Bifurcation Analysis of a Diffusive Virus Infection and Immune Response Model with Two Delays

A reaction-diffusion system with two delays, which describes viral infection spreading in the lymphoid tissue, is investigated. The delays promote very complex dynamics of the model. We get the Hopf bifurcation curves and the stability region for the coexisting steady state on a two-parameter plane by finding the stability switching curves and the subsets of stable region. When two delays cross the boundary of the stable region, the system will undergo stability switches. It is shown that two types of bistability are possible: the coexistence of the stable virus-free steady state and the stable coexisting steady state; the coexistence of the stable virus-free steady state and a stable periodic solution. Numerical simulations suggest that delays can also induce tristability including a steady state and two stable periodic solutions.