A viral infection model with periodic immune response and nonlinear CTL response

This paper investigates a viral infection model with periodic immune response and nonlinear cytotoxic T lymphocyte (CTL) response. Using the periodic rhythms of human immune system, the model can avoid the unreasonable equilibrium in the basic viral model with nonlinear CTL response introduced by Nowak et al. We obtain the global stability of the infection-free equilibrium and the immune-exhausted equilibrium. Numerical simulations show that the oscillation of immune system can affect the pattern of the viral dynamical behaviors. Period doubling bifurcations of the system are observed via simulations. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV and HCV infection patients.