Modelling And Stability Analysis For An Immuno-epidemiological System

In this paper, based on the mechanism of HIV infection in a host and its transmission among hosts, an immuno-epidemicological model is formulated and analysized. We link the immunological system model and the epidemiological system model by introducing an infection-age in the infected class and assuming that the force of infection of the disease transmission is positive proportional to the virables of virus within host.By means of integrated semigroup theory in functional analysis, the well-posed ness of the epidemiological system is proved. The explicit expression of the basic reproduction number Ro is obtained, it is shown that if Ro>1, there exists a unique endemic equilibrium. By using the method of linearizing the system around the equilibria and constructing a suitable Lyapunov function, it is proved that if Ro <1, the disease free equilibrium is globally asymptotically stable, if Ro>1, the endemic equilibrium is globally asymptotically stable.