Global stability in a viral infection model with lytic and nonlytic immune responses **

This paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses. If the basic reproductive ratio of the virus is less than or equal to one, by the LaSalle's invariance principle and center manifold theorem, the disease-free steady state is globally asymptotically stable. If the basic reproductive ratio of the virus is greater than one, then the virus persists in the host and the disease steady state is locally asymptotically stable. Furthermore, by the method of Lyapunov function, the global stability of the disease steady state is established. At the same time, if we neglect the efficacy of the lytic component, using a geometrical approach, we obtain a different type of conditions for the global stability of the disease steady state.