Abstract
In this paper, we study some models with repulsion effect on superinfecting viruses by infected cells [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are the density of uninfected cells, infected cells and viruses at time [Formula: see text] at location [Formula: see text], respectively. The functions [Formula: see text] and [Formula: see text] are assumed to be positive, continuous and bounded. [Formula: see text] denotes the production rate of uninfected cells. The infection rate is [Formula: see text] and the function [Formula: see text] is the production rate of free viruses. And [Formula: see text] is the rate of transfer from uninfected cells to infected cells. The positive constants [Formula: see text] and [Formula: see text] denote the death rate of uninfected cells, infected cells and viruses, respectively. The stability of the infection-free equilibrium solution and infection equilibrium solution is discussed. It is shown that if the basic reproduction number [Formula: see text] then the chemotaxis has no effect, that is, the infection-free constant solution is stable. For the system with chemotactic sensitivity [Formula: see text], if [Formula: see text], then the infection constant solution will be unstable under some conditions.
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