COVID-19 control across urban-rural gradients

Controlling the regional re-emergence of SARS-CoV-2 after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban-rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases, or regional lockdowns in response to local outbreaks, have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test and trace strategies, is pivotal to reduce the overall epidemic size over a wider range of transmission scenarios. We define an urban-rural gradient in epidemic size as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban-rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatics only. Our results emphasise the importance of test-and-tracing strategies and maintaining low transmission rates for efficiently controlling COVID19 spread, both at landscape scale and in urban areas.

landscape scale and in urban areas. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint COVID-19 disease landscapes 3 Author summary 52 The spread of infectious diseases is the outcome of contact patterns and involves source-sink 53 dynamics of how infectious individuals spread the disease through pools of susceptible 54 individuals. Control strategies that aim to reduce disease spread often need to accept ongoing 55 transmission chains and therefore, may not work equally well in different scenarios of how 56 individuals and populations are connected to each other. To understand the efficacy of 57 different control strategies to contain the spread of COVID19 across gradients of urban and 58 rural populations, we simulated a large range of different control strategies in response to 59 regional COVID19 outbreaks, involving regional lockdown and the isolation individuals that 60 express symptoms and those that developed not symptoms but may contribute to disease 61 transmission. Our results suggest that isolation of asymptomatic individuals through intensive 62 test-and-tracing is important for efficiently reducing the epidemic size. Regional lockdowns 63 and the isolation of symptomatic cases only are of limited efficacy for reducing the epidemic 64 size, unless overall transmission rate is kept persistently low. Moreover, we found high 65 overall transmission rates to result in relatively larger epidemics in urban than in rural 66 communities for these control strategies, emphasising the importance of keeping transmission 67 rates constantly low in addition to regional measures to avoid the disease spread at large 68 scale. 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 September 9, 2020. .

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In the absence of a vaccine against COVID-19 during the initial pandemic phase, 79 stakeholders are confronted with challenging decision-making to balance constraints of social pandemic spread, a central aim is to reduce case incidence in order to release the pressure on 88 health systems. A more fundamental, long-term, goal should be to reduce the overall 89 epidemic size and allow particularly those most prone to suffer from the disease to escape 90 infection until a pharmaceutical measure such as a vaccine is in place.

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Control strategies are likely to be regional, and temporal, aiming to reduce the time-93 dependent reproduction number R, while accepting that ongoing transmission is long term. 94 But how should these regional and temporary strategies account for disease spread in ever- The spread of infectious disease is rarely random. It is instead likely driven by the complex 101 and heterogeneous social interaction patterns of humans and the stark gradient between urban 102 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.
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 September 9, 2020.  [3][4][5]. Heterogeneity in contact patters of individuals and among social groups is 107 also assumed to impact the depletion of the pool of susceptible individuals and the build-up 108 of possible herd immunity that prevent further spread [6,7]. Hence, future short-and long-109 term mitigation strategies that focus on managing regional and erratic outbreaks would 110 benefit from a better understanding of which control strategies provide the best possible 111 outcome under variable regional conditions.  Our modelling approach is strategic, in contrast to many tactical COVID-19 simulation 120 models that have focused on replication of specific characteristics of real outbreaks with the 121 aim of predicting the epidemic in specific locations [1,9,10]. Rather than modelling a certain 122 scenario, we aim to define wide ranges and explore the model behaviour across a large array  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 September 9, 2020.  130 In order provide an empirical basis to explore possible COVID-19 spread across an urban-131 rural gradient and the efficacy of different disease control measures, we selected four 132 counties in southwestern Wales (Pembrokeshire, Carmarthenshire, Swansea, Neath Port 133 Talbot) with a total human population size of 701,995 (hereafter termed 'metapopulation') 134 dispersed over an area of 4,811 km 2 as a case study. This area was selected because of its 135 strong urban-rural gradient, from city centres to sparsely occupied farming localities, and 136 readily available demographic data.  We used a gravity model to define the connections between populations, as it is capable of 144 reflecting the connectivity underpinning landscape-scale epidemics [11,12]. In particular, a is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

Case study of a rural-urban metapopulation in Wales
The copyright holder for this this version posted September 9, 2020. if the attractant population is closely surrounded by others; Fig S1). The scaling factor  (0  158   1) is a sampled parameter that may vary across scenarios, accounting for the uncertainty 159 in population connectivity. For each population i, we computed a regional gravity index (with 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 September 9, 2020.   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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint COVID-19 disease landscapes where  is the disease transmission parameter, and k is a scaling factor of infectiousness of 203 asymptomatic relative to infectious individuals with 0 < i,t < 1. 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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint encounters between citizens and higher contact frequencies between individuals of the same 226 community in urban areas [14].   iii) Regional temporary reduction of transmission rates ('regional lockdown') in response to a 242 regional outbreak within the modelled LSOA administrative units, with four parameters to 243 vary for decision making and control: (1) a threshold  defining the proportion of the  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 September 9, 2020. To be able to assess the efficacy of these control strategies as compared to a reference, we  Table S1 for ranges of parameter 267 values used. 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 September 9, 2020. from Spearman rank correlation) between the regional relative epidemic size and the 289 respective regional gravity index ('urban-rural gradient in relative epidemic size') in order to 290 explore whether control strategies varied in their efficacy across urban-rural gradients. A 291 strong positive correlation can be interpreted as a strong urban-rural gradient of disease 292 spread, with smaller relative epidemic sizes in rural areas, where connectivity is generally 293 lower. We also computed the strength of correlation between the epidemic sizes of baseline 294 scenarios (uncontrolled outbreaks) and the respective regional gravity index. 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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint COVID-19 disease landscapes 13 terms of direction of effects (i.e. decrease/increase in relative epidemic size, reflecting 300 higher/lower control efficacy) and relative influence (i.e. % of variance explained by various 301 parameters in the corresponding BRT model) for those parameters that appear to show 302 'significant' effects in both GLM and BRT (i.e. GLM coefficients clearly distinct from zero, 303 relative parameter influence > 5%).

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The urban-rural gradient in epidemic sizes (expressed as rank correlation coefficient between 309 the regional epidemic size and the regional gravity index) considerably decreased among 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 September 9, 2020.  Fig 2).  Regional lockdown scenarios appeared to be of limited efficacy in our simulations (Fig 1) 335 and largely depend on small transmission parameters (, 70% relative influence) (Fig 2). 336 Their efficacy was sensitive to the regional threshold levels for lockdown implementation (, 337 10% relative influence) and lockdown stringency (, 6% relative influence). A reduction of 338 relative epidemic sizes to 5% of those of the respective baseline scenarios through regional 339 lockdowns was only achieved for regional lockdown threshold levels of  1% the populations 340 being symptomatic. 343 The strength of the urban-rural gradient in relative epidemic sizes resulting from isolation of is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

Variation in control efficacy across urban-rural gradients
The copyright holder for this this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint contained in urban environments (i.e. resulting in less strong urban-rural gradients in relative 350 epidemic size), despite a concentration of cases there, as depicted by mostly positive 351 correlation coefficients of the urban-rural gradient in relative epidemic size (Fig 4).  In response to regional lockdown strategies, the strength of the urban-rural gradient in 365 relative epidemic size increased with increasing transmission parameters (, 34% relative 366 influence), increasing travel frequencies (27% relative influence), and stronger distance 367 weighting in the underlying gravity model (, 18% relative influence, Fig 3). 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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint unless overall transmission rate is kept persistently low. Isolation of non-symptomatic 375 infected individuals, which may be detected by effective test and trace approaches, is pivotal 376 to reduce overall epidemic size over a wider range of transmission scenarios. By considering 377 an 'urban-rural epidemic gradient' as the strength of correlation between regional epidemic    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 September 9, 2020. In practice, the prominent example of the locally restricted lockdown implemented in the city 401 of Leicester in the UK, which began in June 2020 is just one example of mounting evidence 402 that regional lockdowns do not necessarily see an reduction in disease transmission during 403 the following weeks [25], which would ideally prevent spread of the virus beyond the local 404 context. This slow response of incidence decline following regional lockdowns is in line with Surprisingly, we found travel frequency and possible density dependence in contact 409 frequency to have rather small relative impact on overall epidemic size compared to the 410 transmission parameter (Fig 2). Despite the recognised importance of connectivity, travel  We found the magnitude of transmission rate to also determine the success of different 419 control strategies in urban versus rural areas, leading to varying urban-rural epidemic 420 gradients in response to varying transmission rates and different control strategies (Fig 3). 421 For interventions focused on isolating both non-symptomatic and symptomatic individuals 422 and regional lockdowns, our results reveal the strongest urban-rural epidemic gradients at 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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint under these conditions. These results suggest that at high transmission rates, the urban-rural 425 epidemic gradient is enforced by the overall poorly curbed disease spread at metapopulation 426 level (see Fig 4). Conversely, we found the urban-rural gradient in epidemic sizes to be 427 mostly masked at high transmission rates for measures targeted at symptomatics only, 428 suggesting that that these measures (which are generally of moderate to low efficacy), would 429 not contain disease spread at metapopulation level unless transmission rates are kept 430 constantly low (see Fig 4). Exploring such effects warrants further investigation based on 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 September 9, 2020.   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 September 9, 2020. Acknowledgments 476 We acknowledge the support of funding from the Welsh Government for this project, and 477 also the Supercomputing Wales project, which is part-funded by the European Regional 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 September 9, 2020.      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 September 9, 2020. On the use of human mobility proxies for modeling epidemics. PLoS Comp Biol.    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 September 9, 2020.   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 September 9, 2020.  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 September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189597 doi: medRxiv preprint