Abstract
We present an approach to extend the endemic–epidemic (EE) modelling framework for the analysis of infectious disease data. In its spatiotemporal formulation, spatial dependencies have originally been captured by static neighbourhood matrices. These weight matrices are adjusted over time to reflect changes in spatial connectivity between geographical units. We illustrate this extension by modelling the spread of COVID-19 disease between Swiss and bordering Italian regions in the first wave of the COVID-19 pandemic. The spatial weights are adjusted with data describing the daily changes in population mobility patterns, and indicators of border closures describing the state of travel restrictions since the beginning of the pandemic. These time-dependent weights are used to fit an EE model to the region-stratified time series of new COVID-19 cases. We then adjust the weight matrices to reflect two counterfactual scenarios of border closures and draw counterfactual predictions based on these, to retrospectively assess the usefulness of border closures. Predictions based on a scenario where no closure of the Swiss-Italian border occurred increased the number of cumulative cases in Switzerland by a factor of 2.7 (10th to 90th percentile: 2.2 to 3.6) over the study period. Conversely, a closure of the Swiss-Italian border two weeks earlier than implemented would have resulted in only a 12% (8% to 18%) decrease in the number of cases and merely delayed the epidemic spread by a couple of weeks. Our study provides useful insight into modelling the effect of epidemic countermeasures on the spatiotemporal spread of COVID-19.
Highlights
The many types of uncertainty surrounding an ongoing emerging infectious disease outbreak with future endemic potential, such as coronavirus disease 2019 (COVID-19), motivates the use of statistical modelling to investigate current and future outbreaks of the disease
We examined the role of a border closure between Italy and Switzerland on the spatiotemporal spread of COVID-19 through the following steps: 1. Fit an EE model to the region-stratified time series of number of confirmed new COVID-19 cases from
Since other endemic-epidemic models of COVID-19 cases [8] as well as estimates of the serial interval from the literature [15] indicate that its serial interval is likely to be in the range of days, rather than weeks, we considered a maximum lag of p = 7
Summary
The many types of uncertainty surrounding an ongoing emerging infectious disease outbreak with future endemic potential, such as coronavirus disease 2019 (COVID-19), motivates the use of statistical modelling to investigate current and future outbreaks of the disease. Not understanding the uncertainty of the true scale of the disease, e.g. through unreported cases, leads to difficulties in assessing the impact of required interventions [1, 2]. Multiple epidemic data sources provide valuable information on different aspects of such an outbreak, but require appropriate statistical techniques to incorporate the associated uncertainties. One such statistical tool is the endemic-epidemic (EE) modelling framework, created for the analysis of infectious disease surveillance data [3]. It is a multivariate time series model that additively decomposes incidence into an endemic and an epidemic component. The epidemic component captures incidence driven by previous case counts, or force of infection, and the endemic component captures exogenous contributions to incidence (such as seasonal, socio-economic or demographic factors) [1, 3]
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