Dynamics of reaction–diffusion equations for modeling CD4[formula omitted] T cells decline with general infection mechanism and distinct dispersal rates

Abstract

In this paper, we are concerned with a diffusive viral infection dynamical model with general infection mechanism and distinct dispersal rates. In a general setting in which the model parameters are spatially heterogeneous, it is shown that if ℛ0≤1, the infection-free steady state is globally asymptotically stable; while if ℛ0>1, the model is uniformly persistent. The asymptotic profiles of the infection steady state are discussed as the dispersal rate of uninfected CD4+ T cells approaches zero by means of the persistence theory of semidynamical systems and the eigenvalue theory of elliptic equations.