Dynamics of an epidemic model arising in a spatial segregation control strategy.

Abstract

In this paper, we propose a free boundary problem to model the spread of an epidemic by introducing a spatial segregation control strategy. The model consists of two coupled reaction-diffusion equations along with an ordinary differential equation, while the free boundary is described by an integro-differential equation. The results reveal a trichotomy in which the epidemic can shrink, reach equilibrium, or expand spatially. Moreover, we establish the final size of the cumulative number of infected populations and characterize the threshold phenomenon of epidemic outbreak using the principal eigenvalue of an elliptic operator. Additionally, we apply this model to simulate the spatial spread of the COVID-19 epidemic in Xi'an, China, during 2021-2022. This study provides valuable model references for dynamically designing spatial isolation control strategies for newly emerging major infectious diseases.