A diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis

From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R0 of the model without chemotaxis. That is, the infection-free steady state E0 is globally asymptotically stable if R0 < 1, and the virus is uniformly persistent if R0 > 1. In addition, we use the cross iteration method and the Schauder’s fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.