key: cord-1037633-e32jy784
authors: Sachak-Patwa, R.; Byrne, H. M.; Dyson, L.; Thompson, R. N.
title: The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions
date: 2021-05-22
journal: nan
DOI: 10.1101/2021.05.21.21257589
sha: fbc7117889f49b1c2cb6af4b5b9cda9ea242ee88
doc_id: 1037633
cord_uid: e32jy784

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed. Here, using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases introduced into new locations initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations in which the vaccine rollout has progressed quickly - specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel. We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed, even once the vaccine programmes in these locations are complete. Specifically, the risk that an imported case initiates an outbreak following the vaccine rollout and removal of NPIs is projected to be 0.373 (0.223,0.477) for the Isle of Man and 0.506 (0.387,0.588) for Israel. Key factors underlying these risks are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility. Combined, these factors suggest that when travel restrictions are relaxed, it will still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and isolating contacts of detected infected passengers, should remain in place to suppress potential outbreaks until case numbers globally are reduced.

virus transmission in the initial stages of a potential outbreak. In the model, following the 117 arrival of a case in the local population, new infections occur at rate (1 − Λ( )) and 118 infected individuals have a mean infectious period of 1/ days (Fig 1a) . have received two vaccine doses at time (Fig 1b) . The parameters η " and η & reflect 126 the effectiveness of the vaccine at preventing infection after one and two doses, 127 respectively, and the parameter represents the delay between a vaccine dose being 128 administered and being effective in the recipient. In our main analyses, since we are 129 modelling relatively low prevalence settings, we do not consider immunity due to prior 130 infections, although we present a supplementary analysis in which we considered the 131 robustness of our results to this assumption. (2) 136 137 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 22, 2021. ; https://doi.org/10.1101/2021.05.21.21257589 doi: medRxiv preprint proportion of individuals in the population who have been vaccinated with one ( # ) or two ( $ ) doses. The 150 first vaccine dose is assumed to have effectiveness η # and the second vaccine dose has effectiveness η $ .

Vaccine doses are effective days after they are administered. This leads to declining population 152 susceptibility as a vaccine is rolled out across the population. To explore how the risk of outbreaks is likely to change in future, we projected the 164 vaccine rollout forwards beyond these dates in the following way. We considered the 165 total population size of the location under consideration (denoted ), as well as the 166 numbers of individuals ( " ( ) and & ( )) vaccinated with one or two doses, so that 167

We assumed that a constant number of vaccine 168 doses are available each day in future (denoted ), and that there is a target period of 169 days between each vaccine dose. On any day in future, each available dose is assigned 170 to an individual who has been vaccinated with their first dose at least days ago, with 171 remaining doses then assigned to unvaccinated individuals. Resulting values of " ( ) 172

and & ( ) were then converted to corresponding values of " ( ) and & ( ). To reflect the 173 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) it does not reflect changing population immunity due to vaccination over the initial phase 194 of the potential outbreak. This standard metric is often used to assess the risk of 195 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 22, 2021. ; https://doi.org/10.1101/2021.05.21.21257589 doi: medRxiv preprint

As described in the Methods, we first generated projections of the number of vaccinated 228 individuals in future for the Isle of Man (Fig 2a) and Israel (Fig 2d) , based on past 229 vaccination data in those locations. To explore the impact of vaccination on virus 230 transmission, we calculated the time-dependent reproduction number ( ' ( ); equation 231

(2)) throughout the vaccination campaign. We considered two different scenarios. In the 232 first, we set the median value of % (i.e., the reproduction number in the absence of 233 vaccination) equal to 3, as was the situation early in the COVID-19 pandemic (Fig 2b,e) . 234

In the second scenario, we set the median value of % equal to 5 (Fig 2c,f) Parameter values are shown in Table 1 .

We then calculated the values of the four different outbreak risk metrics throughout the 253 period considered (18 th December 2020 to 20 th August 2021) based on these 254 vaccination projections (Fig 3) . This involves a scenario in which NPIs are removed 255 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. In contrast, we found close agreement between the COR, SOR and NOR. Due to the 272 high assumed vaccine uptake in the Isle of Man, the outbreak risk at the end of the 273 vaccination programme there was calculated to be lower than when the vaccine rollout 274 was completed in Israel (although we also considered supplementary analyses with 275 different assumed vaccine uptake values - Fig S1) . In the first scenario that we 276 considered (median % = 3), which is representative of the transmissibility of the original 277 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

(b) Analogous to panel b but with % = 5 (see Fig 2c) . (c) Analogous to panel a but using vaccination 296 data for Israel (see Fig 2e) . (d). Analogous to panel a but using vaccination data for Israel with % = 5 297 (see Fig 2f) . Ticks on the x-axes refer to the starts of the months labelled. Parameter values are shown in 298 the time-dependent reproduction number, ' ( ) (Fig 2) . However, even when the 317 vaccine rollout is completed, a combination of vaccines not preventing transmission 318 entirely, incomplete vaccine uptake and the emergence of novel SARS-CoV-2 variants 319 suggests that the risk of outbreaks initiated by infected individuals arriving from 320 elsewhere will not be eliminated when NPIs are removed (Fig 3) . This conclusion 321 remained true unless the vaccine uptake was very high (Fig S1) . This suggests that, 322

when NPIs such as travel restrictions are relaxed, it will still be advisable to be aware of 323 the potential for local transmission. Ensuring that case numbers are reduced elsewhere 324 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. then the IOR is expected to be high. This is because the IOR reflects the outbreak risk 346 based on the conditions at the precise instance when the virus is introduced into the 347 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 22, 2021. ; https://doi.org/10.1101/2021.05.21.21257589 doi: medRxiv preprint favourable for transmission in the near future, then the values of the other risk metrics 349 are lower than the IOR, since those metrics account for changes in transmissibility over 350 the initial phase of the potential outbreak. Although in general we found a close 351 agreement between the four metrics that we considered, a background of decreasing 352 population susceptibility can lead to a similar effect in which the IOR is larger than the 353 COR, SOR or NOR (e.g . Fig 3a,c) . 354

In this study, we used a simple branching process model to investigate the risk of 356 outbreaks when NPIs are removed during a vaccination programme. This involved 357 considering whether introduced cases are likely to lead to sustained local transmission 358 or instead fade out without causing an outbreak. We made the standard branching 359 process modelling assumption that population immunity is unaffected by infections in 360 the earliest stages of potential outbreaks [19] [20] [21] [22] 47, 48] . In other words, infection-361 acquired immunity following the arrival of the pathogen in the host population is not 362 considered. While this is reasonable when case numbers are low in the initial stages of 363 potential outbreaks, a more detailed model is needed to explore other quantities, such 364 as the eventual size of outbreaks. Following a vaccination programme, outbreaks are 365 likely to be smaller than those that occur before vaccines are widely administered. 366

Another simplification of our model is that we only accounted for changes in population 368 susceptibility due to the vaccine rollout. We did not account for prior immunity of some 369 members of the population due to previous exposures to the virus. At the time of writing 370 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 22, 2021. ; https://doi.org/10.1101/2021.05.21.21257589 doi: medRxiv preprint confirmed cases in Israel. Since these case numbers correspond to a relatively small 372 proportion of the host population (representing 1.35% and 9.55% of the population in 373 the Isle of Man and Israel, respectively), we do not expect this assumption to affect our 374 key findings. Furthermore, immunity is likely to wane over time [49, 50] , reducing the 375 effect of previous exposures on the outbreak risk. To test the potential impact of 376 infection-induced immunity arising from cases occurring before May 2021, we also 377 conducted a supplementary analysis in which the value of % is reduced by 1.35% in the 378

Isle of Man and 9.55% in Israel, and we found qualitatively similar results ( Fig S2) : even 379 in this "best case" scenario, there is still a risk of outbreaks due to imported cases once 380 the vaccination programmes are completed. Importantly, in other countries in which 381 higher numbers of cases have occurred, prior immunity may play a larger role in 382 reducing the risk of outbreaks compared to the low prevalence settings considered 383

here. Understanding the extent of this effect, based on the rate at which immunity 384 wanes, is an important target for further study. 385

In this research, we assumed that vaccines reduce transmission by lowering the 387 probability that a vaccinated host becomes infected compared to an unvaccinated host. These measures are necessary, since only once the global prevalence of SARS-CoV-2 416 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 22, 2021. ; https://doi.org/10.1101/2021.05.21.21257589 doi: medRxiv preprint

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