Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response

A viral infection model with nonlinear incidence rate and delayed immune response is investigated. It is shown that if the basic reproduction ratio of the virus is less than unity, the infection-free equilibrium is globally asymptotically stable. By analyzing the characteristic equation, the local stability of the chronic infection equilibrium of the system is discussed. Furthermore, the existence of Hopf bifurcations at the chronic infection equilibrium is also studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the chronic infection equilibrium. Numerical simulations are carried out to illustrate the main results.

► The model is with nonlinear incidence rate and delayed immune response.
► We study the global behaviors of the equilibria.
► The effect of the time delay and nonlinear incidence rate is considered.
► The existence of Hopf bifurcations is investigated.
► Stability switches are observed.