key: cord-0693421-vct8lx32
authors: Silk, M. J.; Carrignon, S.; Bentley, R. A.; Fefferman, N. H.
title: Where to learn to flatten the curve: a modelling study
date: 2021-03-24
journal: nan
DOI: 10.1101/2021.03.23.21254166
sha: 2f83682cca99727890530c468d4b6839d46c7e40
doc_id: 693421
cord_uid: vct8lx32

Background: Individual behavioural decisions are responses to both a persons perceived social norms and could be driven by both their physical and social environment. In the context of the COVID-19 pandemic, these environments correspond to epidemiological risk from contacts and the social construction of risk by communication within networks of friends. Understanding when, and under which circumstances, each modality of influence can foster the widespread adoption of protective behaviours is critical for shaping useful, practical public health messaging that will best enhance the public response. Methods: We use a multiplex network approach to explore how information from both physical contact and social communication networks is driving a mitigating behavioural response to disease risk. Findings: We show that maintaining focus on awareness of risk in each individuals physical layer contacts promotes the greatest reduction in disease spread, but only when an individual is aware of the symptoms of a non-trivial proportion of their physical contacts (approximately 20% or more). Information from the communication layer was less useful when these connections matched less well with physical contacts and contributed little in combination with accurate information from the physical layer. Interpretation: We conclude that maintaining social focus on local outbreak status will allow individuals to structure their perceived social norms appropriately and respond more rapidly when risk increases. Finding ways to relay accurate local information from trusted community leaders could improve mitigation even where more intrusive/costly strategies, such as contact-tracing, are not possible.

practical public health messaging that will best enhance the public response. Our current best public health recommendations for mitigation of the COVID-19 pandemic 41 rely on using behavioural interventions such as social distancing and mask wearing, and 42 behaviourally driven acceptance of vaccines (where available) to curtail transmission of 43 infection. The success of these policies requires widespread adherence to achieve epidemic 44 control; as with herd immunity, threshold effects in efficacy mean that gaps in adoption can 45 quickly compromise any benefits [1, 2] . Therefore, identifying how the adoption of these 46 behaviours is shaped over the course of an epidemic is a key challenge in designing effective 47 mitigation strategies [3] [4] [5] [6] . 48 Adherence, however, relies on individual behavioural choices and so can be complicated to 49 understand and predict [3, 7] f. Well-established theory from psychology acknowledges that the 50 factors influencing whether or not people take action are complicated [8, 9] . One of the 51 dominant theories (the theory of planned behaviour [10] ), posits that action is the composite 52 result of the individual's attitudes and beliefs, the individual's perception of social norms 53 regarding that behaviour, and the individual's perception of their own behavioural control 54 over their actions (alternative theories of behaviour, such as Value-Belief-Norm theory [11] 55 also posit similar influences, though in different relation to each other). In the case of 56 COVID-19, adoption of and adherence to behavioural interventions are therefore likely to be 57 predicated on perception of two main features: a) individual attitudes and beliefs about 58 personal risk of infection and its consequences [12] , and b) the social norms around adherence 59 in the individual's community [13] . distancing). Despite this, we still understand relatively little about the potential implications 73 of acquiring information from these two different sets of contacts. 74 The dynamics triggered by the spread of awareness through the population are further 75 complicated by the timescales of observable risk due to the etiology of COVID-19. The 76 latency in the development of symptoms and the capacity for presymptomatic, or even 77 asymptomatic, transmission make estimation of real-time risk by surveillance complicated, 78 even without considering different sources of information [18] . In terms of understanding 79 disease prevalence, the relative reliance of individuals in shaping their beliefs, and thus their 80 actions, on their own direct observation of health among their daily physical contact network 81 may have an effect that is distinct from that of their (potentially more geographically distant) 82 communication network. The balance of these distinct network effects may therefore be the 83 critical feature in determining the success of behavioural public health measures to combat 84 COVID-19. 85 We employ a multiplex network method to test the relative adoption of behavioural 86 interventions in populations of individuals who rely on a) their communication network layer 87 only (henceforth referred to as simply the "communication layer"), b) their physical contact 88 network layer only (henceforth referred to as the "infection layer"), and c) both layers 89 simultaneously to inform their understanding of COVID-19, and therefore their individual 90 adherence to protective behaviours such as mask wearing or social distancing. We further 91 consider the influence of structure in both layers of the network and how that structure might 92 impact the behaviour of populations as they rely on perceptions constructed from contacts in 93 those layers. Geographic and social heterogeneity in contact structure are modelled at low 94 and high levels of modularity (i.e. differences in local versus global density of contacts; see 95 Methods). In addition to homogeneous mixing, we consider homophily based upon 96 predisposition, which are modelled as social norms that can be shared in the communication 

Overview 103 We used stochastic models to test how the awareness of symptomatic neighbours in either a) 104 the set of people that a person who communicates with on a regular basis (their communication layer), b) the set of people that a person is in close proximity to (their 106 infection layer), or c) both of these sets of contacts can impact epidemic spread of an 107 infection with COVID-19 like dynamics. We simulated realistic, multiplex social networks 108 for our populations that coupled a layer of infection-relevant contacts through which the 109 epidemic was simulated and a communication layer through which concern about the disease 110 could simultaneously spread. All modelling was conducted in R3.6.1 [19] and the code used is 111 provided on GitHub (https://github.com/matthewsilk/CoupledDynamics2_layeruse). The 112 general modelling framework was the same as that used by Silk et al. [20] and is described in Population generation 116 We generated populations of 2000 individuals (a balance between minimising stochasticity in 117 early epidemic outcomes and computational efficiency), which consisted of children (24%), 118 young adults (63%) and old adults (13%). Age classes could differ in the social connections, 119 epidemiological outcomes and concern about the disease (as detailed below). Individuals also 120 had one of two baseline predispositions and homophily by predisposition impacted patterns 121 of social connections (in either or both layers of the multiplex network).

Social network generation 124 We used the same 9 multiplex social networks as detailed in Silk et al. [20] . These were 125 coupled, multiplex networks that connected all individuals within a communication layer that 126 influenced the spread of concern about the disease and an infection layer that influenced the layers was set to 0·4, both to 0·6, or the infection layer was set to 0·6 and the communication 134 layer to 0·4. Each child was assigned two parents from the same predisposition and 135 community. If children shared one parent they also shared the other but parents could be is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Concern model 144 We used the same concern model as Silk et al. [20] . Concern about the disease was modelled as 145 a complex contagion [21] through the communication layer. Whether an individual was 146 adherent to mitigation measures or not (a binary trait) was based on a Bernoulli draw in 147 which the probability of adherence depended on an underlying trait continuous we term 148 concern. As a result, individuals could fluctuate between adherent or non-adherent states and 149 this was more likely if they had intermediate values of concern. Concern could be influenced Our infectious disease model is the same stochastic network model described in Silk et al. [20] 167 with parameter values adapted from [22, 23] . The model contains susceptible (S), exposed (E), is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Effect is more effective in flattening the curve when people respond to illness in their 205 infection layer rather than in their communication layer (panels a versus b in Figs. 1 and 2).

When this is the case, even relatively weak Awareness Effects can contribute to flattening the 207 curve. Using information from the infection layer is nearly as effective as using information 

Consequently, we focus on the case when Social Construction is weak for subsequent results. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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The copyright holder for this this version posted March 24, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint When we assume that individual can partially identify the symptomatic contacts in their 242 infection layer, the mitigating effect is reduced considerably in our networks (Fig. 3) . When 243 there is a 50% chance of an individual detecting an ill neighbour in their infection layer, the 244 height of the epidemic peak remains lower than when an individual gains information on the 245 prevalence of infection from their communication layer with the difference increasing as the 246 strength of the Awareness Effect gets stronger. When there is a 20% chance of detection in 247 the infection layer, the epidemic peak is marginally higher than when (accurate) information 248 is used from the communication layer with a weak Awareness Effect and slightly lower with 249 a strong Awareness Effect. When there is a 5% chance of detection the mitigating influence 250 of the Awareness Effect is very limited indeed and restricted to strong Awareness Effects.

The structure of the network was relatively unimportant in determining the success with 252 which populations were able to "flatten the curve" (Fig. 4, Fig. S1 ). Most strikingly, there is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 24, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 24, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 24, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Despite the natural inclination to believe that the influence of community leaders and trusted 296 social contacts can help us each to make better decisions, in this case, the results of our study 297 demonstrate that the impact of that trusted community may instead compromise our ability to 298 respond to the actual risks around us (see Figs. 1,2, and 3) if the alternative is accurate 299 information on prevalence in an individual's likely physical contacts. However, the The former result suggests that populations comprised of individuals who tend more towards 326 independent risk assessment than on reliance on community leadership may respond better to 327 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 24, 2021. ; https://doi.org/10.1101 https://doi.org/10. /2021 public health interventions. However, the latter result indicates the importance of highly 328 accurate information from the infection layer at a community level. Therefore any social 329 norms that reduce observability of infection in a local community can undercut the efficacy 330 of recommended behavioural interventions. This is especially important in shaping public 331 messaging since both within group density (i.e. modularity) and closeness of beliefs within a 332 community (i.e. homophily) have less of an impact than the information on which the 333 members of that community rely (see Fig. 4 ). We therefore strongly support the adoption of 334 public reports of identified cases in local communities that come into regular potential 335 contact with each other. While, of course, this requires sensitivity to personal privacy, regular 336 announcements/reminders at a city, company, school, or neighbourhood level of active 337 disease prevalence can potentially provide critical and effective reinforcement for the 338 individual adoption of behaviours that can protect everyone.

Awareness itself is not without complexity. The centralized collection and analysis of data at 340 regional or national scales involves logistical challenges and can cause delay in reporting that 341 information back to the public [24] . It is also frequently the case that communities pay more 342 attention to, and place greater trust in, local sources of information than in more remote 343 sources [25] . Policies that focus on community leadership to ensure a local focus for awareness 344 helps to address both of these difficulties. One of the most fundamental challenges in creating effective public health policies is the 358 design of recommendations that will not only achieve theoretical outcomes but will be 359 adopted by enough of a willing public to accomplish those outcomes in the real world. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Integrating an understanding of how individual perceptions shape behaviours, and how social 361 context itself shapes perceptions has become one of the critical stumbling points in our local, 362 national, and global response to the COVID-19 pandemic. Our results clearly show that local, 363 accurate, rapid, and trusted information can enable better emergent behaviours. Thankfully, 364 these paths are within the capability of our public health community and local community 365 leadership to provide. concern about the disease could simultaneously spread. All modelling was conducted in R3.6.1 [19] and 380 the code used is provided on GitHub (https://github.com/matthewsilk/CoupledDynamics2_layeruse). 381

The general modelling framework was the same as that used by Silk et al. [20] . 382 383

We generated populations of 2000 individuals (a balance between minimising stochasticity in early 385 epidemic outcomes and computational efficiency), which consisted of children (24%), young adults 386 (63%) and old adults (13%). These proportions were set to match recent US demographic data. Age 387 classes could differ in the social connections, epidemiological outcomes and concern about the 388 disease (as detailed below). Individuals also had one of two baseline predispositions, with 50% of 389 each predisposition. Homophily by predisposition impacted only patterns of social connections (in 390 either or both layers of the multiplex network). 391 392

We generated 9 multiplex social networks as detailed in Silk et al. [20] . These were coupled, multiplex 394 networks that connected all individuals within a communication layer that influenced the spread of 395 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 24, 2021. ; https://doi.org/10.1101 https://doi.org/10. /2021 concern about the disease and an infection layer that influenced the transmission of the pathogen 396 itself. Briefly, networks were generated as follows: 397

For each layer, within age class and within predisposition connections were simulated as 398

Erdös-Renyi random graphs using igraph [26] . We specified age-specific edge densities for within 399 predisposition connections. For this study, global edge densities were always higher in the infection 400 layer than in the communication layer. 401

Between predisposition connections were then added to form three overall networks for each 402 age class in each layer. We specified age-specific between-predisposition edge densities (which could 403 differ from within-predisposition densities). The level of homophily according to predisposition is 404 defined by the difference between within-and between-predisposition edge densities. We included 405 three types of homophily in the multiplex network: a) no homophily in either layer, b) homophily in 406 the communication layer, or c) homophily in both layers. 407

We then introduced community structure into each network layer. A rewiring algorithm was 408 used to impose community structure within the three age-class networks as per Silk et al. [20] . We 409 implemented a block model with 10 communities and re-assigned edges to achieve a target 410 modularity while maintaining the initial edge density and level of homophily. We used 0·4 and 0·6 as 411 target relative modularity [27] for our community structure. The proportion of each predisposition 412 within each community was the same as the overall population. In this study either both layers had a 413 modularity of 0·4, both had a modularity of 0·6, or the infection layer had a modularity of 0·6 and the 414 communication layer a modularity of 0·4 (as per Silk et al. [20] ). 415

Each child was assigned two parents from the same predisposition and community. If children 416

shared one parent they also shared the other but parents could be connected or unconnected. 417

Each young adult formed connections with a number of old adults of the same predisposition 418 (representing older relatives, friends or community members). The number of connections for each 419 young adult was a drawn from a Poisson distribution ( ). Connections could occur within or 420 between communities with the probability of within-community connections being the same as the 421 modularity of the network. Children shared the same connections to old adults as their parents. 422

We used 8 different simulated networks in total for this study (four for the communication layer and 423 four for the infection layer), which when combined generated nine different multiplex networks that 424 were a full combination of the three homophily conditions and three modularity conditions defined 425 above. When the multiplex network was constructed we re-assigned parents from the infection layer 426 to match those in the communication layer. Child-old adult connections were re-assigned accordingly. 427 428

We used the same concern model as Silk et al. [20] . Concern about the disease was modelled as a 430 complex contagion [21] through the communication layer. Whether an individual was adherent to 431 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 24, 2021. ; https://doi.org/10.1101 https://doi.org/10. /2021 mitigation measures or not (a binary trait) was based on a Bernoulli draw in which the probability of 432 adherence depended on an underlying trait continuous we term concern. As a result, individuals could 433 fluctuate between adherent or non-adherent states and this was more likely if they had intermediate 434 values of concern. Concern could be influenced by the following factors with changes modelled on a 435 logit scale. 436

For this study all adults started with the same concern. The initial level of concern was 437 defined with an expectation of 20% of adults being adherent to mitigation measures at the start of 438 each simulation run. 439

Social Construction of concern -concern could change based on the proportion of immediate 440 neighbours in the communication layer of the network that were adherent in the previous day. We 441 modelled this change as a linear increase in belief as the proportion of adherent connections increased. 442

We allowed the strength of this relationship to vary, drawing 50 different values from a uniform 443 distribution between 0 and 0·5 for the effect size per day. This range of parameter values were 444 selected based on prior use of the model (Silk et al. [20] ). 445

Reassurance effect from communication neighbours -concern could be reduced at each day 446 that all of an individual's connections in the communication layer were symptom free (whether 447 susceptible, exposed, pre-symptomatic or recovered). We drew 50 values from a uniform distribution 448 between -0·1 and 0 (which we paired with equivalent values of the Social Construction effect). 449

Awareness effect based on prevalence of symptomatic contacts -concern could increase 450 based on the number of an individual's connections that were symptomatic. We assigned 10 values (0, 451 0·1, 0·2, 0·4, 0·6, 0·8, 1, 1·2, 1·4 and 1·6) for this per day increase in concern per symptomatic 452 imperfect detection of symptomatic contacts in the infection layer. We used detection probabilities of 457 50%, 20% and 5%. 458

The concern of children was not modelled. They were assigned as adherent if either or both of 459 their parents were adherent. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted March 24, 2021. ; https://doi.org/10.1101/2021.03.23.21254166 doi: medRxiv preprint 1.

Ten random individuals were seeded with infection (in the exposed [E] class of the 504 compartmental model). 505

Individuals were allocated initial values of belief based on pre-defined starting values and 506 these were used to calculate which individuals were adherent on the first day. 507

The algorithm repeated a sequence events on each day, namely: 508

a)

The infection layer of the network was rewired so that adherent individuals cut a 50% of their 509 connections to have negligible edge weight. 510

b)

The infection layer of the network was rewired so that newly symptomatic individuals cut 511 their connections to have negligible edge weight. 512

c)

The infection layer of the network was rewired so that newly recovered individuals restored 513 their full connections (edge weights increased to 1) 514 d)

We recorded the identity of all individuals that were currently symptomatic or hospitalised. 515

We ran the concern model to update the concern and adherence of individuals. 516

We ran the infectious disease model to update the infection status of all individuals 517

The algorithm moves on to the next day until the end of the defined time period (300 days). 518

From each run of the simulations we recorded the total number of individuals who were infected on 519 each day in each social community. We also recorded the proportion of each social community that 520 was concerned or adherent to social distancing on each day. 521 522

To compare between different runs of the simulations we quantified the height of the epidemic peak at 524 a population level by aggregating the daily counts of symptomatic infections in all 10 communities 525 and calculating the maximum prevalence of infected individuals (I1) in the population. This measure 526 of the height of the epidemic peak indicated how successfully each simulated population managed to 527 "flatten the curve" with their adherence to mitigating behaviours [4] . We present these results by 528 comparing epidemic peaks when individuals learned about symptomatic network neighbours from 529 different types of social contact while considering different values of the Social Construction and 530

To help explain some of the differences between the infection and communication layers in their 532 ability to "flatten the curve" when used to provide information on local prevalence (to the Awareness 533 effect), we also examined the similarity of connections in these layers by quantifying the proportion 534 of contacts in each layer that were also present in the other (Fig. S1) for each of the nine multiplex 535 networks that differed in homophily and modularity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Daily probability of symptomatic case becoming hospitalised for young adults and children

Daily probability of symptomatic case becoming hospitalised for old adults 0·025

Daily probability of death in hospitalised cases for young adults 0·012

Daily probability of death in hospitalised cases for young old adults is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

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Our infectious disease model is the same stochastic network model described in Silk et al. [20] with 468 parameter values adapted from Weitz et al. [22] and Lofgren et al. [23] . The model contains susceptible 469 (S), exposed (E), pre-symptomatic (I1), symptomatic (I2), hospitalised (I3), recovered (R) and dead 470 (D) compartments. The transition between compartments is detailed below and parameter values are 471 provided in Table S1 (reproduced from Silk et al. [20] ). The infection model proceeded as follows 472 (reproduced from Silk et al. [20] ): 473

The transition from susceptible to exposed depended on the number of contacts each 474 susceptible individual had with infected individuals (I1, I2, I3). Each contact was associated with a 475 pre-defined probability of transmission. We selected a value for the transmission probability that 476 resulted in unmitigated epidemics infecting approximately 80% of the population as per Ferguson et 477 al. [28] . 478

The length, in days, of the incubation period (exposed; E) and of each infectious period (I1-3) 479were set using draws from Poisson distribution (Table S1) . 480

Individuals could transition from symptomatic (and at home) to hospitalised, and from 481 hospitalised to dead with pre-defined daily probabilities which differed for young (low risk) adults 482 and old (high risk) adults. These daily probabilities were calculated based on Weitz et al. [22] and 483Lofgren et al. [23] and then adapted to produce a realistic proportion of cases being hospitalised during 484 trial runs of the simulations (c.f. Reno et al. [29] ). Children could be symptomatic (I2) but were never 485 hospitalised reflecting the very low probability of this occurring in reality [30] . All individuals that 486 reached the end of each infectious period without further progression of the disease were deemed to 487 have recovered. repeated the full set of simulations with 0·5, 0·2 and 0·05 probability of symptomatic contacts being 500 detected at each day. This resulted in a total of 27,000 independent simulation runs. For each 501 simulation run we simulated a time period of 300 days. 502