Stationary Patterns of a Cross-Diffusion Epidemic Model

Abstract

We investigate the complex dynamics of cross-diffusion $SI$ epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.