Global dynamics of a diffusive viral infection model with spatial heterogeneity

Abstract

To explore the joint impact of cell-free infection and cytokine-enhanced viral infection, we propose a PDE model with spatial heterogeneity by taking into account a general cell reproduction function, free-virus infection function and cytokine-enhanced viral infection function. Mathematical challenges lie in the facts that (i) the solution map of the model system loses its compactness; and (ii) the definition of the basic reproduction number and the global asymptotic stability of the infection-free steady state become challenging since the linear system at the infection-free steady state is constituted by three equations. We define the basic reproduction number R0 as the spectral radius of the sum of two linear operators corresponding to cell-free infection and cytokine-enhanced viral infection, and prove its threshold role: if R0<1, the infection-free steady state is globally asymptotically stable; if R0=1, the infection-free steady state is locally asymptotically stable; and if R0>1, the model system is uniformly persistent. A special case is given to show the global attractiveness of the infection steady state.