Global Properties for A Virus Dynamics Model with Lytic and Non-Lytic Immune Responses, and Nonlinear Immune Attack Rates

We consider a mathematical model that describes a viral infection with lytic and non-lytic immune responses. One of the main features of the model is that it includes a rate of linear activation of cytotoxic T lymphocytes (CTLs) immune response, a constant production rate of CTLs export from thymus, and a nonlinear attack rate for each immune effector mechanism. Stability of the infection-free equilibrium, and existence, uniqueness and stability of an immune-controlled equilibrium, are investigated. The stability results are given in terms of the basic reproductive number. We use the method of Lyapunov functions to study the global stability of the infection-free equilibrium and the immune-controlled equilibrium. We give a sufficient condition on the non-lytic-immune attack rate for the global asymptotic stability of the immune-controlled equilibrium. By theoretical analysis and numerical simulations, we show that the lytic and non-lytic activities are required to combat a viral infection.