Estimating Cross-Border Mobility from the Difference in Peak Timing: A Case Study of Poland–Germany Border Regions

Human mobility contributes to the fast spatiotemporal propagation of infectious diseases. During an outbreak, monitoring the infection on either side of an international border is crucial as cross-border migration increases the risk of disease importation. Due to the unavailability of cross-border mobility data, mainly during pandemics, it becomes difficult to propose reliable, model-based strategies. In this study, we propose a method for estimating commuting-type cross-border mobility flux between any pair of regions that share an international border from the observed difference in their infection peak timings. Assuming the underlying disease dynamics are governed by a Susceptible–Infected–Recovered (SIR) model, we employ stochastic simulations to obtain the maximum likelihood cross-border mobility estimate for any pair of regions. We then investigate how the estimate of cross-border mobility flux varies depending on the transmission rate. We further show that the uncertainty in the estimates decreases for higher transmission rates and larger observed differences in peak timing. Finally, as a case study, we apply the method to some selected regions along the Poland–Germany border that are directly connected through multiple modes of transportation and quantify the cross-border fluxes from the COVID-19 cases data from 20 February to 20 June 2021.