
cord-326631-7gd3hjc3	418	24	moments	moment	NNS
cord-326631-7gd3hjc3	418	25	of	of	IN
cord-326631-7gd3hjc3	418	26	the	the	DT
cord-326631-7gd3hjc3	418	27	final	final	JJ
cord-326631-7gd3hjc3	418	28	size	size	NN
cord-326631-7gd3hjc3	418	29	distribution	distribution	NN
cord-326631-7gd3hjc3	418	30	.	.	.
cord-326631-7gd3hjc3	419	1	Kurtz	Kurtz	NNP
cord-326631-7gd3hjc3	419	2	(	(	-LRB-
cord-326631-7gd3hjc3	419	3	1980	1980	CD
cord-326631-7gd3hjc3	419	4	)	)	-RRB-
cord-326631-7gd3hjc3	419	5	proved	prove	VBD
cord-326631-7gd3hjc3	419	6	that	that	IN
cord-326631-7gd3hjc3	419	7	in	in	IN
cord-326631-7gd3hjc3	419	8	the	the	DT
cord-326631-7gd3hjc3	419	9	limit	limit	NN
cord-326631-7gd3hjc3	419	10	that	that	IN
cord-326631-7gd3hjc3	419	11	the	the	DT
cord-326631-7gd3hjc3	419	12	population	population	NN
cord-326631-7gd3hjc3	419	13	size	size	NN
cord-326631-7gd3hjc3	419	14	goes	go	VBZ
cord-326631-7gd3hjc3	419	15	to	to	IN
cord-326631-7gd3hjc3	419	16	infinity	infinity	NN
cord-326631-7gd3hjc3	419	17	,	,	,
cord-326631-7gd3hjc3	419	18	the	the	DT
cord-326631-7gd3hjc3	419	19	ensemble	ensemble	NN
cord-326631-7gd3hjc3	419	20	mean	mean	NN
cord-326631-7gd3hjc3	419	21	of	of	IN
cord-326631-7gd3hjc3	419	22	the	the	DT
cord-326631-7gd3hjc3	419	23	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	419	24	SIR	SIR	NNP
cord-326631-7gd3hjc3	419	25	model	model	NN
cord-326631-7gd3hjc3	419	26	with	with	IN
cord-326631-7gd3hjc3	419	27	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	419	28	distributed	distribute	VBN
cord-326631-7gd3hjc3	419	29	infectious	infectious	JJ
cord-326631-7gd3hjc3	419	30	period	period	NN
cord-326631-7gd3hjc3	419	31	converges	converge	VBZ
cord-326631-7gd3hjc3	419	32	to	to	IN
cord-326631-7gd3hjc3	419	33	the	the	DT
cord-326631-7gd3hjc3	419	34	solutions	solution	NNS
cord-326631-7gd3hjc3	419	35	of	of	IN
cord-326631-7gd3hjc3	419	36	the	the	DT
cord-326631-7gd3hjc3	419	37	integro	integro	JJ
cord-326631-7gd3hjc3	419	38	-	-	HYPH
cord-326631-7gd3hjc3	419	39	differential	differential	JJ
cord-326631-7gd3hjc3	419	40	equation	equation	NN
cord-326631-7gd3hjc3	419	41	model	model	NN
cord-326631-7gd3hjc3	419	42	specified	specify	VBN
cord-326631-7gd3hjc3	419	43	in	in	IN
cord-326631-7gd3hjc3	419	44	our	-PRON-	PRP$
cord-326631-7gd3hjc3	419	45	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	419	46	.	.	.
cord-326631-7gd3hjc3	420	1	(	(	-LRB-
cord-326631-7gd3hjc3	420	2	11	11	CD
cord-326631-7gd3hjc3	420	3	)	)	-RRB-
cord-326631-7gd3hjc3	420	4	.	.	.
cord-326631-7gd3hjc3	421	1	Hence	hence	RB
cord-326631-7gd3hjc3	421	2	,	,	,
cord-326631-7gd3hjc3	421	3	the	the	DT
cord-326631-7gd3hjc3	421	4	standard	standard	JJ
cord-326631-7gd3hjc3	421	5	final	final	JJ
cord-326631-7gd3hjc3	421	6	size	size	NN
cord-326631-7gd3hjc3	421	7	formula	formula	NN
cord-326631-7gd3hjc3	421	8	gives	give	VBZ
cord-326631-7gd3hjc3	421	9	the	the	DT
cord-326631-7gd3hjc3	421	10	mean	mean	JJ
cord-326631-7gd3hjc3	421	11	final	final	JJ
cord-326631-7gd3hjc3	421	12	size	size	NN
cord-326631-7gd3hjc3	421	13	of	of	IN
cord-326631-7gd3hjc3	421	14	the	the	DT
cord-326631-7gd3hjc3	421	15	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	421	16	SIR	SIR	NNP
cord-326631-7gd3hjc3	421	17	model	model	NN
cord-326631-7gd3hjc3	421	18	.	.	.
cord-326631-7gd3hjc3	422	1	However	however	RB
cord-326631-7gd3hjc3	422	2	,	,	,
cord-326631-7gd3hjc3	422	3	it	-PRON-	PRP
cord-326631-7gd3hjc3	422	4	is	be	VBZ
cord-326631-7gd3hjc3	422	5	difficult	difficult	JJ
cord-326631-7gd3hjc3	422	6	to	to	TO
cord-326631-7gd3hjc3	422	7	deduce	deduce	VB
cord-326631-7gd3hjc3	422	8	the	the	DT
cord-326631-7gd3hjc3	422	9	distribution	distribution	NN
cord-326631-7gd3hjc3	422	10	of	of	IN
cord-326631-7gd3hjc3	422	11	the	the	DT
cord-326631-7gd3hjc3	422	12	final	final	JJ
cord-326631-7gd3hjc3	422	13	size	size	NN
cord-326631-7gd3hjc3	422	14	,	,	,
cord-326631-7gd3hjc3	422	15	and	and	CC
cord-326631-7gd3hjc3	422	16	this	this	DT
cord-326631-7gd3hjc3	422	17	remains	remain	VBZ
cord-326631-7gd3hjc3	422	18	an	an	DT
cord-326631-7gd3hjc3	422	19	open	open	JJ
cord-326631-7gd3hjc3	422	20	problem	problem	NN
cord-326631-7gd3hjc3	422	21	for	for	IN
cord-326631-7gd3hjc3	422	22	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	422	23	SIR	SIR	NNP
cord-326631-7gd3hjc3	422	24	models	model	NNS
cord-326631-7gd3hjc3	422	25	with	with	IN
cord-326631-7gd3hjc3	422	26	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	422	27	distributed	distribute	VBN
cord-326631-7gd3hjc3	422	28	infectious	infectious	JJ
cord-326631-7gd3hjc3	422	29	periods	period	NNS
cord-326631-7gd3hjc3	422	30	.	.	.
cord-326631-7gd3hjc3	423	1	For	for	IN
cord-326631-7gd3hjc3	423	2	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	423	3	SEIR	SEIR	NNP
cord-326631-7gd3hjc3	423	4	models	model	NNS
cord-326631-7gd3hjc3	423	5	with	with	IN
cord-326631-7gd3hjc3	423	6	Gamma	Gamma	NNP
cord-326631-7gd3hjc3	423	7	distributed	distribute	VBN
cord-326631-7gd3hjc3	423	8	latent	latent	JJ
cord-326631-7gd3hjc3	423	9	and	and	CC
cord-326631-7gd3hjc3	423	10	infectious	infectious	JJ
cord-326631-7gd3hjc3	423	11	periods	period	NNS
cord-326631-7gd3hjc3	423	12	,	,	,
cord-326631-7gd3hjc3	423	13	Anderson	Anderson	NNP
cord-326631-7gd3hjc3	423	14	and	and	CC
cord-326631-7gd3hjc3	423	15	Watsons	Watsons	NNP
cord-326631-7gd3hjc3	423	16	(	(	-LRB-
cord-326631-7gd3hjc3	423	17	1980	1980	CD
cord-326631-7gd3hjc3	423	18	)	)	-RRB-
cord-326631-7gd3hjc3	423	19	derived	derive	VBD
cord-326631-7gd3hjc3	423	20	a	a	DT
cord-326631-7gd3hjc3	423	21	normal	normal	JJ
cord-326631-7gd3hjc3	423	22	approximation	approximation	NN
cord-326631-7gd3hjc3	423	23	to	to	IN
cord-326631-7gd3hjc3	423	24	the	the	DT
cord-326631-7gd3hjc3	423	25	final	final	JJ
cord-326631-7gd3hjc3	423	26	size	size	NN
cord-326631-7gd3hjc3	423	27	distribution	distribution	NN
cord-326631-7gd3hjc3	423	28	that	that	WDT
cord-326631-7gd3hjc3	423	29	is	be	VBZ
cord-326631-7gd3hjc3	423	30	valid	valid	JJ
cord-326631-7gd3hjc3	423	31	in	in	IN
cord-326631-7gd3hjc3	423	32	the	the	DT
cord-326631-7gd3hjc3	423	33	limit	limit	NN
cord-326631-7gd3hjc3	423	34	of	of	IN
cord-326631-7gd3hjc3	423	35	large	large	JJ
cord-326631-7gd3hjc3	423	36	population	population	NN
cord-326631-7gd3hjc3	423	37	size	size	NN
cord-326631-7gd3hjc3	423	38	.	.	.
cord-326631-7gd3hjc3	424	1	If	if	IN
cord-326631-7gd3hjc3	424	2	there	there	EX
cord-326631-7gd3hjc3	424	3	is	be	VBZ
cord-326631-7gd3hjc3	424	4	little	little	JJ
cord-326631-7gd3hjc3	424	5	variation	variation	NN
cord-326631-7gd3hjc3	424	6	in	in	IN
cord-326631-7gd3hjc3	424	7	the	the	DT
cord-326631-7gd3hjc3	424	8	length	length	NN
cord-326631-7gd3hjc3	424	9	of	of	IN
cord-326631-7gd3hjc3	424	10	the	the	DT
cord-326631-7gd3hjc3	424	11	latent	latent	JJ
cord-326631-7gd3hjc3	424	12	period	period	NN
cord-326631-7gd3hjc3	424	13	,	,	,
cord-326631-7gd3hjc3	424	14	and	and	CC
cord-326631-7gd3hjc3	424	15	the	the	DT
cord-326631-7gd3hjc3	424	16	infectious	infectious	JJ
cord-326631-7gd3hjc3	424	17	period	period	NN
cord-326631-7gd3hjc3	424	18	is	be	VBZ
cord-326631-7gd3hjc3	424	19	short	short	JJ
cord-326631-7gd3hjc3	424	20	,	,	,
cord-326631-7gd3hjc3	424	21	the	the	DT
cord-326631-7gd3hjc3	424	22	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	424	23	SEIR	seir	NN
cord-326631-7gd3hjc3	424	24	model	model	NN
cord-326631-7gd3hjc3	424	25	can	can	MD
cord-326631-7gd3hjc3	424	26	be	be	VB
cord-326631-7gd3hjc3	424	27	approximated	approximate	VBN
cord-326631-7gd3hjc3	424	28	by	by	IN
cord-326631-7gd3hjc3	424	29	a	a	DT
cord-326631-7gd3hjc3	424	30	chain	chain	NN
cord-326631-7gd3hjc3	424	31	binomial	binomial	NN
cord-326631-7gd3hjc3	424	32	model	model	NN
cord-326631-7gd3hjc3	424	33	(	(	-LRB-
cord-326631-7gd3hjc3	424	34	Bailey	Bailey	NNP
cord-326631-7gd3hjc3	424	35	,	,	,
cord-326631-7gd3hjc3	424	36	1975	1975	CD
cord-326631-7gd3hjc3	424	37	)	)	-RRB-
cord-326631-7gd3hjc3	424	38	,	,	,
cord-326631-7gd3hjc3	424	39	which	which	WDT
cord-326631-7gd3hjc3	424	40	is	be	VBZ
cord-326631-7gd3hjc3	424	41	a	a	DT
cord-326631-7gd3hjc3	424	42	discrete	discrete	JJ
cord-326631-7gd3hjc3	424	43	time	time	NN
cord-326631-7gd3hjc3	424	44	Markov	Markov	NNP
cord-326631-7gd3hjc3	424	45	chain	chain	NN
cord-326631-7gd3hjc3	424	46	.	.	.
cord-326631-7gd3hjc3	425	1	The	the	DT
cord-326631-7gd3hjc3	425	2	time	time	NN
cord-326631-7gd3hjc3	425	3	step	step	NN
cord-326631-7gd3hjc3	425	4	for	for	IN
cord-326631-7gd3hjc3	425	5	this	this	DT
cord-326631-7gd3hjc3	425	6	chain	chain	NN
cord-326631-7gd3hjc3	425	7	is	be	VBZ
cord-326631-7gd3hjc3	425	8	equal	equal	JJ
cord-326631-7gd3hjc3	425	9	to	to	IN
cord-326631-7gd3hjc3	425	10	the	the	DT
cord-326631-7gd3hjc3	425	11	fixed	fix	VBN
cord-326631-7gd3hjc3	425	12	-	-	HYPH
cord-326631-7gd3hjc3	425	13	length	length	NN
cord-326631-7gd3hjc3	425	14	latent	latent	JJ
cord-326631-7gd3hjc3	425	15	period	period	NN
cord-326631-7gd3hjc3	425	16	,	,	,
cord-326631-7gd3hjc3	425	17	since	since	IN
cord-326631-7gd3hjc3	425	18	the	the	DT
cord-326631-7gd3hjc3	425	19	infectious	infectious	JJ
cord-326631-7gd3hjc3	425	20	period	period	NN
cord-326631-7gd3hjc3	425	21	is	be	VBZ
cord-326631-7gd3hjc3	425	22	presumed	presume	VBN
cord-326631-7gd3hjc3	425	23	infinitesimal	infinitesimal	JJ
cord-326631-7gd3hjc3	425	24	(	(	-LRB-
cord-326631-7gd3hjc3	425	25	all	all	DT
cord-326631-7gd3hjc3	425	26	contacts	contact	NNS
cord-326631-7gd3hjc3	425	27	occur	occur	VBP
cord-326631-7gd3hjc3	425	28	instantaneously	instantaneously	RB
cord-326631-7gd3hjc3	425	29	at	at	IN
cord-326631-7gd3hjc3	425	30	the	the	DT
cord-326631-7gd3hjc3	425	31	end	end	NN
cord-326631-7gd3hjc3	425	32	of	of	IN
cord-326631-7gd3hjc3	425	33	the	the	DT
cord-326631-7gd3hjc3	425	34	latent	latent	JJ
cord-326631-7gd3hjc3	425	35	period	period	NN
cord-326631-7gd3hjc3	425	36	)	)	-RRB-
cord-326631-7gd3hjc3	425	37	.	.	.
cord-326631-7gd3hjc3	426	1	For	for	IN
cord-326631-7gd3hjc3	426	2	such	such	JJ
cord-326631-7gd3hjc3	426	3	models	model	NNS
cord-326631-7gd3hjc3	426	4	,	,	,
cord-326631-7gd3hjc3	426	5	the	the	DT
cord-326631-7gd3hjc3	426	6	only	only	JJ
cord-326631-7gd3hjc3	426	7	parameter	parameter	NN
cord-326631-7gd3hjc3	426	8	is	be	VBZ
cord-326631-7gd3hjc3	426	9	the	the	DT
cord-326631-7gd3hjc3	426	10	probability	probability	NN
cord-326631-7gd3hjc3	426	11	q	q	NN
cord-326631-7gd3hjc3	426	12	that	that	IN
cord-326631-7gd3hjc3	426	13	a	a	DT
cord-326631-7gd3hjc3	426	14	contact	contact	NN
cord-326631-7gd3hjc3	426	15	between	between	IN
cord-326631-7gd3hjc3	426	16	an	an	DT
cord-326631-7gd3hjc3	426	17	infectious	infectious	JJ
cord-326631-7gd3hjc3	426	18	individual	individual	NN
cord-326631-7gd3hjc3	426	19	and	and	CC
cord-326631-7gd3hjc3	426	20	a	a	DT
cord-326631-7gd3hjc3	426	21	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	426	22	individual	individual	JJ
cord-326631-7gd3hjc3	426	23	leads	lead	VBZ
cord-326631-7gd3hjc3	426	24	to	to	IN
cord-326631-7gd3hjc3	426	25	infection	infection	NN
cord-326631-7gd3hjc3	426	26	.	.	.
cord-326631-7gd3hjc3	427	1	With	with	IN
cord-326631-7gd3hjc3	427	2	the	the	DT
cord-326631-7gd3hjc3	427	3	assumption	assumption	NN
cord-326631-7gd3hjc3	427	4	that	that	IN
cord-326631-7gd3hjc3	427	5	q	q	NNP
cord-326631-7gd3hjc3	427	6	=	=	SYM
cord-326631-7gd3hjc3	427	7	1	1	CD
cord-326631-7gd3hjc3	427	8	−	−	NN
cord-326631-7gd3hjc3	427	9	e	e	NN
cord-326631-7gd3hjc3	427	10	−R0	−R0	NNP
cord-326631-7gd3hjc3	427	11	,	,	,
cord-326631-7gd3hjc3	427	12	Von	Von	NNP
cord-326631-7gd3hjc3	427	13	Bahr	Bahr	NNP
cord-326631-7gd3hjc3	427	14	and	and	CC
cord-326631-7gd3hjc3	427	15	Martin	Martin	NNP
cord-326631-7gd3hjc3	427	16	-	-	HYPH
cord-326631-7gd3hjc3	427	17	Lof	Lof	NNP
cord-326631-7gd3hjc3	427	18	(	(	-LRB-
cord-326631-7gd3hjc3	427	19	1980	1980	CD
cord-326631-7gd3hjc3	427	20	)	)	-RRB-
cord-326631-7gd3hjc3	427	21	and	and	CC
cord-326631-7gd3hjc3	427	22	Scalia	Scalia	NNP
cord-326631-7gd3hjc3	427	23	-	-	HYPH
cord-326631-7gd3hjc3	427	24	Tomba	Tomba	NNP
cord-326631-7gd3hjc3	427	25	(	(	-LRB-
cord-326631-7gd3hjc3	427	26	1985	1985	CD
cord-326631-7gd3hjc3	427	27	)	)	-RRB-
cord-326631-7gd3hjc3	427	28	showed	show	VBD
cord-326631-7gd3hjc3	427	29	that	that	IN
cord-326631-7gd3hjc3	427	30	final	final	JJ
cord-326631-7gd3hjc3	427	31	size	size	NN
cord-326631-7gd3hjc3	427	32	distribution	distribution	NN
cord-326631-7gd3hjc3	427	33	for	for	IN
cord-326631-7gd3hjc3	427	34	the	the	DT
cord-326631-7gd3hjc3	427	35	traditional	traditional	JJ
cord-326631-7gd3hjc3	427	36	chain	chain	NN
cord-326631-7gd3hjc3	427	37	binomial	binomial	NN
cord-326631-7gd3hjc3	427	38	model	model	NN
cord-326631-7gd3hjc3	427	39	is	be	VBZ
cord-326631-7gd3hjc3	427	40	asymptotically	asymptotically	RB
cord-326631-7gd3hjc3	427	41	normal	normal	JJ
cord-326631-7gd3hjc3	427	42	in	in	IN
cord-326631-7gd3hjc3	427	43	the	the	DT
cord-326631-7gd3hjc3	427	44	limit	limit	NN
cord-326631-7gd3hjc3	427	45	of	of	IN
cord-326631-7gd3hjc3	427	46	large	large	JJ
cord-326631-7gd3hjc3	427	47	population	population	NN
cord-326631-7gd3hjc3	427	48	size	size	NN
cord-326631-7gd3hjc3	427	49	.	.	.
cord-326631-7gd3hjc3	428	1	Scalia	Scalia	NNP
cord-326631-7gd3hjc3	428	2	-	-	HYPH
cord-326631-7gd3hjc3	428	3	Tomba	Tomba	NNP
cord-326631-7gd3hjc3	428	4	(	(	-LRB-
cord-326631-7gd3hjc3	428	5	1986	1986	CD
cord-326631-7gd3hjc3	428	6	)	)	-RRB-
cord-326631-7gd3hjc3	428	7	and	and	CC
cord-326631-7gd3hjc3	428	8	Andersson	Andersson	NNP
cord-326631-7gd3hjc3	428	9	(	(	-LRB-
cord-326631-7gd3hjc3	428	10	1999	1999	CD
cord-326631-7gd3hjc3	428	11	)	)	-RRB-
cord-326631-7gd3hjc3	428	12	studied	study	VBD
cord-326631-7gd3hjc3	428	13	more	more	JJR
cord-326631-7gd3hjc3	428	14	general	general	JJ
cord-326631-7gd3hjc3	428	15	chain	chain	NN
cord-326631-7gd3hjc3	428	16	binomial	binomial	NN
cord-326631-7gd3hjc3	428	17	models	model	NNS
cord-326631-7gd3hjc3	428	18	(	(	-LRB-
cord-326631-7gd3hjc3	428	19	with	with	IN
cord-326631-7gd3hjc3	428	20	heterogeneous	heterogeneous	JJ
cord-326631-7gd3hjc3	428	21	contact	contact	NN
cord-326631-7gd3hjc3	428	22	structures	structure	NNS
cord-326631-7gd3hjc3	428	23	equivalent	equivalent	JJ
cord-326631-7gd3hjc3	428	24	to	to	IN
cord-326631-7gd3hjc3	428	25	those	those	DT
cord-326631-7gd3hjc3	428	26	we	-PRON-	PRP
cord-326631-7gd3hjc3	428	27	discussed	discuss	VBD
cord-326631-7gd3hjc3	428	28	in	in	IN
cord-326631-7gd3hjc3	428	29	Sections	section	NNS
cord-326631-7gd3hjc3	428	30	9	9	CD
cord-326631-7gd3hjc3	428	31	and	and	CC
cord-326631-7gd3hjc3	428	32	10	10	CD
cord-326631-7gd3hjc3	428	33	)	)	-RRB-
cord-326631-7gd3hjc3	428	34	and	and	CC
cord-326631-7gd3hjc3	428	35	found	find	VBD
cord-326631-7gd3hjc3	428	36	asymptotic	asymptotic	JJ
cord-326631-7gd3hjc3	428	37	final	final	JJ
cord-326631-7gd3hjc3	428	38	size	size	NN
cord-326631-7gd3hjc3	428	39	distributions	distribution	NNS
cord-326631-7gd3hjc3	428	40	.	.	.
cord-326631-7gd3hjc3	429	1	Their	-PRON-	PRP$
cord-326631-7gd3hjc3	429	2	results	result	NNS
cord-326631-7gd3hjc3	429	3	imply	imply	VBP
cord-326631-7gd3hjc3	429	4	that	that	IN
cord-326631-7gd3hjc3	429	5	if	if	IN
cord-326631-7gd3hjc3	429	6	q	q	NNP
cord-326631-7gd3hjc3	430	1	=	=	SYM
cord-326631-7gd3hjc3	430	2	1	1	CD
cord-326631-7gd3hjc3	430	3	−	−	NN
cord-326631-7gd3hjc3	430	4	e	e	NN
cord-326631-7gd3hjc3	430	5	−R0	−r0	ADD
cord-326631-7gd3hjc3	431	1	then	then	RB
cord-326631-7gd3hjc3	431	2	the	the	DT
cord-326631-7gd3hjc3	431	3	ensemble	ensemble	NN
cord-326631-7gd3hjc3	431	4	mean	mean	VBP
cord-326631-7gd3hjc3	431	5	final	final	JJ
cord-326631-7gd3hjc3	431	6	size	size	NN
cord-326631-7gd3hjc3	431	7	in	in	IN
cord-326631-7gd3hjc3	431	8	these	these	DT
cord-326631-7gd3hjc3	431	9	chain	chain	NN
cord-326631-7gd3hjc3	431	10	binomial	binomial	NN
cord-326631-7gd3hjc3	431	11	models	model	NNS
cord-326631-7gd3hjc3	431	12	is	be	VBZ
cord-326631-7gd3hjc3	431	13	the	the	DT
cord-326631-7gd3hjc3	431	14	solution	solution	NN
cord-326631-7gd3hjc3	431	15	of	of	IN
cord-326631-7gd3hjc3	431	16	our	-PRON-	PRP$
cord-326631-7gd3hjc3	431	17	Eqs	Eqs	NNP
cord-326631-7gd3hjc3	431	18	.	.	.
cord-326631-7gd3hjc3	432	1	(	(	-LRB-
cord-326631-7gd3hjc3	432	2	27	27	CD
cord-326631-7gd3hjc3	432	3	)	)	-RRB-
cord-326631-7gd3hjc3	432	4	.	.	.
cord-326631-7gd3hjc3	433	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	433	2	emphasized	emphasize	VBD
cord-326631-7gd3hjc3	433	3	two	two	CD
cord-326631-7gd3hjc3	433	4	circumstances	circumstance	NNS
cord-326631-7gd3hjc3	433	5	under	under	IN
cord-326631-7gd3hjc3	433	6	which	which	WDT
cord-326631-7gd3hjc3	433	7	the	the	DT
cord-326631-7gd3hjc3	433	8	usual	usual	JJ
cord-326631-7gd3hjc3	433	9	final	final	JJ
cord-326631-7gd3hjc3	433	10	size	size	NN
cord-326631-7gd3hjc3	433	11	formula	formula	NN
cord-326631-7gd3hjc3	433	12	will	will	MD
cord-326631-7gd3hjc3	433	13	not	not	RB
cord-326631-7gd3hjc3	433	14	apply	apply	VB
cord-326631-7gd3hjc3	433	15	.	.	.
cord-326631-7gd3hjc3	434	1	One	one	CD
cord-326631-7gd3hjc3	434	2	was	be	VBD
cord-326631-7gd3hjc3	434	3	the	the	DT
cord-326631-7gd3hjc3	434	4	case	case	NN
cord-326631-7gd3hjc3	434	5	of	of	IN
cord-326631-7gd3hjc3	434	6	age	age	NN
cord-326631-7gd3hjc3	434	7	-	-	HYPH
cord-326631-7gd3hjc3	434	8	structured	structure	VBN
cord-326631-7gd3hjc3	434	9	heterogeneity	heterogeneity	NN
cord-326631-7gd3hjc3	434	10	of	of	IN
cord-326631-7gd3hjc3	434	11	transmission	transmission	NN
cord-326631-7gd3hjc3	434	12	;	;	:
cord-326631-7gd3hjc3	434	13	while	while	IN
cord-326631-7gd3hjc3	434	14	this	this	DT
cord-326631-7gd3hjc3	434	15	would	would	MD
cord-326631-7gd3hjc3	434	16	influence	influence	VB
cord-326631-7gd3hjc3	434	17	the	the	DT
cord-326631-7gd3hjc3	434	18	final	final	JJ
cord-326631-7gd3hjc3	434	19	size	size	NN
cord-326631-7gd3hjc3	434	20	,	,	,
cord-326631-7gd3hjc3	434	21	it	-PRON-	PRP
cord-326631-7gd3hjc3	434	22	is	be	VBZ
cord-326631-7gd3hjc3	434	23	unlikely	unlikely	JJ
cord-326631-7gd3hjc3	434	24	that	that	IN
cord-326631-7gd3hjc3	434	25	we	-PRON-	PRP
cord-326631-7gd3hjc3	434	26	would	would	MD
cord-326631-7gd3hjc3	434	27	be	be	VB
cord-326631-7gd3hjc3	434	28	able	able	JJ
cord-326631-7gd3hjc3	434	29	to	to	TO
cord-326631-7gd3hjc3	434	30	parameterize	parameterize	VB
cord-326631-7gd3hjc3	434	31	the	the	DT
cord-326631-7gd3hjc3	434	32	age	age	NN
cord-326631-7gd3hjc3	434	33	-	-	HYPH
cord-326631-7gd3hjc3	434	34	structured	structure	VBN
cord-326631-7gd3hjc3	434	35	contact	contact	NN
cord-326631-7gd3hjc3	434	36	patterns	pattern	NNS
cord-326631-7gd3hjc3	434	37	sufficiently	sufficiently	RB
cord-326631-7gd3hjc3	434	38	well	well	RB
cord-326631-7gd3hjc3	434	39	to	to	TO
cord-326631-7gd3hjc3	434	40	improve	improve	VB
cord-326631-7gd3hjc3	434	41	on	on	IN
cord-326631-7gd3hjc3	434	42	the	the	DT
cord-326631-7gd3hjc3	434	43	final	final	JJ
cord-326631-7gd3hjc3	434	44	size	size	NN
cord-326631-7gd3hjc3	434	45	estimate	estimate	NN
cord-326631-7gd3hjc3	434	46	generated	generate	VBN
cord-326631-7gd3hjc3	434	47	with	with	IN
cord-326631-7gd3hjc3	434	48	the	the	DT
cord-326631-7gd3hjc3	434	49	assumption	assumption	NN
cord-326631-7gd3hjc3	434	50	of	of	IN
cord-326631-7gd3hjc3	434	51	homogeneous	homogeneous	JJ
cord-326631-7gd3hjc3	434	52	mixing	mixing	NN
cord-326631-7gd3hjc3	434	53	.	.	.
cord-326631-7gd3hjc3	435	1	The	the	DT
cord-326631-7gd3hjc3	435	2	other	other	JJ
cord-326631-7gd3hjc3	435	3	case	case	NN
cord-326631-7gd3hjc3	435	4	we	-PRON-	PRP
cord-326631-7gd3hjc3	435	5	discussed	discuss	VBD
cord-326631-7gd3hjc3	435	6	was	be	VBD
cord-326631-7gd3hjc3	435	7	the	the	DT
cord-326631-7gd3hjc3	435	8	existence	existence	NN
cord-326631-7gd3hjc3	435	9	of	of	IN
cord-326631-7gd3hjc3	435	10	social	social	JJ
cord-326631-7gd3hjc3	435	11	core	core	NN
cord-326631-7gd3hjc3	435	12	groups	group	NNS
cord-326631-7gd3hjc3	435	13	,	,	,
cord-326631-7gd3hjc3	435	14	which	which	WDT
cord-326631-7gd3hjc3	435	15	are	be	VBP
cord-326631-7gd3hjc3	435	16	extremely	extremely	RB
cord-326631-7gd3hjc3	435	17	important	important	JJ
cord-326631-7gd3hjc3	435	18	in	in	IN
cord-326631-7gd3hjc3	435	19	the	the	DT
cord-326631-7gd3hjc3	435	20	epidemiological	epidemiological	JJ
cord-326631-7gd3hjc3	435	21	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	435	22	of	of	IN
cord-326631-7gd3hjc3	435	23	sexually	sexually	RB
cord-326631-7gd3hjc3	435	24	transmitted	transmit	VBN
cord-326631-7gd3hjc3	435	25	diseases	disease	NNS
cord-326631-7gd3hjc3	435	26	;	;	:
cord-326631-7gd3hjc3	435	27	in	in	IN
cord-326631-7gd3hjc3	435	28	this	this	DT
cord-326631-7gd3hjc3	435	29	case	case	NN
cord-326631-7gd3hjc3	435	30	,	,	,
cord-326631-7gd3hjc3	435	31	some	some	DT
cord-326631-7gd3hjc3	435	32	estimate	estimate	NN
cord-326631-7gd3hjc3	435	33	of	of	IN
cord-326631-7gd3hjc3	435	34	the	the	DT
cord-326631-7gd3hjc3	435	35	difference	difference	NN
cord-326631-7gd3hjc3	435	36	in	in	IN
cord-326631-7gd3hjc3	435	37	transmission	transmission	NN
cord-326631-7gd3hjc3	435	38	rates	rate	NNS
cord-326631-7gd3hjc3	435	39	in	in	IN
cord-326631-7gd3hjc3	435	40	different	different	JJ
cord-326631-7gd3hjc3	435	41	social	social	JJ
cord-326631-7gd3hjc3	435	42	groups	group	NNS
cord-326631-7gd3hjc3	435	43	would	would	MD
cord-326631-7gd3hjc3	435	44	likely	likely	RB
cord-326631-7gd3hjc3	435	45	be	be	VB
cord-326631-7gd3hjc3	435	46	needed	need	VBN
cord-326631-7gd3hjc3	435	47	to	to	TO
cord-326631-7gd3hjc3	435	48	obtain	obtain	VB
cord-326631-7gd3hjc3	435	49	a	a	DT
cord-326631-7gd3hjc3	435	50	useful	useful	JJ
cord-326631-7gd3hjc3	435	51	estimate	estimate	NN
cord-326631-7gd3hjc3	435	52	of	of	IN
cord-326631-7gd3hjc3	435	53	the	the	DT
cord-326631-7gd3hjc3	435	54	final	final	JJ
cord-326631-7gd3hjc3	435	55	size	size	NN
cord-326631-7gd3hjc3	435	56	.	.	.
cord-326631-7gd3hjc3	436	1	In	in	IN
cord-326631-7gd3hjc3	436	2	computing	compute	VBG
cord-326631-7gd3hjc3	436	3	the	the	DT
cord-326631-7gd3hjc3	436	4	final	final	JJ
cord-326631-7gd3hjc3	436	5	size	size	NN
cord-326631-7gd3hjc3	436	6	,	,	,
cord-326631-7gd3hjc3	436	7	we	-PRON-	PRP
cord-326631-7gd3hjc3	436	8	have	have	VBP
cord-326631-7gd3hjc3	436	9	always	always	RB
cord-326631-7gd3hjc3	436	10	assumed	assume	VBN
cord-326631-7gd3hjc3	436	11	that	that	IN
cord-326631-7gd3hjc3	436	12	there	there	EX
cord-326631-7gd3hjc3	436	13	are	be	VBP
cord-326631-7gd3hjc3	436	14	no	no	DT
cord-326631-7gd3hjc3	436	15	temporal	temporal	JJ
cord-326631-7gd3hjc3	436	16	changes	change	NNS
cord-326631-7gd3hjc3	436	17	in	in	IN
cord-326631-7gd3hjc3	436	18	the	the	DT
cord-326631-7gd3hjc3	436	19	transmission	transmission	NN
cord-326631-7gd3hjc3	436	20	rate	rate	NN
cord-326631-7gd3hjc3	436	21	β	β	NN
cord-326631-7gd3hjc3	436	22	.	.	.
cord-326631-7gd3hjc3	437	1	Temporal	temporal	JJ
cord-326631-7gd3hjc3	437	2	variations	variation	NNS
cord-326631-7gd3hjc3	437	3	in	in	IN
cord-326631-7gd3hjc3	437	4	β	β	NN
cord-326631-7gd3hjc3	437	5	could	could	MD
cord-326631-7gd3hjc3	437	6	result	result	VB
cord-326631-7gd3hjc3	437	7	from	from	IN
cord-326631-7gd3hjc3	437	8	intrinsic	intrinsic	JJ
cord-326631-7gd3hjc3	437	9	seasonality	seasonality	NN
cord-326631-7gd3hjc3	437	10	of	of	IN
cord-326631-7gd3hjc3	437	11	contact	contact	NN
cord-326631-7gd3hjc3	437	12	rates	rate	NNS
cord-326631-7gd3hjc3	437	13	,	,	,
cord-326631-7gd3hjc3	437	14	imposition	imposition	NN
cord-326631-7gd3hjc3	437	15	of	of	IN
cord-326631-7gd3hjc3	437	16	control	control	NN
cord-326631-7gd3hjc3	437	17	measures	measure	NNS
cord-326631-7gd3hjc3	437	18	,	,	,
cord-326631-7gd3hjc3	437	19	or	or	CC
cord-326631-7gd3hjc3	437	20	behavioral	behavioral	JJ
cord-326631-7gd3hjc3	437	21	change	change	NN
cord-326631-7gd3hjc3	437	22	in	in	IN
cord-326631-7gd3hjc3	437	23	response	response	NN
cord-326631-7gd3hjc3	437	24	to	to	IN
cord-326631-7gd3hjc3	437	25	epidemic	epidemic	NN
cord-326631-7gd3hjc3	437	26	alerts	alert	NNS
cord-326631-7gd3hjc3	437	27	.	.	.
cord-326631-7gd3hjc3	438	1	Small	small	JJ
cord-326631-7gd3hjc3	438	2	seasonal	seasonal	JJ
cord-326631-7gd3hjc3	438	3	variations	variation	NNS
cord-326631-7gd3hjc3	438	4	in	in	IN
cord-326631-7gd3hjc3	438	5	β	β	NN
cord-326631-7gd3hjc3	438	6	cause	cause	NN
cord-326631-7gd3hjc3	438	7	only	only	RB
cord-326631-7gd3hjc3	438	8	small	small	JJ
cord-326631-7gd3hjc3	438	9	perturbations	perturbation	NNS
cord-326631-7gd3hjc3	438	10	to	to	IN
cord-326631-7gd3hjc3	438	11	the	the	DT
cord-326631-7gd3hjc3	438	12	final	final	JJ
cord-326631-7gd3hjc3	438	13	size	size	NN
cord-326631-7gd3hjc3	438	14	formula	formula	NN
cord-326631-7gd3hjc3	438	15	,	,	,
cord-326631-7gd3hjc3	438	16	and	and	CC
cord-326631-7gd3hjc3	438	17	substantial	substantial	JJ
cord-326631-7gd3hjc3	438	18	seasonality	seasonality	NN
cord-326631-7gd3hjc3	438	19	is	be	VBZ
cord-326631-7gd3hjc3	438	20	generally	generally	RB
cord-326631-7gd3hjc3	438	21	associated	associate	VBN
cord-326631-7gd3hjc3	438	22	with	with	IN
cord-326631-7gd3hjc3	438	23	school	school	NN
cord-326631-7gd3hjc3	438	24	-	-	HYPH
cord-326631-7gd3hjc3	438	25	age	age	NN
cord-326631-7gd3hjc3	438	26	children	child	NNS
cord-326631-7gd3hjc3	438	27	(	(	-LRB-
cord-326631-7gd3hjc3	438	28	London	London	NNP
cord-326631-7gd3hjc3	438	29	and	and	CC
cord-326631-7gd3hjc3	438	30	Yorke	Yorke	NNP
cord-326631-7gd3hjc3	438	31	,	,	,
cord-326631-7gd3hjc3	438	32	1973	1973	CD
cord-326631-7gd3hjc3	438	33	)	)	-RRB-
cord-326631-7gd3hjc3	438	34	who	who	WP
cord-326631-7gd3hjc3	438	35	form	form	VBP
cord-326631-7gd3hjc3	438	36	a	a	DT
cord-326631-7gd3hjc3	438	37	small	small	JJ
cord-326631-7gd3hjc3	438	38	fraction	fraction	NN
cord-326631-7gd3hjc3	438	39	of	of	IN
cord-326631-7gd3hjc3	438	40	the	the	DT
cord-326631-7gd3hjc3	438	41	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	438	42	pool	pool	NN
cord-326631-7gd3hjc3	438	43	when	when	WRB
cord-326631-7gd3hjc3	438	44	a	a	DT
cord-326631-7gd3hjc3	438	45	new	new	JJ
cord-326631-7gd3hjc3	438	46	infection	infection	NN
cord-326631-7gd3hjc3	438	47	enters	enter	VBZ
cord-326631-7gd3hjc3	438	48	a	a	DT
cord-326631-7gd3hjc3	438	49	population	population	NN
cord-326631-7gd3hjc3	438	50	.	.	.
cord-326631-7gd3hjc3	439	1	Infection	infection	NN
cord-326631-7gd3hjc3	439	2	control	control	NN
cord-326631-7gd3hjc3	439	3	measures	measure	NNS
cord-326631-7gd3hjc3	439	4	,	,	,
cord-326631-7gd3hjc3	439	5	such	such	JJ
cord-326631-7gd3hjc3	439	6	as	as	IN
cord-326631-7gd3hjc3	439	7	those	those	DT
cord-326631-7gd3hjc3	439	8	adopted	adopt	VBN
cord-326631-7gd3hjc3	439	9	during	during	IN
cord-326631-7gd3hjc3	439	10	the	the	DT
cord-326631-7gd3hjc3	439	11	2003	2003	CD
cord-326631-7gd3hjc3	439	12	SARS	SARS	NNP
cord-326631-7gd3hjc3	439	13	epidemic	epidemic	NN
cord-326631-7gd3hjc3	439	14	(	(	-LRB-
cord-326631-7gd3hjc3	439	15	Lipsitch	Lipsitch	NNP
cord-326631-7gd3hjc3	439	16	et	et	NNP
cord-326631-7gd3hjc3	439	17	al	al	NNP
cord-326631-7gd3hjc3	439	18	.	.	NNP
cord-326631-7gd3hjc3	439	19	,	,	,
cord-326631-7gd3hjc3	439	20	2003	2003	CD
cord-326631-7gd3hjc3	439	21	;	;	:
cord-326631-7gd3hjc3	439	22	Wallinga	Wallinga	NNP
cord-326631-7gd3hjc3	439	23	and	and	CC
cord-326631-7gd3hjc3	439	24	Teunis	Teunis	NNP
cord-326631-7gd3hjc3	439	25	,	,	,
cord-326631-7gd3hjc3	439	26	2004	2004	CD
cord-326631-7gd3hjc3	439	27	)	)	-RRB-
cord-326631-7gd3hjc3	439	28	,	,	,
cord-326631-7gd3hjc3	439	29	could	could	MD
cord-326631-7gd3hjc3	439	30	have	have	VB
cord-326631-7gd3hjc3	439	31	a	a	DT
cord-326631-7gd3hjc3	439	32	dramatic	dramatic	JJ
cord-326631-7gd3hjc3	439	33	effect	effect	NN
cord-326631-7gd3hjc3	439	34	on	on	IN
cord-326631-7gd3hjc3	439	35	the	the	DT
cord-326631-7gd3hjc3	439	36	final	final	JJ
cord-326631-7gd3hjc3	439	37	size	size	NN
cord-326631-7gd3hjc3	439	38	;	;	:
cord-326631-7gd3hjc3	439	39	in	in	IN
cord-326631-7gd3hjc3	439	40	this	this	DT
cord-326631-7gd3hjc3	439	41	case	case	NN
cord-326631-7gd3hjc3	439	42	,	,	,
cord-326631-7gd3hjc3	439	43	rather	rather	RB
cord-326631-7gd3hjc3	439	44	than	than	IN
cord-326631-7gd3hjc3	439	45	R	r	NN
cord-326631-7gd3hjc3	439	46	0	0	CD
cord-326631-7gd3hjc3	439	47	,	,	,
cord-326631-7gd3hjc3	439	48	the	the	DT
cord-326631-7gd3hjc3	439	49	reproduction	reproduction	NN
cord-326631-7gd3hjc3	439	50	number	number	NN
cord-326631-7gd3hjc3	439	51	that	that	WDT
cord-326631-7gd3hjc3	439	52	is	be	VBZ
cord-326631-7gd3hjc3	439	53	relevant	relevant	JJ
cord-326631-7gd3hjc3	439	54	for	for	IN
cord-326631-7gd3hjc3	439	55	the	the	DT
cord-326631-7gd3hjc3	439	56	final	final	JJ
cord-326631-7gd3hjc3	439	57	size	size	NN
cord-326631-7gd3hjc3	439	58	formula	formula	NN
cord-326631-7gd3hjc3	439	59	must	must	MD
cord-326631-7gd3hjc3	439	60	be	be	VB
cord-326631-7gd3hjc3	439	61	calculated	calculate	VBN
cord-326631-7gd3hjc3	439	62	after	after	IN
cord-326631-7gd3hjc3	439	63	sustainable	sustainable	JJ
cord-326631-7gd3hjc3	439	64	precautionary	precautionary	JJ
cord-326631-7gd3hjc3	439	65	measures	measure	NNS
cord-326631-7gd3hjc3	439	66	have	have	VBP
cord-326631-7gd3hjc3	439	67	been	be	VBN
cord-326631-7gd3hjc3	439	68	put	put	VBN
cord-326631-7gd3hjc3	439	69	into	into	IN
cord-326631-7gd3hjc3	439	70	place	place	NN
cord-326631-7gd3hjc3	439	71	.	.	.
cord-326631-7gd3hjc3	440	1	Individual	individual	JJ
cord-326631-7gd3hjc3	440	2	behavioral	behavioral	JJ
cord-326631-7gd3hjc3	440	3	change	change	NN
cord-326631-7gd3hjc3	440	4	could	could	MD
cord-326631-7gd3hjc3	440	5	alter	alter	VB
cord-326631-7gd3hjc3	440	6	the	the	DT
cord-326631-7gd3hjc3	440	7	transmission	transmission	NN
cord-326631-7gd3hjc3	440	8	rate	rate	NN
cord-326631-7gd3hjc3	440	9	through	through	IN
cord-326631-7gd3hjc3	440	10	time	time	NN
cord-326631-7gd3hjc3	440	11	-	-	HYPH
cord-326631-7gd3hjc3	440	12	dependence	dependence	NN
cord-326631-7gd3hjc3	440	13	(	(	-LRB-
cord-326631-7gd3hjc3	440	14	β	β	NN
cord-326631-7gd3hjc3	440	15	=	=	SYM
cord-326631-7gd3hjc3	440	16	β(t	β(t	NNP
cord-326631-7gd3hjc3	440	17	)	)	-RRB-
cord-326631-7gd3hjc3	440	18	,	,	,
cord-326631-7gd3hjc3	440	19	as	as	IN
cord-326631-7gd3hjc3	440	20	in	in	IN
cord-326631-7gd3hjc3	440	21	the	the	DT
cord-326631-7gd3hjc3	440	22	case	case	NN
cord-326631-7gd3hjc3	440	23	of	of	IN
cord-326631-7gd3hjc3	440	24	imposed	impose	VBN
cord-326631-7gd3hjc3	440	25	control	control	NN
cord-326631-7gd3hjc3	440	26	measures	measure	NNS
cord-326631-7gd3hjc3	440	27	)	)	-RRB-
cord-326631-7gd3hjc3	440	28	or	or	CC
cord-326631-7gd3hjc3	440	29	through	through	IN
cord-326631-7gd3hjc3	440	30	density	density	NN
cord-326631-7gd3hjc3	440	31	-	-	HYPH
cord-326631-7gd3hjc3	440	32	dependence	dependence	NN
cord-326631-7gd3hjc3	440	33	(	(	-LRB-
cord-326631-7gd3hjc3	440	34	β	β	NN
cord-326631-7gd3hjc3	440	35	=	=	SYM
cord-326631-7gd3hjc3	440	36	β(I	β(I	NNP
cord-326631-7gd3hjc3	440	37	)	)	-RRB-
cord-326631-7gd3hjc3	440	38	,	,	,
cord-326631-7gd3hjc3	440	39	with	with	IN
cord-326631-7gd3hjc3	440	40	β	β	NN
cord-326631-7gd3hjc3	440	41	decreasing	decrease	VBG
cord-326631-7gd3hjc3	440	42	as	as	IN
cord-326631-7gd3hjc3	440	43	I	-PRON-	PRP
cord-326631-7gd3hjc3	440	44	increases	increase	VBZ
cord-326631-7gd3hjc3	440	45	,	,	,
cord-326631-7gd3hjc3	440	46	which	which	WDT
cord-326631-7gd3hjc3	440	47	would	would	MD
cord-326631-7gd3hjc3	440	48	arise	arise	VB
cord-326631-7gd3hjc3	440	49	if	if	IN
cord-326631-7gd3hjc3	440	50	people	people	NNS
cord-326631-7gd3hjc3	440	51	tend	tend	VBP
cord-326631-7gd3hjc3	440	52	to	to	TO
cord-326631-7gd3hjc3	440	53	be	be	VB
cord-326631-7gd3hjc3	440	54	more	more	RBR
cord-326631-7gd3hjc3	440	55	careful	careful	JJ
cord-326631-7gd3hjc3	440	56	when	when	WRB
cord-326631-7gd3hjc3	440	57	they	-PRON-	PRP
cord-326631-7gd3hjc3	440	58	are	be	VBP
cord-326631-7gd3hjc3	440	59	aware	aware	JJ
cord-326631-7gd3hjc3	440	60	of	of	IN
cord-326631-7gd3hjc3	440	61	more	more	JJR
cord-326631-7gd3hjc3	440	62	cases	case	NNS
cord-326631-7gd3hjc3	440	63	)	)	-RRB-
cord-326631-7gd3hjc3	440	64	.	.	.
cord-326631-7gd3hjc3	441	1	In	in	IN
cord-326631-7gd3hjc3	441	2	either	either	DT
cord-326631-7gd3hjc3	441	3	case	case	NN
cord-326631-7gd3hjc3	441	4	,	,	,
cord-326631-7gd3hjc3	441	5	the	the	DT
cord-326631-7gd3hjc3	441	6	standard	standard	JJ
cord-326631-7gd3hjc3	441	7	final	final	JJ
cord-326631-7gd3hjc3	441	8	size	size	NN
cord-326631-7gd3hjc3	441	9	formula	formula	NN
cord-326631-7gd3hjc3	441	10	might	may	MD
cord-326631-7gd3hjc3	441	11	yield	yield	VB
cord-326631-7gd3hjc3	441	12	a	a	DT
cord-326631-7gd3hjc3	441	13	poor	poor	JJ
cord-326631-7gd3hjc3	441	14	approximation	approximation	NN
cord-326631-7gd3hjc3	441	15	of	of	IN
cord-326631-7gd3hjc3	441	16	the	the	DT
cord-326631-7gd3hjc3	441	17	true	true	JJ
cord-326631-7gd3hjc3	441	18	final	final	JJ
cord-326631-7gd3hjc3	441	19	size	size	NN
cord-326631-7gd3hjc3	441	20	.	.	.
cord-326631-7gd3hjc3	442	1	All	all	DT
cord-326631-7gd3hjc3	442	2	of	of	IN
cord-326631-7gd3hjc3	442	3	our	-PRON-	PRP$
cord-326631-7gd3hjc3	442	4	analysis	analysis	NN
cord-326631-7gd3hjc3	442	5	is	be	VBZ
cord-326631-7gd3hjc3	442	6	predicated	predicate	VBN
cord-326631-7gd3hjc3	442	7	on	on	IN
cord-326631-7gd3hjc3	442	8	the	the	DT
cord-326631-7gd3hjc3	442	9	assumption	assumption	NN
cord-326631-7gd3hjc3	442	10	that	that	IN
cord-326631-7gd3hjc3	442	11	vital	vital	JJ
cord-326631-7gd3hjc3	442	12	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	442	13	(	(	-LRB-
cord-326631-7gd3hjc3	442	14	births	birth	NNS
cord-326631-7gd3hjc3	442	15	and	and	CC
cord-326631-7gd3hjc3	442	16	deaths	death	NNS
cord-326631-7gd3hjc3	442	17	)	)	-RRB-
cord-326631-7gd3hjc3	442	18	,	,	,
cord-326631-7gd3hjc3	442	19	and	and	CC
cord-326631-7gd3hjc3	442	20	more	more	RBR
cord-326631-7gd3hjc3	442	21	generally	generally	RB
cord-326631-7gd3hjc3	442	22	any	any	DT
cord-326631-7gd3hjc3	442	23	source	source	NN
cord-326631-7gd3hjc3	442	24	of	of	IN
cord-326631-7gd3hjc3	442	25	new	new	JJ
cord-326631-7gd3hjc3	442	26	susceptible	susceptible	JJ
cord-326631-7gd3hjc3	442	27	individuals	individual	NNS
cord-326631-7gd3hjc3	442	28	,	,	,
cord-326631-7gd3hjc3	442	29	can	can	MD
cord-326631-7gd3hjc3	442	30	be	be	VB
cord-326631-7gd3hjc3	442	31	ignored	ignore	VBN
cord-326631-7gd3hjc3	442	32	.	.	.
cord-326631-7gd3hjc3	443	1	This	this	DT
cord-326631-7gd3hjc3	443	2	approximation	approximation	NN
cord-326631-7gd3hjc3	443	3	is	be	VBZ
cord-326631-7gd3hjc3	443	4	not	not	RB
cord-326631-7gd3hjc3	443	5	valid	valid	JJ
cord-326631-7gd3hjc3	443	6	in	in	IN
cord-326631-7gd3hjc3	443	7	circumstances	circumstance	NNS
cord-326631-7gd3hjc3	443	8	where	where	WRB
cord-326631-7gd3hjc3	443	9	infectious	infectious	JJ
cord-326631-7gd3hjc3	443	10	periods	period	NNS
cord-326631-7gd3hjc3	443	11	are	be	VBP
cord-326631-7gd3hjc3	443	12	substantial	substantial	JJ
cord-326631-7gd3hjc3	443	13	compared	compare	VBN
cord-326631-7gd3hjc3	443	14	with	with	IN
cord-326631-7gd3hjc3	443	15	life	life	NN
cord-326631-7gd3hjc3	443	16	expectancy	expectancy	NN
cord-326631-7gd3hjc3	443	17	or	or	CC
cord-326631-7gd3hjc3	443	18	where	where	WRB
cord-326631-7gd3hjc3	443	19	immunity	immunity	NN
cord-326631-7gd3hjc3	443	20	decays	decay	VBZ
cord-326631-7gd3hjc3	443	21	rapidly	rapidly	RB
cord-326631-7gd3hjc3	443	22	.	.	.
cord-326631-7gd3hjc3	444	1	It	-PRON-	PRP
cord-326631-7gd3hjc3	444	2	will	will	MD
cord-326631-7gd3hjc3	444	3	,	,	,
cord-326631-7gd3hjc3	444	4	however	however	RB
cord-326631-7gd3hjc3	444	5	,	,	,
cord-326631-7gd3hjc3	444	6	typically	typically	RB
cord-326631-7gd3hjc3	444	7	be	be	VB
cord-326631-7gd3hjc3	444	8	relevant	relevant	JJ
cord-326631-7gd3hjc3	444	9	whenever	whenever	WRB
cord-326631-7gd3hjc3	444	10	a	a	DT
cord-326631-7gd3hjc3	444	11	new	new	JJ
cord-326631-7gd3hjc3	444	12	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	444	13	pathogen	pathogen	NN
cord-326631-7gd3hjc3	444	14	emerges	emerge	VBZ
cord-326631-7gd3hjc3	444	15	,	,	,
cord-326631-7gd3hjc3	444	16	as	as	IN
cord-326631-7gd3hjc3	444	17	in	in	IN
cord-326631-7gd3hjc3	444	18	the	the	DT
cord-326631-7gd3hjc3	444	19	case	case	NN
cord-326631-7gd3hjc3	444	20	of	of	IN
cord-326631-7gd3hjc3	444	21	the	the	DT
cord-326631-7gd3hjc3	444	22	SARS	SARS	NNP
cord-326631-7gd3hjc3	444	23	outbreak	outbreak	NN
cord-326631-7gd3hjc3	444	24	in	in	IN
cord-326631-7gd3hjc3	444	25	2003	2003	CD
cord-326631-7gd3hjc3	445	1	(	(	-LRB-
cord-326631-7gd3hjc3	445	2	Donnelly	Donnelly	NNP
cord-326631-7gd3hjc3	445	3	et	et	NNP
cord-326631-7gd3hjc3	445	4	al	al	NNP
cord-326631-7gd3hjc3	445	5	.	.	NNP
cord-326631-7gd3hjc3	445	6	,	,	,
cord-326631-7gd3hjc3	445	7	2003	2003	CD
cord-326631-7gd3hjc3	445	8	)	)	-RRB-
cord-326631-7gd3hjc3	445	9	or	or	CC
cord-326631-7gd3hjc3	445	10	the	the	DT
cord-326631-7gd3hjc3	445	11	emergence	emergence	NN
cord-326631-7gd3hjc3	445	12	of	of	IN
cord-326631-7gd3hjc3	445	13	a	a	DT
cord-326631-7gd3hjc3	445	14	new	new	JJ
cord-326631-7gd3hjc3	445	15	subtype	subtype	NN
cord-326631-7gd3hjc3	445	16	of	of	IN
cord-326631-7gd3hjc3	445	17	influenza	influenza	NN
cord-326631-7gd3hjc3	445	18	(	(	-LRB-
cord-326631-7gd3hjc3	445	19	Earn	earn	VB
cord-326631-7gd3hjc3	445	20	et	et	FW
cord-326631-7gd3hjc3	445	21	al	al	NNP
cord-326631-7gd3hjc3	445	22	.	.	NNP
cord-326631-7gd3hjc3	445	23	,	,	,
cord-326631-7gd3hjc3	445	24	2002	2002	CD
cord-326631-7gd3hjc3	445	25	)	)	-RRB-
cord-326631-7gd3hjc3	445	26	.	.	.
cord-326631-7gd3hjc3	446	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	446	2	are	be	VBP
cord-326631-7gd3hjc3	446	3	interested	interested	JJ
cord-326631-7gd3hjc3	446	4	in	in	IN
cord-326631-7gd3hjc3	446	5	growth	growth	NN
cord-326631-7gd3hjc3	446	6	or	or	CC
cord-326631-7gd3hjc3	446	7	decay	decay	NN
cord-326631-7gd3hjc3	446	8	of	of	IN
cord-326631-7gd3hjc3	446	9	I(β	I(β	NNP
cord-326631-7gd3hjc3	446	10	,	,	,
cord-326631-7gd3hjc3	446	11	)	)	-RRB-
cord-326631-7gd3hjc3	446	12	,	,	,
cord-326631-7gd3hjc3	446	13	which	which	WDT
cord-326631-7gd3hjc3	446	14	is	be	VBZ
cord-326631-7gd3hjc3	446	15	determined	determine	VBN
cord-326631-7gd3hjc3	446	16	only	only	RB
cord-326631-7gd3hjc3	446	17	by	by	IN
cord-326631-7gd3hjc3	446	18	Eq	Eq	NNP
cord-326631-7gd3hjc3	446	19	.	.	.
cord-326631-7gd3hjc3	447	1	(	(	-LRB-
cord-326631-7gd3hjc3	447	2	D.1b	D.1b	NNP
cord-326631-7gd3hjc3	447	3	)	)	-RRB-
cord-326631-7gd3hjc3	447	4	.	.	.
cord-326631-7gd3hjc3	448	1	Defining	define	VBG
cord-326631-7gd3hjc3	448	2	X(t	X(t	NNP
cord-326631-7gd3hjc3	448	3	)	)	-RRB-
cord-326631-7gd3hjc3	449	1	=	=	NFP
cord-326631-7gd3hjc3	450	1	∞	∞	NNP
cord-326631-7gd3hjc3	450	2	0	0	CD
cord-326631-7gd3hjc3	450	3	β	β	NN
cord-326631-7gd3hjc3	450	4	I(β	I(β	NNP
cord-326631-7gd3hjc3	450	5	,	,	,
cord-326631-7gd3hjc3	450	6	t	t	NNP
cord-326631-7gd3hjc3	450	7	)	)	-RRB-
cord-326631-7gd3hjc3	450	8	dβ	dβ	NNP
cord-326631-7gd3hjc3	450	9	,	,	,
cord-326631-7gd3hjc3	450	10	multiplying	multiply	VBG
cord-326631-7gd3hjc3	450	11	both	both	DT
cord-326631-7gd3hjc3	450	12	sides	side	NNS
cord-326631-7gd3hjc3	450	13	of	of	IN
cord-326631-7gd3hjc3	450	14	Eq	Eq	NNP
cord-326631-7gd3hjc3	450	15	.	.	.
cord-326631-7gd3hjc3	451	1	(	(	-LRB-
cord-326631-7gd3hjc3	451	2	D.1b	D.1b	NNP
cord-326631-7gd3hjc3	451	3	)	)	-RRB-
cord-326631-7gd3hjc3	451	4	by	by	IN
cord-326631-7gd3hjc3	451	5	β	β	NNP
cord-326631-7gd3hjc3	451	6	,	,	,
cord-326631-7gd3hjc3	451	7	and	and	CC
cord-326631-7gd3hjc3	451	8	integrating	integrate	VBG
cord-326631-7gd3hjc3	451	9	with	with	IN
cord-326631-7gd3hjc3	451	10	respect	respect	NN
cord-326631-7gd3hjc3	451	11	to	to	IN
cord-326631-7gd3hjc3	451	12	β	β	NN
cord-326631-7gd3hjc3	451	13	,	,	,
cord-326631-7gd3hjc3	451	14	we	-PRON-	PRP
cord-326631-7gd3hjc3	451	15	find	find	VBP
cord-326631-7gd3hjc3	451	16	On	on	IN
cord-326631-7gd3hjc3	451	17	the	the	DT
cord-326631-7gd3hjc3	451	18	other	other	JJ
cord-326631-7gd3hjc3	451	19	hand	hand	NN
cord-326631-7gd3hjc3	451	20	,	,	,
cord-326631-7gd3hjc3	451	21	recall	recall	VBP
cord-326631-7gd3hjc3	451	22	that	that	IN
cord-326631-7gd3hjc3	451	23	I(t	I(t	NNP
cord-326631-7gd3hjc3	451	24	)	)	-RRB-
cord-326631-7gd3hjc3	452	1	=	=	NFP
cord-326631-7gd3hjc3	453	1	∞	∞	NNP
cord-326631-7gd3hjc3	453	2	0	0	CD
cord-326631-7gd3hjc3	453	3	I(β	I(β	NNP
cord-326631-7gd3hjc3	453	4	,	,	,
cord-326631-7gd3hjc3	453	5	t	t	NN
cord-326631-7gd3hjc3	453	6	)	)	-RRB-
cord-326631-7gd3hjc3	453	7	dt	dt	NNP
cord-326631-7gd3hjc3	453	8	(	(	-LRB-
cord-326631-7gd3hjc3	453	9	the	the	DT
cord-326631-7gd3hjc3	453	10	total	total	JJ
cord-326631-7gd3hjc3	453	11	number	number	NN
cord-326631-7gd3hjc3	453	12	of	of	IN
cord-326631-7gd3hjc3	453	13	infectious	infectious	JJ
cord-326631-7gd3hjc3	453	14	individuals	individual	NNS
cord-326631-7gd3hjc3	453	15	at	at	IN
cord-326631-7gd3hjc3	453	16	time	time	NN
cord-326631-7gd3hjc3	453	17	t	t	NNP
cord-326631-7gd3hjc3	453	18	)	)	-RRB-
cord-326631-7gd3hjc3	453	19	.	.	.
cord-326631-7gd3hjc3	454	1	Therefore	therefore	RB
cord-326631-7gd3hjc3	454	2	,	,	,
cord-326631-7gd3hjc3	454	3	integrating	integrate	VBG
cord-326631-7gd3hjc3	454	4	Eq	Eq	NNP
cord-326631-7gd3hjc3	454	5	.	.	.
cord-326631-7gd3hjc3	455	1	(	(	-LRB-
cord-326631-7gd3hjc3	455	2	B.2b	B.2b	NNP
cord-326631-7gd3hjc3	455	3	)	)	-RRB-
cord-326631-7gd3hjc3	455	4	with	with	IN
cord-326631-7gd3hjc3	455	5	respect	respect	NN
cord-326631-7gd3hjc3	455	6	to	to	IN
cord-326631-7gd3hjc3	455	7	β	β	NN
cord-326631-7gd3hjc3	455	8	,	,	,
cord-326631-7gd3hjc3	455	9	noting	note	VBG
cord-326631-7gd3hjc3	455	10	that	that	IN
cord-326631-7gd3hjc3	455	11	q(β	q(β	NNP
cord-326631-7gd3hjc3	455	12	)	)	-RRB-
cord-326631-7gd3hjc3	455	13	is	be	VBZ
cord-326631-7gd3hjc3	455	14	a	a	DT
cord-326631-7gd3hjc3	455	15	probability	probability	NN
cord-326631-7gd3hjc3	455	16	density	density	NN
cord-326631-7gd3hjc3	455	17	function	function	NN
cord-326631-7gd3hjc3	456	1	so	so	RB
cord-326631-7gd3hjc3	456	2	The	the	DT
cord-326631-7gd3hjc3	456	3	origin	origin	NN
cord-326631-7gd3hjc3	456	4	of	of	IN
cord-326631-7gd3hjc3	456	5	this	this	DT
cord-326631-7gd3hjc3	456	6	system	system	NN
cord-326631-7gd3hjc3	456	7	of	of	IN
cord-326631-7gd3hjc3	456	8	two	two	CD
cord-326631-7gd3hjc3	456	9	ordinary	ordinary	JJ
cord-326631-7gd3hjc3	456	10	differential	differential	JJ
cord-326631-7gd3hjc3	456	11	equations	equation	NNS
cord-326631-7gd3hjc3	456	12	is	be	VBZ
cord-326631-7gd3hjc3	456	13	locally	locally	RB
cord-326631-7gd3hjc3	456	14	stable	stable	JJ
cord-326631-7gd3hjc3	456	15	if	if	IN
cord-326631-7gd3hjc3	456	16	and	and	CC
cord-326631-7gd3hjc3	456	17	only	only	RB
cord-326631-7gd3hjc3	456	18	if	if	IN
cord-326631-7gd3hjc3	456	19	∞	∞	NNP
cord-326631-7gd3hjc3	456	20	0	0	CD
cord-326631-7gd3hjc3	456	21	βq(β	βq(β	NNP
cord-326631-7gd3hjc3	456	22	)	)	-RRB-
cord-326631-7gd3hjc3	456	23	dβ	dβ	IN
cord-326631-7gd3hjc3	456	24	−	−	CD
cord-326631-7gd3hjc3	456	25	γ	γ	NN
cord-326631-7gd3hjc3	456	26	<	<	XX
cord-326631-7gd3hjc3	456	27	0	0	NFP
cord-326631-7gd3hjc3	456	28	or	or	CC
cord-326631-7gd3hjc3	456	29	,	,	,
cord-326631-7gd3hjc3	456	30	equivalently	equivalently	RB
cord-326631-7gd3hjc3	456	31	,	,	,
cord-326631-7gd3hjc3	456	32	R	r	NN
cord-326631-7gd3hjc3	456	33	0	0	CD
cord-326631-7gd3hjc3	456	34	<	<	XX
cord-326631-7gd3hjc3	456	35	1	1	CD
cord-326631-7gd3hjc3	456	36	.	.	.
cord-326631-7gd3hjc3	457	1	Thus	thus	RB
cord-326631-7gd3hjc3	457	2	,	,	,
cord-326631-7gd3hjc3	457	3	the	the	DT
cord-326631-7gd3hjc3	457	4	DFE	DFE	NNP
cord-326631-7gd3hjc3	457	5	is	be	VBZ
cord-326631-7gd3hjc3	457	6	stable	stable	JJ
cord-326631-7gd3hjc3	457	7	if	if	IN
cord-326631-7gd3hjc3	457	8	R	r	NN
cord-326631-7gd3hjc3	457	9	0	0	CD
cord-326631-7gd3hjc3	457	10	<	<	XX
cord-326631-7gd3hjc3	457	11	1	1	CD
cord-326631-7gd3hjc3	457	12	and	and	CC
cord-326631-7gd3hjc3	457	13	unstable	unstable	JJ
cord-326631-7gd3hjc3	457	14	if	if	IN
cord-326631-7gd3hjc3	457	15	R	r	NN
cord-326631-7gd3hjc3	457	16	0	0	CD
cord-326631-7gd3hjc3	457	17	>	>	SYM
cord-326631-7gd3hjc3	457	18	1	1	CD
cord-326631-7gd3hjc3	457	19	.	.	.
cord-326631-7gd3hjc3	458	1	We	-PRON-	PRP
cord-326631-7gd3hjc3	458	2	can	can	MD
cord-326631-7gd3hjc3	458	3	expand	expand	VB
cord-326631-7gd3hjc3	458	4	model	model	NN
cord-326631-7gd3hjc3	458	5	(	(	-LRB-
cord-326631-7gd3hjc3	458	6	21	21	CD
cord-326631-7gd3hjc3	458	7	)	)	-RRB-
cord-326631-7gd3hjc3	458	8	to	to	TO
cord-326631-7gd3hjc3	458	9	include	include	VB
cord-326631-7gd3hjc3	458	10	multiple	multiple	JJ
cord-326631-7gd3hjc3	458	11	stages	stage	NNS
cord-326631-7gd3hjc3	458	12	.	.	.
cord-326631-7gd3hjc3	459	1	Using	use	VBG
cord-326631-7gd3hjc3	459	2	the	the	DT
cord-326631-7gd3hjc3	459	3	same	same	JJ
cord-326631-7gd3hjc3	459	4	techniques	technique	NNS
cord-326631-7gd3hjc3	459	5	,	,	,
cord-326631-7gd3hjc3	459	6	we	-PRON-	PRP
cord-326631-7gd3hjc3	459	7	find	find	VBP
cord-326631-7gd3hjc3	459	8	that	that	IN
cord-326631-7gd3hjc3	459	9	the	the	DT
cord-326631-7gd3hjc3	459	10	conclusion	conclusion	NN
cord-326631-7gd3hjc3	459	11	that	that	IN
cord-326631-7gd3hjc3	459	12	the	the	DT
cord-326631-7gd3hjc3	459	13	epidemic	epidemic	NN
cord-326631-7gd3hjc3	459	14	threshold	threshold	NN
cord-326631-7gd3hjc3	459	15	is	be	VBZ
cord-326631-7gd3hjc3	459	16	given	give	VBN
cord-326631-7gd3hjc3	459	17	by	by	IN
cord-326631-7gd3hjc3	459	18	R	r	NN
cord-326631-7gd3hjc3	459	19	0	0	CD
cord-326631-7gd3hjc3	460	1	=	=	SYM
cord-326631-7gd3hjc3	460	2	1	1	CD
cord-326631-7gd3hjc3	460	3	remains	remain	VBZ
cord-326631-7gd3hjc3	460	4	valid	valid	JJ
cord-326631-7gd3hjc3	460	5	.	.	.
cord-326631-7gd3hjc3	461	1	On	on	IN
cord-326631-7gd3hjc3	461	2	the	the	DT
cord-326631-7gd3hjc3	461	3	spread	spread	NN
cord-326631-7gd3hjc3	461	4	of	of	IN
cord-326631-7gd3hjc3	461	5	a	a	DT
cord-326631-7gd3hjc3	461	6	disease	disease	NN
cord-326631-7gd3hjc3	461	7	with	with	IN
cord-326631-7gd3hjc3	461	8	gamma	gamma	NN
cord-326631-7gd3hjc3	461	9	distributed	distribute	VBN
cord-326631-7gd3hjc3	461	10	latent	latent	JJ
cord-326631-7gd3hjc3	461	11	and	and	CC
cord-326631-7gd3hjc3	461	12	infectious	infectious	JJ
cord-326631-7gd3hjc3	461	13	periods	period	NNS
cord-326631-7gd3hjc3	461	14	Infectious	infectious	JJ
cord-326631-7gd3hjc3	461	15	Diseases	disease	NNS
cord-326631-7gd3hjc3	461	16	of	of	IN
cord-326631-7gd3hjc3	461	17	Humans	human	NNS
cord-326631-7gd3hjc3	461	18	:	:	:
cord-326631-7gd3hjc3	462	1	Dynamics	dynamic	NNS
cord-326631-7gd3hjc3	462	2	and	and	CC
cord-326631-7gd3hjc3	462	3	Control	Control	NNP
cord-326631-7gd3hjc3	462	4	A	a	DT
cord-326631-7gd3hjc3	462	5	preliminary	preliminary	JJ
cord-326631-7gd3hjc3	462	6	study	study	NN
cord-326631-7gd3hjc3	462	7	of	of	IN
cord-326631-7gd3hjc3	462	8	the	the	DT
cord-326631-7gd3hjc3	462	9	transmission	transmission	NN
cord-326631-7gd3hjc3	462	10	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	462	11	of	of	IN
cord-326631-7gd3hjc3	462	12	the	the	DT
cord-326631-7gd3hjc3	462	13	human	human	JJ
cord-326631-7gd3hjc3	462	14	immunodeficiency	immunodeficiency	NN
cord-326631-7gd3hjc3	462	15	virus	virus	NN
cord-326631-7gd3hjc3	462	16	(	(	-LRB-
cord-326631-7gd3hjc3	462	17	HIV	HIV	NNP
cord-326631-7gd3hjc3	462	18	)	)	-RRB-
cord-326631-7gd3hjc3	462	19	,	,	,
cord-326631-7gd3hjc3	462	20	the	the	DT
cord-326631-7gd3hjc3	462	21	causative	causative	JJ
cord-326631-7gd3hjc3	462	22	agent	agent	NN
cord-326631-7gd3hjc3	462	23	of	of	IN
cord-326631-7gd3hjc3	462	24	AIDS	AIDS	NNP
cord-326631-7gd3hjc3	462	25	Stochastic	stochastic	JJ
cord-326631-7gd3hjc3	462	26	epidemic	epidemic	NN
cord-326631-7gd3hjc3	462	27	models	model	NNS
cord-326631-7gd3hjc3	462	28	and	and	CC
cord-326631-7gd3hjc3	462	29	their	-PRON-	PRP$
cord-326631-7gd3hjc3	462	30	statistical	statistical	JJ
cord-326631-7gd3hjc3	462	31	analysis	analysis	NN
cord-326631-7gd3hjc3	463	1	The	the	DT
cord-326631-7gd3hjc3	463	2	asymptotic	asymptotic	JJ
cord-326631-7gd3hjc3	463	3	final	final	JJ
cord-326631-7gd3hjc3	463	4	size	size	NN
cord-326631-7gd3hjc3	463	5	distribution	distribution	NN
cord-326631-7gd3hjc3	463	6	of	of	IN
cord-326631-7gd3hjc3	463	7	multitype	multitype	JJ
cord-326631-7gd3hjc3	463	8	chain	chain	NN
cord-326631-7gd3hjc3	463	9	-	-	HYPH
cord-326631-7gd3hjc3	463	10	binomial	binomial	NN
cord-326631-7gd3hjc3	463	11	epidemic	epidemic	NN
cord-326631-7gd3hjc3	463	12	processes	process	NNS
cord-326631-7gd3hjc3	463	13	Dynamics	dynamic	NNS
cord-326631-7gd3hjc3	463	14	of	of	IN
cord-326631-7gd3hjc3	463	15	annual	annual	JJ
cord-326631-7gd3hjc3	463	16	influenza	influenza	NN
cord-326631-7gd3hjc3	463	17	a	a	DT
cord-326631-7gd3hjc3	463	18	epidemics	epidemic	NNS
cord-326631-7gd3hjc3	463	19	with	with	IN
cord-326631-7gd3hjc3	463	20	immuno	immuno	JJ
cord-326631-7gd3hjc3	463	21	-	-	NN
cord-326631-7gd3hjc3	463	22	selection	selection	JJ
cord-326631-7gd3hjc3	464	1	The	the	DT
cord-326631-7gd3hjc3	464	2	Mathematical	Mathematical	NNP
cord-326631-7gd3hjc3	464	3	Theory	Theory	NNP
cord-326631-7gd3hjc3	464	4	of	of	IN
cord-326631-7gd3hjc3	464	5	Infectious	Infectious	NNP
cord-326631-7gd3hjc3	464	6	Diseases	Diseases	NNPS
cord-326631-7gd3hjc3	464	7	and	and	CC
cord-326631-7gd3hjc3	464	8	its	-PRON-	PRP$
cord-326631-7gd3hjc3	464	9	Application	Application	NNP
cord-326631-7gd3hjc3	464	10	Mathematical	mathematical	JJ
cord-326631-7gd3hjc3	464	11	models	model	NNS
cord-326631-7gd3hjc3	464	12	in	in	IN
cord-326631-7gd3hjc3	464	13	population	population	NN
cord-326631-7gd3hjc3	464	14	biology	biology	NN
cord-326631-7gd3hjc3	464	15	and	and	CC
cord-326631-7gd3hjc3	464	16	epidemiology	epidemiology	NN
cord-326631-7gd3hjc3	464	17	Mathematical	mathematical	JJ
cord-326631-7gd3hjc3	464	18	epidemiology	epidemiology	NN
cord-326631-7gd3hjc3	464	19	of	of	IN
cord-326631-7gd3hjc3	464	20	infectious	infectious	JJ
cord-326631-7gd3hjc3	464	21	diseases	disease	NNS
cord-326631-7gd3hjc3	464	22	:	:	:
cord-326631-7gd3hjc3	464	23	Model	model	NN
cord-326631-7gd3hjc3	464	24	building	building	NN
cord-326631-7gd3hjc3	464	25	,	,	,
cord-326631-7gd3hjc3	464	26	analysis	analysis	NN
cord-326631-7gd3hjc3	464	27	and	and	CC
cord-326631-7gd3hjc3	464	28	interpretation	interpretation	NN
cord-326631-7gd3hjc3	464	29	Epidemiological	epidemiological	JJ
cord-326631-7gd3hjc3	464	30	determinants	determinant	NNS
cord-326631-7gd3hjc3	464	31	of	of	IN
cord-326631-7gd3hjc3	464	32	spread	spread	NN
cord-326631-7gd3hjc3	464	33	of	of	IN
cord-326631-7gd3hjc3	464	34	causal	causal	JJ
cord-326631-7gd3hjc3	464	35	agent	agent	NN
cord-326631-7gd3hjc3	464	36	of	of	IN
cord-326631-7gd3hjc3	464	37	severe	severe	JJ
cord-326631-7gd3hjc3	464	38	acute	acute	JJ
cord-326631-7gd3hjc3	464	39	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	464	40	syndrome	syndrome	NN
cord-326631-7gd3hjc3	464	41	in	in	IN
cord-326631-7gd3hjc3	464	42	Hong	Hong	NNP
cord-326631-7gd3hjc3	464	43	Kong	Kong	NNP
cord-326631-7gd3hjc3	464	44	Pathogen	Pathogen	NNP
cord-326631-7gd3hjc3	464	45	-	-	HYPH
cord-326631-7gd3hjc3	464	46	driven	drive	VBN
cord-326631-7gd3hjc3	464	47	outbreaks	outbreak	NNS
cord-326631-7gd3hjc3	464	48	in	in	IN
cord-326631-7gd3hjc3	464	49	forest	forest	NN
cord-326631-7gd3hjc3	464	50	defoliators	defoliator	NNS
cord-326631-7gd3hjc3	464	51	revisited	revisit	VBD
cord-326631-7gd3hjc3	464	52	:	:	:
cord-326631-7gd3hjc3	465	1	Building	building	NN
cord-326631-7gd3hjc3	465	2	models	model	NNS
cord-326631-7gd3hjc3	465	3	from	from	IN
cord-326631-7gd3hjc3	465	4	exprimental	exprimental	NNP
cord-326631-7gd3hjc3	465	5	data	data	NNP
cord-326631-7gd3hjc3	465	6	Ecology	Ecology	NNP
cord-326631-7gd3hjc3	465	7	and	and	CC
cord-326631-7gd3hjc3	465	8	evolution	evolution	NN
cord-326631-7gd3hjc3	465	9	of	of	IN
cord-326631-7gd3hjc3	465	10	the	the	DT
cord-326631-7gd3hjc3	465	11	flu	flu	NN
cord-326631-7gd3hjc3	465	12	Coherence	coherence	NN
cord-326631-7gd3hjc3	465	13	and	and	CC
cord-326631-7gd3hjc3	465	14	conservation	conservation	NN
cord-326631-7gd3hjc3	465	15	A	a	DT
cord-326631-7gd3hjc3	465	16	simple	simple	JJ
cord-326631-7gd3hjc3	465	17	model	model	NN
cord-326631-7gd3hjc3	465	18	for	for	IN
cord-326631-7gd3hjc3	465	19	complex	complex	JJ
cord-326631-7gd3hjc3	465	20	dynamical	dynamical	JJ
cord-326631-7gd3hjc3	465	21	transitions	transition	NNS
cord-326631-7gd3hjc3	465	22	in	in	IN
cord-326631-7gd3hjc3	465	23	epidemics	epidemic	NNS
cord-326631-7gd3hjc3	465	24	Endemic	endemic	JJ
cord-326631-7gd3hjc3	465	25	models	model	NNS
cord-326631-7gd3hjc3	465	26	with	with	IN
cord-326631-7gd3hjc3	465	27	arbitrarily	arbitrarily	RB
cord-326631-7gd3hjc3	465	28	distributed	distribute	VBN
cord-326631-7gd3hjc3	465	29	periods	period	NNS
cord-326631-7gd3hjc3	465	30	of	of	IN
cord-326631-7gd3hjc3	465	31	infection	infection	NN
cord-326631-7gd3hjc3	466	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	466	2	:	:	:
cord-326631-7gd3hjc3	467	1	Fundamental	fundamental	JJ
cord-326631-7gd3hjc3	467	2	properties	property	NNS
cord-326631-7gd3hjc3	467	3	of	of	IN
cord-326631-7gd3hjc3	467	4	the	the	DT
cord-326631-7gd3hjc3	467	5	model	model	NN
cord-326631-7gd3hjc3	468	1	The	the	DT
cord-326631-7gd3hjc3	468	2	mathematical	mathematical	JJ
cord-326631-7gd3hjc3	468	3	analysis	analysis	NN
cord-326631-7gd3hjc3	468	4	of	of	IN
cord-326631-7gd3hjc3	468	5	an	an	DT
cord-326631-7gd3hjc3	468	6	epidemic	epidemic	NN
cord-326631-7gd3hjc3	468	7	with	with	IN
cord-326631-7gd3hjc3	468	8	two	two	CD
cord-326631-7gd3hjc3	468	9	kinds	kind	NNS
cord-326631-7gd3hjc3	468	10	of	of	IN
cord-326631-7gd3hjc3	468	11	susceptibles	susceptible	NNS
cord-326631-7gd3hjc3	468	12	Metapopulation	Metapopulation	NNP
cord-326631-7gd3hjc3	468	13	Biology	Biology	NNP
cord-326631-7gd3hjc3	468	14	:	:	:
cord-326631-7gd3hjc3	468	15	Ecology	Ecology	NNP
cord-326631-7gd3hjc3	468	16	,	,	,
cord-326631-7gd3hjc3	468	17	Genetics	Genetics	NNP
cord-326631-7gd3hjc3	468	18	,	,	,
cord-326631-7gd3hjc3	468	19	and	and	CC
cord-326631-7gd3hjc3	468	20	Evolution	Evolution	NNP
cord-326631-7gd3hjc3	468	21	Matrix	Matrix	NNP
cord-326631-7gd3hjc3	468	22	Analysis	Analysis	NNP
cord-326631-7gd3hjc3	469	1	The	the	DT
cord-326631-7gd3hjc3	469	2	differential	differential	JJ
cord-326631-7gd3hjc3	469	3	infectivity	infectivity	NN
cord-326631-7gd3hjc3	469	4	and	and	CC
cord-326631-7gd3hjc3	469	5	staged	stage	VBD
cord-326631-7gd3hjc3	469	6	progression	progression	NN
cord-326631-7gd3hjc3	469	7	models	model	NNS
cord-326631-7gd3hjc3	469	8	for	for	IN
cord-326631-7gd3hjc3	469	9	the	the	DT
cord-326631-7gd3hjc3	469	10	transmission	transmission	NN
cord-326631-7gd3hjc3	469	11	of	of	IN
cord-326631-7gd3hjc3	469	12	HIV	HIV	NNP
cord-326631-7gd3hjc3	469	13	A	A	NNP
cord-326631-7gd3hjc3	469	14	contribution	contribution	NN
cord-326631-7gd3hjc3	469	15	to	to	IN
cord-326631-7gd3hjc3	469	16	the	the	DT
cord-326631-7gd3hjc3	469	17	mathematical	mathematical	JJ
cord-326631-7gd3hjc3	469	18	theory	theory	NN
cord-326631-7gd3hjc3	469	19	of	of	IN
cord-326631-7gd3hjc3	469	20	epidemics	epidemic	NNS
cord-326631-7gd3hjc3	469	21	Relationships	relationship	NNS
cord-326631-7gd3hjc3	469	22	between	between	IN
cord-326631-7gd3hjc3	469	23	stochastic	stochastic	JJ
cord-326631-7gd3hjc3	469	24	and	and	CC
cord-326631-7gd3hjc3	469	25	deterministic	deterministic	JJ
cord-326631-7gd3hjc3	469	26	population	population	NN
cord-326631-7gd3hjc3	469	27	models	model	NNS
cord-326631-7gd3hjc3	469	28	Transmission	transmission	NN
cord-326631-7gd3hjc3	469	29	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	469	30	and	and	CC
cord-326631-7gd3hjc3	469	31	control	control	NN
cord-326631-7gd3hjc3	469	32	of	of	IN
cord-326631-7gd3hjc3	469	33	severe	severe	JJ
cord-326631-7gd3hjc3	469	34	acute	acute	JJ
cord-326631-7gd3hjc3	469	35	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	469	36	syndrome	syndrome	NN
cord-326631-7gd3hjc3	469	37	Destabilization	destabilization	NN
cord-326631-7gd3hjc3	469	38	of	of	IN
cord-326631-7gd3hjc3	469	39	epidemic	epidemic	NN
cord-326631-7gd3hjc3	469	40	models	model	NNS
cord-326631-7gd3hjc3	469	41	with	with	IN
cord-326631-7gd3hjc3	469	42	the	the	DT
cord-326631-7gd3hjc3	469	43	inclusion	inclusion	NN
cord-326631-7gd3hjc3	469	44	of	of	IN
cord-326631-7gd3hjc3	469	45	realistic	realistic	JJ
cord-326631-7gd3hjc3	469	46	distributions	distribution	NNS
cord-326631-7gd3hjc3	469	47	of	of	IN
cord-326631-7gd3hjc3	469	48	infectious	infectious	JJ
cord-326631-7gd3hjc3	469	49	periods	period	NNS
cord-326631-7gd3hjc3	469	50	Realistic	realistic	JJ
cord-326631-7gd3hjc3	469	51	distributions	distribution	NNS
cord-326631-7gd3hjc3	469	52	of	of	IN
cord-326631-7gd3hjc3	469	53	infectious	infectious	JJ
cord-326631-7gd3hjc3	469	54	periods	period	NNS
cord-326631-7gd3hjc3	469	55	in	in	IN
cord-326631-7gd3hjc3	469	56	epidemic	epidemic	NN
cord-326631-7gd3hjc3	469	57	models	model	NNS
cord-326631-7gd3hjc3	469	58	:	:	:
cord-326631-7gd3hjc3	469	59	Changing	change	VBG
cord-326631-7gd3hjc3	469	60	patterns	pattern	NNS
cord-326631-7gd3hjc3	469	61	of	of	IN
cord-326631-7gd3hjc3	469	62	persistence	persistence	NN
cord-326631-7gd3hjc3	469	63	and	and	CC
cord-326631-7gd3hjc3	469	64	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	469	65	.	.	.
cord-326631-7gd3hjc3	470	1	Theor	theor	JJ
cord-326631-7gd3hjc3	470	2	Recurrent	recurrent	JJ
cord-326631-7gd3hjc3	470	3	outbreaks	outbreak	NNS
cord-326631-7gd3hjc3	470	4	of	of	IN
cord-326631-7gd3hjc3	470	5	measles	measle	NNS
cord-326631-7gd3hjc3	470	6	,	,	,
cord-326631-7gd3hjc3	470	7	chickenpox	chickenpox	NN
cord-326631-7gd3hjc3	470	8	and	and	CC
cord-326631-7gd3hjc3	470	9	mumps	mump	NNS
cord-326631-7gd3hjc3	470	10	.	.	.
cord-326631-7gd3hjc3	471	1	I	-PRON-	PRP
cord-326631-7gd3hjc3	471	2	Seasonal	seasonal	JJ
cord-326631-7gd3hjc3	471	3	variation	variation	NN
cord-326631-7gd3hjc3	471	4	in	in	IN
cord-326631-7gd3hjc3	471	5	contact	contact	NN
cord-326631-7gd3hjc3	471	6	rates	rate	NNS
cord-326631-7gd3hjc3	472	1	SARS	SARS	NNP
cord-326631-7gd3hjc3	472	2	-	-	HYPH
cord-326631-7gd3hjc3	472	3	one	one	CD
cord-326631-7gd3hjc3	472	4	year	year	NN
cord-326631-7gd3hjc3	472	5	later	later	RB
cord-326631-7gd3hjc3	472	6	Identification	identification	NN
cord-326631-7gd3hjc3	472	7	of	of	IN
cord-326631-7gd3hjc3	472	8	severe	severe	JJ
cord-326631-7gd3hjc3	472	9	acute	acute	JJ
cord-326631-7gd3hjc3	472	10	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	472	11	syndrome	syndrome	NN
cord-326631-7gd3hjc3	472	12	in	in	IN
cord-326631-7gd3hjc3	472	13	Canada	Canada	NNP
cord-326631-7gd3hjc3	473	1	The	the	DT
cord-326631-7gd3hjc3	473	2	Walter	Walter	NNP
cord-326631-7gd3hjc3	473	3	Reed	Reed	NNP
cord-326631-7gd3hjc3	473	4	staging	stage	VBG
cord-326631-7gd3hjc3	473	5	classification	classification	NN
cord-326631-7gd3hjc3	473	6	for	for	IN
cord-326631-7gd3hjc3	473	7	HTLV	HTLV	NNP
cord-326631-7gd3hjc3	473	8	-	-	HYPH
cord-326631-7gd3hjc3	473	9	III	III	NNP
cord-326631-7gd3hjc3	473	10	/	/	SYM
cord-326631-7gd3hjc3	473	11	LAV	LAV	NNP
cord-326631-7gd3hjc3	473	12	infection	infection	NN
cord-326631-7gd3hjc3	474	1	Asymptotic	asymptotic	JJ
cord-326631-7gd3hjc3	474	2	final	final	JJ
cord-326631-7gd3hjc3	474	3	size	size	NN
cord-326631-7gd3hjc3	474	4	distribution	distribution	NN
cord-326631-7gd3hjc3	474	5	for	for	IN
cord-326631-7gd3hjc3	474	6	some	some	DT
cord-326631-7gd3hjc3	474	7	chain	chain	NN
cord-326631-7gd3hjc3	474	8	-	-	HYPH
cord-326631-7gd3hjc3	474	9	binomial	binomial	NN
cord-326631-7gd3hjc3	474	10	processes	process	NNS
cord-326631-7gd3hjc3	475	1	Asymptotic	asymptotic	JJ
cord-326631-7gd3hjc3	475	2	final	final	JJ
cord-326631-7gd3hjc3	475	3	size	size	NN
cord-326631-7gd3hjc3	475	4	distribution	distribution	NN
cord-326631-7gd3hjc3	475	5	of	of	IN
cord-326631-7gd3hjc3	475	6	the	the	DT
cord-326631-7gd3hjc3	475	7	multitype	multitype	JJ
cord-326631-7gd3hjc3	475	8	Reed	Reed	NNP
cord-326631-7gd3hjc3	475	9	-	-	HYPH
cord-326631-7gd3hjc3	475	10	Frost	Frost	NNP
cord-326631-7gd3hjc3	475	11	process	process	NN
cord-326631-7gd3hjc3	476	1	An	an	DT
cord-326631-7gd3hjc3	476	2	age	age	NN
cord-326631-7gd3hjc3	476	3	-	-	HYPH
cord-326631-7gd3hjc3	476	4	structured	structure	VBN
cord-326631-7gd3hjc3	476	5	model	model	NN
cord-326631-7gd3hjc3	476	6	of	of	IN
cord-326631-7gd3hjc3	476	7	pre	pre	JJ
cord-326631-7gd3hjc3	476	8	-	-	JJ
cord-326631-7gd3hjc3	476	9	and	and	CC
cord-326631-7gd3hjc3	476	10	post	post	JJ
cord-326631-7gd3hjc3	476	11	-	-	JJ
cord-326631-7gd3hjc3	476	12	vaccination	vaccination	JJ
cord-326631-7gd3hjc3	476	13	measles	measles	NN
cord-326631-7gd3hjc3	476	14	transmission	transmission	NN
cord-326631-7gd3hjc3	476	15	Infinite	infinite	JJ
cord-326631-7gd3hjc3	476	16	subharmonic	subharmonic	JJ
cord-326631-7gd3hjc3	476	17	bifurcation	bifurcation	NN
cord-326631-7gd3hjc3	476	18	in	in	IN
cord-326631-7gd3hjc3	476	19	an	an	DT
cord-326631-7gd3hjc3	476	20	SEIR	SEIR	NNP
cord-326631-7gd3hjc3	476	21	model	model	NN
cord-326631-7gd3hjc3	476	22	Reproduction	reproduction	NN
cord-326631-7gd3hjc3	476	23	numbers	number	NNS
cord-326631-7gd3hjc3	476	24	and	and	CC
cord-326631-7gd3hjc3	476	25	subthreadold	subthreadold	VBD
cord-326631-7gd3hjc3	476	26	endemic	endemic	JJ
cord-326631-7gd3hjc3	476	27	equilibria	equilibrium	NNS
cord-326631-7gd3hjc3	476	28	for	for	IN
cord-326631-7gd3hjc3	476	29	compartmental	compartmental	JJ
cord-326631-7gd3hjc3	476	30	models	model	NNS
cord-326631-7gd3hjc3	476	31	fo	fo	IN
cord-326631-7gd3hjc3	476	32	disease	disease	NN
cord-326631-7gd3hjc3	476	33	transmission	transmission	NN
cord-326631-7gd3hjc3	476	34	Threshold	Threshold	NNP
cord-326631-7gd3hjc3	476	35	limit	limit	NN
cord-326631-7gd3hjc3	476	36	theorems	theorem	NNS
cord-326631-7gd3hjc3	476	37	for	for	IN
cord-326631-7gd3hjc3	476	38	some	some	DT
cord-326631-7gd3hjc3	476	39	epidemic	epidemic	NN
cord-326631-7gd3hjc3	476	40	processes	process	VBZ
cord-326631-7gd3hjc3	476	41	Different	different	JJ
cord-326631-7gd3hjc3	476	42	epidemic	epidemic	NN
cord-326631-7gd3hjc3	476	43	curves	curve	NNS
cord-326631-7gd3hjc3	476	44	for	for	IN
cord-326631-7gd3hjc3	476	45	severe	severe	JJ
cord-326631-7gd3hjc3	476	46	acute	acute	JJ
cord-326631-7gd3hjc3	476	47	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	476	48	syndrome	syndrome	NN
cord-326631-7gd3hjc3	476	49	reveal	reveal	VBP
cord-326631-7gd3hjc3	476	50	similar	similar	JJ
cord-326631-7gd3hjc3	476	51	impacts	impact	NNS
cord-326631-7gd3hjc3	476	52	of	of	IN
cord-326631-7gd3hjc3	476	53	control	control	NN
cord-326631-7gd3hjc3	476	54	measures	measure	NNS
cord-326631-7gd3hjc3	476	55	From	from	IN
cord-326631-7gd3hjc3	476	56	MathWorld	MathWorld	NNP
cord-326631-7gd3hjc3	476	57	-	-	HYPH
cord-326631-7gd3hjc3	476	58	A	a	DT
cord-326631-7gd3hjc3	476	59	Wolfram	Wolfram	NNP
cord-326631-7gd3hjc3	476	60	Web	web	NN
cord-326631-7gd3hjc3	476	61	Resource	Resource	NNP
cord-326631-7gd3hjc3	476	62	.	.	.
cord-326631-7gd3hjc3	477	1	http:\math	http:\math	NNP
cord-326631-7gd3hjc3	477	2	world.wolfram.com/LambertW-Function.html	world.wolfram.com/LambertW-Function.html	.
cord-326631-7gd3hjc3	478	1	Severe	severe	JJ
cord-326631-7gd3hjc3	478	2	acute	acute	JJ
cord-326631-7gd3hjc3	478	3	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	478	4	syndrome	syndrome	NN
cord-326631-7gd3hjc3	478	5	(	(	-LRB-
cord-326631-7gd3hjc3	478	6	SARS	SARS	NNP
cord-326631-7gd3hjc3	478	7	)	)	-RRB-
cord-326631-7gd3hjc3	479	1	,	,	,
cord-326631-7gd3hjc3	479	2	multi	multi	JJ
cord-326631-7gd3hjc3	479	3	-	-	JJ
cord-326631-7gd3hjc3	479	4	country	country	JJ
cord-326631-7gd3hjc3	479	5	outbreak	outbreak	NN
cord-326631-7gd3hjc3	479	6	Severe	severe	JJ
cord-326631-7gd3hjc3	479	7	acute	acute	JJ
cord-326631-7gd3hjc3	479	8	respiratory	respiratory	JJ
cord-326631-7gd3hjc3	479	9	syndrome	syndrome	NN
cord-326631-7gd3hjc3	479	10	(	(	-LRB-
cord-326631-7gd3hjc3	479	11	SARS	SARS	NNP
cord-326631-7gd3hjc3	479	12	)	)	-RRB-
cord-326631-7gd3hjc3	479	13	,	,	,
cord-326631-7gd3hjc3	479	14	multi	multi	JJ
cord-326631-7gd3hjc3	479	15	-	-	JJ
cord-326631-7gd3hjc3	479	16	country	country	JJ
cord-326631-7gd3hjc3	479	17	outbreak	outbreak	NN
cord-326631-7gd3hjc3	479	18	Gonorrhea	gonorrhea	NN
cord-326631-7gd3hjc3	479	19	:	:	:
cord-326631-7gd3hjc3	480	1	Transmission	transmission	NN
cord-326631-7gd3hjc3	480	2	dynamics	dynamic	NNS
cord-326631-7gd3hjc3	480	3	and	and	CC
cord-326631-7gd3hjc3	480	4	control	control	NN
cord-326631-7gd3hjc3	481	1	An	an	DT
cord-326631-7gd3hjc3	481	2	explicit	explicit	JJ
cord-326631-7gd3hjc3	481	3	solution	solution	NN
cord-326631-7gd3hjc3	481	4	for	for	IN
cord-326631-7gd3hjc3	481	5	Z	z	NN
cord-326631-7gd3hjc3	481	6	expressed	express	VBD
cord-326631-7gd3hjc3	481	7	in	in	IN
cord-326631-7gd3hjc3	481	8	terms	term	NNS
cord-326631-7gd3hjc3	481	9	of	of	IN
cord-326631-7gd3hjc3	481	10	elementary	elementary	JJ
cord-326631-7gd3hjc3	481	11	functions	function	NNS
cord-326631-7gd3hjc3	481	12	is	be	VBZ
cord-326631-7gd3hjc3	481	13	not	not	RB
cord-326631-7gd3hjc3	481	14	possible	possible	JJ
cord-326631-7gd3hjc3	481	15	,	,	,
cord-326631-7gd3hjc3	481	16	but	but	CC
cord-326631-7gd3hjc3	481	17	Eq	Eq	NNP
cord-326631-7gd3hjc3	481	18	.	.	.
cord-326631-7gd3hjc3	482	1	(	(	-LRB-
cord-326631-7gd3hjc3	482	2	4	4	LS
cord-326631-7gd3hjc3	482	3	)	)	-RRB-
cord-326631-7gd3hjc3	482	4	can	can	MD
cord-326631-7gd3hjc3	482	5	be	be	VB
cord-326631-7gd3hjc3	482	6	solved	solve	VBN
cord-326631-7gd3hjc3	482	7	explicitly	explicitly	RB
cord-326631-7gd3hjc3	482	8	for	for	IN
cord-326631-7gd3hjc3	482	9	Z	z	NN
cord-326631-7gd3hjc3	482	10	in	in	IN
cord-326631-7gd3hjc3	482	11	terms	term	NNS
cord-326631-7gd3hjc3	482	12	of	of	IN
cord-326631-7gd3hjc3	482	13	the	the	DT
cord-326631-7gd3hjc3	482	14	Lambert	Lambert	NNP
cord-326631-7gd3hjc3	482	15	W	W	NNP
cord-326631-7gd3hjc3	482	16	function	function	NN
cord-326631-7gd3hjc3	482	17	(	(	-LRB-
cord-326631-7gd3hjc3	482	18	Weisstein	Weisstein	NNP
cord-326631-7gd3hjc3	482	19	)	)	-RRB-
cord-326631-7gd3hjc3	482	20	,	,	,
cord-326631-7gd3hjc3	482	21	 	 	_SP
cord-326631-7gd3hjc3	482	22	When	when	WRB
cord-326631-7gd3hjc3	482	23	the	the	DT
cord-326631-7gd3hjc3	482	24	infectious	infectious	JJ
cord-326631-7gd3hjc3	482	25	period	period	NN
cord-326631-7gd3hjc3	482	26	is	be	VBZ
cord-326631-7gd3hjc3	482	27	exponentially	exponentially	RB
cord-326631-7gd3hjc3	482	28	distributed	distribute	VBN
cord-326631-7gd3hjc3	482	29	,	,	,
cord-326631-7gd3hjc3	482	30	i.e.	i.e.	FW
cord-326631-7gd3hjc3	482	31	,	,	,
cord-326631-7gd3hjc3	482	32	f	f	FW
cord-326631-7gd3hjc3	482	33	(	(	-LRB-
cord-326631-7gd3hjc3	482	34	t	t	NN
cord-326631-7gd3hjc3	482	35	)	)	-RRB-
cord-326631-7gd3hjc3	482	36	=	=	NFP
cord-326631-7gd3hjc3	483	1	γ	γ	NNP
cord-326631-7gd3hjc3	484	1	e	e	LS
cord-326631-7gd3hjc3	484	2	−γ	−γ	NNP
cord-326631-7gd3hjc3	484	3	t	t	NN
cord-326631-7gd3hjc3	484	4	,	,	,
cord-326631-7gd3hjc3	484	5	we	-PRON-	PRP
cord-326631-7gd3hjc3	484	6	have	have	VBP
cord-326631-7gd3hjc3	484	7	l(τ	l(τ	NNP
cord-326631-7gd3hjc3	484	8	,	,	,
cord-326631-7gd3hjc3	484	9	t	t	NN
cord-326631-7gd3hjc3	484	10	)	)	-RRB-
cord-326631-7gd3hjc3	484	11	=	=	NFP
cord-326631-7gd3hjc3	485	1	f	f	LS
cord-326631-7gd3hjc3	485	2	(	(	-LRB-
cord-326631-7gd3hjc3	485	3	t	t	NN
cord-326631-7gd3hjc3	485	4	)	)	-RRB-
cord-326631-7gd3hjc3	485	5	.	.	.
cord-326631-7gd3hjc3	486	1	Thus	thus	RB
cord-326631-7gd3hjc3	486	2	Eq	Eq	NNP
cord-326631-7gd3hjc3	486	3	.	.	.
cord-326631-7gd3hjc3	487	1	(	(	-LRB-
cord-326631-7gd3hjc3	487	2	11f	11f	NNS
cord-326631-7gd3hjc3	487	3	)	)	-RRB-
cord-326631-7gd3hjc3	487	4	can	can	MD
cord-326631-7gd3hjc3	487	5	be	be	VB
cord-326631-7gd3hjc3	487	6	writtenLet	writtenLet	.