Global dynamics of a delayed diffusive virus infection model with cell-mediated immunity and cell-to-cell transmission

In this paper, we propose and analyze a delayed diffusive viral dynamic model incorporating cell-mediated immunity and both cell-free and cell-to-cell transmission. After discussing the well-posedness, we provide some preliminary results on solutions. Then we study the existence and uniqueness of homogeneous steady states, which turned out to be completely determined by the basic reproduction number of infection R-0 and the basic reproduction number of immunity R-1. Note that when R-1 is defined, it is necessary that R-0 > 1. The main result is a threefold dynamics. Roughly speaking, when R-0 < 1. the infection-free steady state is globally asymptotically stable; when R-1 <= 1 < R-0 the immunity-free infected steady state is globally asymptotically stable; when R-1 > 1 the infected-immune steady state is globally asymptotically stable. The approaches are linearization technique and the Lyapunov functional method. The theoretical results are also illustrated with numerical simulations.