A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment.

Abstract

To explore the impact of the periodic evolution in habitats on the prevention and control of the infectious disease, we consider a diffusive SIS epidemic model in a heterogeneous and periodically evolving domain. By assuming that the evolving domain is uniform and isotropic, the epidemic model in a evolving domain is converted to the reaction diffusion problem in a fixed domain. The basic reproduction number, which depends on the evolving rate of the domain and spatial heterogeneity, is defined. The driving mechanism of the model is obtained by using the principal eigenvalue and the upper and lower solutions method, and a biological explanation of the impact of regional evolution on disease is given. Our theoretical results and numerical simulations show that small evolving rate benefits the control of the infectious disease.