Hopf bifurcation in a CTL-inclusive HIV-1 infection model with two time delays

In this paper, we investigate a delayed HIV-1 infection model with immune response. Though a logistic growth is incorporated in the growth of the target cells, our focus is on the effect of delays on the infection dynamics. We first study the existence of steady states, which depends on the basic reproduction number R₀. When R₀≤1, there is only the infection-free steady state, which is globally asymptotically stable if R₀ < 1when=""r₀="" > 1, besides the unstable infection-free steady state, there is a unique infected steady state. We then study the local stability of the infected steady state and local Hopf bifurcation at it. The theoretical analysis indicates that the dynamics scenario is complicated. For example, there can be three sequences of critical values, stability switches and double Hopf bifurcation can occur. Some of the theoretical results are also illustrated with numerical simulations.