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

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 $${R_{0}}$$R0. Particularly, the asymptotic behaviors of $${R_{0}}$$R0 with respect to the diffusion rate $${D_{I}}$$DI of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of $${R_{0}}$$R0. Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease.