Computation and analysis on dynamics of a virus-infection-immune model with diffusion and time-delay effects

This paper considers a simian immunodeficiency virus-infection-immune model with diffusion and time-delay effects. The stability of equilibria and Hopf bifurcation analysis are carried out, the formulas determining the direction, stability and periodic of Hopf bifurcation are given and the numerical examples are presented to complement the theoretical results. It is found that there are critical values of parameters describing the survival probability of infected cells and time-delay respectively which mainly determine the dynamics of the model. The conclusions show that the survival probability of infected cells, the combination of diffusion and time-delay play important roles on the stability of equilibria, and the change of time-delay will affect the existence of Hopf bifurcation. Biologically, the results imply that either the viruses persist with the host cell in a certain period of time or the viruses disappear gradually and can not infect the host cells anymore.