key: cord-0687784-l1jjjxx9 authors: Spooner, Fiona; Abrams, Jesse F.; Morrissey, Karyn; Shaddick, Gavin; Batty, Michael; Milton, Richard; Dennett, Adam; Lomax, Nik; Malleson, Nick; Nelissen, Natalie; Coleman, Alex; Nur, Jamil; Jin, Ying; Greig, Rory; Shenton, Charlie; Birkin, Mark title: A dynamic microsimulation model for epidemics date: 2021-10-18 journal: Soc Sci Med DOI: 10.1016/j.socscimed.2021.114461 sha: 2e0ff526ad66967bec45812dec5e9a7b5cb4ac7f doc_id: 687784 cord_uid: l1jjjxx9 A large evidence base demonstrates that the outcomes of COVID-19 and national and local interventions are not distributed equally across different communities. The need to inform policies and mitigation measures aimed at reducing the spread of COVID-19 highlights the need to understand the complex links between our daily activities and COVID-19 transmission that reflect the characteristics of British society. As a result of a partnership between academic and private sector researchers, we introduce a novel data driven modelling framework together with a computationally efficient approach to running complex simulation models of this type. We demonstrate the power and spatial flexibility of the framework to assess the effects of different interventions in a case study where the effects of the first UK national lockdown are estimated for the county of Devon. Here we find that an earlier lockdown is estimated to result in a lower peak in COVID-19 cases and 47% fewer infections overall during the initial COVID-19 outbreak. The framework we outline here will be crucial in gaining a greater understanding of the effects of policy interventions in different areas and within different populations. Across the world, governments have introduced non-pharmaceutical interventions (NPI) to try and control the spread of COVID-19 through a reduction in the number of contacts between susceptible members of the population and those with the disease (Desvars-Larrive et al., 2020) . Those interventions include social distancing, isolation, wearing face masks and lockdowns at national, regional and local scales. In the UK, each policy has been underpinned by much speculation surrounding its timeliness, extent and subsequent effectiveness. However, what has become clear is that pre-existing systemic health J o u r n a l P r e -p r o o f inequalities (Daras et al., 2021 , Kontopantelis et al., 2021 , McNamara et al., 2020 have meant that regardless of NPI, certain communities have been disproportionately impacted in terms of COVID-19 cases, hospitalisations and mortality outcomes. There is evidence of markedly different impacts on health across various domains, including: geographical region (Kontopantelis et al., 2021) ; level of deprivation (Cabinet Office, 2017, Office for National Statistics, 2021); race and ethnicity (Mathur et al., 2020 , Race Disparity Unit Cabinet Office, 2020 . The causes behind these patterns are complex and interlinked (Bibby et al., 2020 , Zhang et al., 2021 . Such factors include economic circumstances whereby people in more disadvantaged communities are less able to comply with requirements to work from home due to their occupation. Additionally, some communities are less inclined to comply with restrictions due to mistrust of authorities (Daras et al., 2021 , Harris, 2020 , Zhang et al., 2021 . The risk factors leading to COVID-19 cases, hospitalisation, and mortality exist not only at the individual level; neighbourhood-level factors and their interactions with individuallevel factors are also responsible for the observed disparities (Daras et al., 2021 , KC et al., 2020 . Lack of access to health care, unemployment, occupation type, level of education, and housing conditions significantly increase the risk of COVID-19 infection (Bilal et al., 2021 , KC et al., 2020 , Shah et al., 2020 . The varying levels of vulnerability between people and places has been increasingly shown to have important consequences for individual and community responses to the pandemic (Daras et al., 2021 , Harris, 2020 . Given these complexities, it is increasingly clear that to understand the effectiveness of government policies we require detailed data that reflects the everyday lives of the British population. Since the onset of the pandemic, researchers across a variety of disciplines have come together to understand the transmission of COVID-19 at the population level. Compartmental models, specifically the Susceptible -Exposed -Infection -Removed (SEIR; Rvachev and Longini (1985) ) have formed the bedrock of this research. However, with the partial exception of a number of models that allow for the effect of population age structure (Keeling et al., 2020, van Leeuwen and Sandmann, 2020) or specific behaviour changes in response to public health interventions and seasonal change (Dureau et al., 2013 , Ferguson et al., 2006 , Kucharski et al., 2020 through stochastic model extensions, most of this work has largely failed to embed and replicate the complex space and time dynamics that underline the spread of COVID-19 across different populations and communities within their models. In this paper we outline an enhancement of the traditional SEIR model of infectious disease transmission through adoption of a spatial microsimulation modelling framework that brings together epidemiological modelling, urban analytics, spatial analysis and data integration. Specifically, we combine the power of well-established methods within the social and behavioural sciences, namely spatial microsimulation and spatial interaction models, within a dynamic SEIR to offer the best approximation of (i) the daily, individuallevel mobilities that characterise many of the interactions which lead to COVID-19 transmission and (ii) the impact of different NPI based on the complex health, socioeconomic and behavioural attributes of the British population. This framework provides the much-needed ability to assess the effects of past interventions and simulate the effects of future policy decisions on different population groups at a variety of spatial scales. The modelling framework proposed here is based on synthetic georeferenced population which has been enriched with additional socio-economic, demographic, activity and health attributes required to understand individuals' typical mobility patterns and likelihood of being severely impacted by the disease. In each simulated day, the common daily behaviours of the synthetic individuals -currently shopping, schooling and working -are simulated and then, if they have the disease, the individuals impart a hazard to the locations that they visit. Disease-free individuals who also visit these locations receive some exposure which, when combined with their individual vulnerability, may lead to them contracting the disease themselves. The model runs for a user-defined number of simulated days and, on completion, outputs aggregate disease statistics. The remainder of this paper is organised as follows. Section 2 describes the risk modelling framework including how hazards and exposures are estimated and integrated within a compartmental epidemiological risk model. This section also contains details on the generation of a synthetic population (Section 2.2), how health, socio-demographics, and activity information are incorporated into that population (Section 2.2.1) and how individuals are assigned to appropriate locations (e.g. school, home, work) for their activities (Section 2.3). In Section 3 the result of a case study in Devon is presented, showing the effects of the lockdown that started on 23rd March 2020 compared to those predicted if the lockdown had started a week earlier. Finally, Section 4 provides a concluding discussion and ideas for future developments and applications. J o u r n a l P r e -p r o o f Compartmental models have been used widely in infectious disease epidemiology with many based on the Susceptible -Infection -Removed (SIR) model introduced by Kermack and McKendrick (1927) or the Susceptible -Exposed -Infection -Removed (SEIR) model introduced by Rvachev and Longini (1985) . They have been used extensively for modelling with examples including Arcede et al. (2020) , Dureau et al. (2013) , Keeling et al. (2020) , Kucharski et al. (2020) , van Leeuwen and Sandmann (2020). As an important characteristic of COVID-19 is the possibility of transmission when individuals are unknowingly infectious, i.e. in the pre-symptomatic and asymptomatic phases (Arcede et al., 2020) . The SEIR model used here has a further breakdown of the infectious and removed components (Fig. 1) . The additional compartments provide enhanced additional resolution in the disease status of individuals that is important to determine individual behaviour and transmission probabilities (He et al., 2020) . [ Figure 1 about here.] Individuals within the model may progress between compartments based on a probabilistic approach to determine the progression from one compartment (phase of infection) to the next (See Section 2.1.3). SEIR models have been combined with high resolution social interaction networks to explore COVID-19 transmission pathways at local scales (Aleta et al., 2020 , Firth et al., 2020 This daily update is illustrated in Figure 2 . Before simulating daily dynamics, the model estimates an initial disease status for each individual. This initialization is only performed once and, in effect, seeds the disease into the population. After this initial step, in each iteration of the model synthetic individuals spend time at some locations; current locations are their homes, shops, schools, and workplaces. If an individual is infected then they impart some of this infection risk on to the location that will then form the basis of the risk of disease for others at those locations. [ Figure 2 about here.] J o u r n a l P r e -p r o o f In each iteration the synthetic individuals spend time in four possible locations; these are currently homes, shops, schools, and workplaces. If an individual is infected then they impart some of this infection risk on to the location, denoted location hazard, . The overall hazard, , associated with a location, is calculated by summing the individual hazards, ℎ, imparted by each agent/individual, , from a total population of agents, as they visit location, : If an individual, , does not visit location , or if they are not infected, then ℎ , = 0. If the individual is infected, then the individual hazard is proportional to the amount of time per day that the individual spends doing that activity, , and the probability that the individual will visit that particular location . Individuals have a probability of visiting a number of different school, work, and retail locations, so the time spent doing a particular activity is distributed among the possible locations that they might visit -denoted by : Symptomatic individuals impart 'full' hazard on a location, while asymptomatic individuals will impart a reduced amount of hazard due to reduced transmission rates (Koh et al., 2020 , Madewell et al., 2020 , Qiu et al., 2021 . We can scale the transmission asymptomatic In the second stage of each iteration, individuals may receive some exposure to the disease based on the locations they visit. The exposure, , that an individual, , receives per day, is the summation of the hazard, , of all the locations that they visit, , proportioned by the amount of time they spend there, , and the proportion of visits to that particular location that they make, : Hence if an individual spends 24 hours per day in a location that has a hazard score of 1.0, then their exposure will be 1.0. An individual's exposure is then combined with their vulnerability ( ) to give the risk (probability) of infection on that day: where = 1 day and, for the simulations reported here, is set to 1 for all individuals. In future work this mechanism can be used to describe which individuals are more likely to be infected. As disease-free individuals are exposed to the disease through visiting locations with increased hazards. For any given day they will contract the disease with probability = from Equation (4) where a represents the effects of personal characteristics for each individual that determine their behaviour and where they spend their time -the key components of calculating their individual risk of contracting the disease. The Bernoulli distribution is used to assign each individual either a zero (doesn't get exposed) or a one (does get exposed) based on the principle of a coin-flip with the weight of the coin (i.e. the chance of being exposed) being determined by the probability . The higher the probability, , the more likely the random number drawn from the Bernoulli distribution will be a one, and the more likely they are to transition from susceptible (S) to exposed (E). This process is repeated for every individual in the population at each (daily) time step. When an individual is exposed, they are assigned an exposed duration transition time and a pre-symptomatic duration and a symptomatic/asymptomatic duration. Following approaches commonly used in the literature (see for example, , Linton et al. (2020), Wei et al. (2020) ). The first two of these are realisations of Weibull distributions (i.e. non-negative, flexible and allow for long-tails / extended durations) and the latter from a log-normal distribution (non-negative and right-skewed). Details of parameters used for the different stages, together with references of their sources, can be found in Supplementary Information. Once in the Exposed (E) state an individual will next move into the Infectious (I) state. This can mean moving into the asymptomatic or the pre-symptomatic and then symptomatic stage. This will be influenced by an individual's age and BMI, with older and overweight individuals less likely to be asymptomatically infected (Table 1) according to: where , is determined by the symptomatic probabilities outlined in Table 1 . Lastly, individuals will move from the Infectious (I) state to the Removed (R) state. All asymptomatically infected individuals will recover. Symptomatically infected individuals will either recover or die based upon their age and BMI (Table 1) . Older and more overweight individuals are less likely to recover (Table 1 ). This transition is described by the following: where , is determined by the mortality probabilities outlined in Table 1 . [ The underlying population used in the dynamic simulation model comes from a spatial microsimulation model, SPENSER (Synthetic Population Estimation and Scenario Projection Model), developed to provide timely georeferenced population forecasts at a high resolution (individual and household level) for scenario projections (Lomax and Smith, 2017, Smith and Russell, 2018) . SPENSER uses Iterative Proportional Fitting (IPF) techniques (Lovelace et al., 2015) to reweight microdata and area level counts from the 2011 Census of Population for England and Wales to create a micro-level synthetic dataset for the entire population. Spatial microsimulation has been widely employed in support of financial and economic policy analysis across Europe and North America (Tanton, 2018) . Over the last two decades, spatial microsimulation techniques have been used increasingly to examine health and health inequalities (Morrissey et al., 2015) . The SPENSER model comprises four steps: (1) [ Table 2 about here.] In the output from SPENSER, each individual is assigned to a Middle Layer Super Output Area (MSOA) while in the household output, individual households are assigned to a Lower Super Output Area (LSOA). This is due to differences in the constraint tables used to construct the synthetic population, where household constraints variables are available with higher levels of disaggregation for smaller areas than population constraint variables. As individuals are assigned to a household, combining the two files means that information for individuals can ultimately be derived at LSOA scale. MSOA is a census geography in which each area represents a mean population in the order of 7,200 individuals, and LSOA is a finer geography in the order of 1,500 individuals. Following work by Morrissey et al. (2015) , propensity score matching (PSM) using a kernel density algorithm was used to allow each individual simulated by the SPENSER model to be [ Table 3 about here.] [ Figure 3 about here.] Currently three activities, other than spending time at home, are simulated in the model: working, attending school and shopping. Having estimated the amount of time that individuals spend doing these activities (Section 2.2), this section outlines a general method for estimating the probabilities that individuals will visit particular sites of disease transmission. For example, given that an individual might spend an hour per day shopping, which shops are they most likely to visit? The following provides an illustrative example based on trips to supermarkets and schools, but the principle is the same for sending individuals to any point destinations including those not explicitly considered currently such as pubs and restaurants. Workplaces are an exception, as discussed in Section 2.3.2. Having assembled the data for the origin, destination and costs of travel between zones, a spatial interaction model is used to calculate trip probabilities. Details of these models can be found in the Supplementary Materials (Section 7). Figure 5 shows the trip probabilities for South West England region using flow lines. [ Figure 5 about here.] Workplace flows would ideally be estimated through a spatial interaction model similar to that employed in the estimation of flows to schools and shops. However, the problem with journey to work is significantly more difficult because: The first confirmed case of the novel coronavirus in the UK was documented on 21 st January, 2020. This was followed by the first confirmed COVID death in the UK on 5 th and encouraged them to perform no more than one form of exercise a day. In the following, we provide a case study on the potential reduction in cases and subsequently deaths that implementation of the lockdown one week earlier may have had in Devon County, England. Devon is a county in the Southwest of England that extends from the Bristol Channel in the north to the English Channel in the south and is bounded by Cornwall to the west, Somerset to the north-east and Dorset to the east. Devon is a sparsely populated, predominantly rural county with a total population of about 700,000. The simulation of cases during the first lockdown is based on the temporal distribution of cases recorded by Public Health England (PHE; coronavirus.data.gov.uk) . During this period, the Royal Devon & Exeter NHS Foundation Trust and Northern Devon Healthcare Trust estimate that the prevalence of COVID-19 was 2% (personal communication). This equates to ca. 14,000 individuals compared with 790 cases recorded by PHE for the Unitary Authority of Devon over the first 70 days, due to limited testing at the beginning of the outbreak. We smoothed the PHE cases using a negative binomial generalised additive model, ( ), and applied a multiplying factor to give the expected number of cases on day as = ( * ( ) ). The model was 'seeded' by constraining the number of infections in the first 10 days to be equal to after which the number of new daily infections are generated by the model, unrestricted, for a further 60 days. In order to impose lockdown on the simulated J o u r n a l P r e -p r o o f population, the amount of time individuals spent outside their home was scaled according to data from the Google Community Mobility Reports. As Google Community Mobility Reports are available at a regional scale, we used data specific to Devon. These data provide The values from the Google Community Mobility data were smoothed for time spent in residential locations using a 14-day moving average ( ). Using this in conjunction with the average proportion of time spent at home ( ℎ ‾ ) and outside the home ( ‾ ) from the individuals in the population, we created time-series of daily lockdown multipliers ( , Figure 6 ). As can be seen from Figure 6 , the values for proportion of time outside the home from March to June 2020 are all less than 1. For any given day, the amount of time that any individual spends at a location outside the home is reduced in proportion to the lockdown multiplier. Time no longer spent on activities outside the home will be added on to time spent at home for each individual. The only condition under which the lockdown multiplier does not apply is if an individual is in the symptomatic disease status. Here we assume they reduce their activities outside the home by 90% to reflect self-isolation behaviour. Lockdown restrictions are applied universally across the population so that, for example, there is no differentiation for enhanced mobility of key workers or to allow for variations J o u r n a l P r e -p r o o f between business sectors (Batty and Milton, 2021) , which would be a possible avenue for future refinement of the model. [ Figure 6 about here.] Other countries went into lockdown earlier than the UK and here the effects of implementation of a UK-wide lockdown one week earlier than it occurred are simulated. To explore the effect of official lockdown occurring earlier, the time-series of lockdown multipliers ( Figure 6 ) is shifted to be one week earlier. For the purpose of comparing scenarios the lockdown scenario as it happened is referred to as the 'baseline' scenario, while the scenario in which lockdown is imposed one week earlier will be called the 'experimental' scenario. The model simulation in the baseline scenario produced a good fit to the known daily cases of COVID-19 according to PHE data. The total infection count in Devon county at the end of the 70 day simulation is summarised by age group in (Figure 7) . Being able to explore heterogeneity in the transmission of the disease in different groups within the population and over different spatial aggregations and periods of time is one of the key features of the microsimulation approach. The outputs of the model are at the individual level and it is straightforward to aggregate the results from the simulations to any specified groupings. As an example, Table 4 shows the results by age groups and Figure 7 the number of cases over time. Another feature of the model is being able to extract information for individuals within the population according to their disease status at any point in time and this information can be cross-tabulated with other variables to assess heterogeneity in disease status across different groups (over time). As an example, Figure 8 shows the number of people with different disease status by age group, together with the reduction in cases associated with lockdown being a week earlier. This shows a clear difference between age groups with a higher proportion of asymptomatic cases in younger age groups. [ Table 4 The model is spatially explicit, allowing us to explore the geographical distribution of COVID-19 infections in our scenarios. Figure 9 shows that the baseline scenario leads to some distinct hot-spots located around more densely populated MSOAs, such as those in Exeter, which is one of the largest cities in Devon county. In the baseline scenario as much as 6% of the population of an MSOA becomes infected. In the experimental scenario, we see a similar spatial distribution as that seen in the baseline scenario, with hot-spots located J o u r n a l P r e -p r o o f around larger cities with denser populations. However, the maximum infection rate is reduced to under 4% in the experimental scenario. [ Figure 8 about here.] [ Figure 9 about here.] This paper presents a novel, data-driven modelling framework that reflects the complexities of the British population to model the transmission of COVID-19 within communities and to assess the effect of policy interventions. The framework brings together a wide variety of data driven approaches, including epidemiological disease modelling, urban analytics and spatial analysis, as well academic and private sector researchers to develop a computationally efficient framework for its implementation. This enables questions related to the geographical transmission, diffusion, acceleration and the regulation in the incidence of cases to be traced through physical interactions between the many components that determine the way entire populations move and interact with one another in their daily lives. The power and spatial flexibility of the framework to assess the effects of different interventions is demonstrated within the case study where the effects of the first UK national lockdown are estimated for the county of Devon. Here we find that an earlier lockdown is estimated to result in a lower peak in daily infections and 47% fewer infections overall. J o u r n a l P r e -p r o o f As outlined in this paper, the framework is based on a spatial microsimulation model, SPENSER, that reproduces data on household and its constituent population across the whole of Great Britain. The data produced by the spatial microsimulation model replicates the structure and behaviour of the real population in terms of demographic, socioeconomic and health characteristics, along with detailed time use data. Spatial Interaction models including exploring the effects of alternative lockdown scenarios both at an aggregate level, but also across different sub-populations, and the ramifications of the vaccination roll-out. In the case of the former, it will be possible to consider variations in the timing of movements between different mitigation/adaptation strategies on the number and distribution of cases, and the capacity of local health services to meet the associated need. More refined options such as the restriction of specific types of employment type or activity, e.g. schools, restaurants or retail outlets, or the variation of controls across more disaggregate geographies than local authority areas can also be considered. For the latter, scenarios could be designed that explore the nature of long-term equilibrium dynamics, e.g. in a progression towards herd immunity or seasonal cycles of infection, with the model creating projections of future infections, by local area, for example, in relation to efficacy, uptake, compliance, and availability of the vaccines across social and demographic groups. The dynamic simulation model was developed using a combination of R and Python. After the initial development, it was refactored using OpenCL, a framework for parallel programming. OpenCL allows the simulation to be executed on a CPU or GPU, depending on the available hardware, and leads to a significant speedup due to multi-threaded execution. The OpenCL implementation is able to run the simulation for 100 timesteps for the whole population of Devon in around a second, which is in the order of 10,000 times faster than the original implementation. This improved computational speed is crucial if models such as this are going to be used by policy-makers within real decision-making environments. In addition, an interactive Graphical User Interface (GUI) was built (see Figure 10 ). The GUI J o u r n a l P r e -p r o o f allows the user to explore scenarios while they are executing by interactively starting, stopping, stepping and resetting the model. The GUI also allows the values of model parameters to be modified and the model to be re-run with updated parameter values. This allows rapid exploration of the model output and how it changes with different parameter values. [ Figure 10 about here.] The importance of reflecting the real-life behaviours of individuals given their health, demographic and socioeconomic circumstances is reflected in the large evidence base that demonstrates that the outcomes of COVID-19 are not distributed equally across subpopulations and space. This is linked to a variety of factors including occupational profile, housing circumstances and transportation options. To date, COVID-19 transmission models have failed to capture the necessary data to capture the inequality in outcomes across different sub-groups. This paper extends the growing number of COVID-19 transmission models by developing a dynamic SEIR model underpinned by a 'digital twin' British population. The digital twin underpinning the dynamic SEIR model represents the complex health, socio-economic and behavioural attributes, as well as mobility patterns required to understand the transmission of COVID-19 within the community and the impact of different interventions. Importantly, the synthetic modelling approach is reproducible in any country for which small area demographic counts are available, along with nationally representative health and time use data. J o u r n a l P r e -p r o o f (Brazeau et al., 2020 , Popkin et al., 2020 , Davies et al., 2020 . 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