Using hybrid automata to model mitigation of global disease spread via travel restriction

Abstract

<abstract><p>Inspired by the COVID-19 pandemic, we build a large-scale epidemiological model that accounts for coordination between regions, each using travel restrictions in order to attempt to mitigate the spread of disease. There is currently a need for simulations of countries cooperating since travel restriction policies are typically taken without global considerations. It is possible, for instance, that a strategy which appears unfavorable to a region at some point during a pandemic might be best for containing the global spread, or that only by coordinating policies among several regions can a restriction strategy be truly effective. We use the formalism of hybrid automata to model the global disease spread among the coordinating regions. We model a connected network of coupled Susceptible-Exposed-Infected-Recovered (SEIR) models by considering a weighted directed graph with each node corresponding to a single region's disease model. The SEIR dynamics for each region admit terms for inter-regional travel determined by the graph's Laplacian that additionally accounts for travel restrictions between regions. The existence of an edge may change according to so-called guard conditions, which are triggered when the proportion of symptomatic infected individuals in a region reaches a critical value. Lastly, we run simulations in MATLAB of a global disease spreading among regions using automated travel restrictions and analyze the results.</p></abstract>