A reaction–diffusion SIS epidemic model in an almost periodic environment

Abstract

A susceptible–infected–susceptible almost periodic reaction–diffusion epidemic model is studied by means of establishing the theories and properties of the basic reproduction ratio \({R_{0}}\). Particularly, the asymptotic behaviors of \({R_{0}}\) with respect to the diffusion rate \({D_{I}}\) of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of \({R_{0}}\). Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease.