Repulsion effect on superinfecting virions by infected cells for virus infection dynamic model with absorption effect and chemotaxis

A mathematical model for virus infection dynamics with absorption effect and chemotaxis is proposed to study the repulsion effect on superinfecting virions by infected cells. The basic reproduction number R0 is established. Furthermore, we show that the threshold dynamics can be expressed by the basic reproduction number R0 in a bounded domain. It is shown that the infection-free steady state E0 is asymptotically stable if R0<1, and the virus is uniformly persistent if R0>1 in the case of spatially heterogeneous infections. The stability properties and Turing instability of the proposed model have been extensively discussed for the case of spatially homogeneous infections. In addition, the existence of the travelling wave solutions is discussed in unbounded domain. At last, numerical simulations are carried out to illustrate the main results.