An SIR Epidemic Model With Gravity in Patchy Environment: Analyses for Two Patches System

In this study, we propose an explicitly spatial SIR epidemic model under which a population travel is subject to the gravity law. Namely, the migration rates are assumed to be increased with the populations between coupled patches and decreased with the distance. We analyze the model simplified into two patches. The conditions for a stable disease-free equilibrium are derived. Moreover, we show that the derived basic reproduction number corresponds with such conditions. The numerical results shown are in agreement with theory.

Keywords: SIR epidemic model, Gravity model, Asymptotic stability

E-mail: klot@su.ac.th