Global Stability for a Virus Dynamics Model with Nonlinear Incidence of Infection and Removal

Global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct Lyapunov method, where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear. In the case where the functional quotient between the force of infection and the removal rate of the virus is a nonincreasing function of the virus concentration, the existence of a threshold parameter, i.e., the basic reproduction number or basic reproductive ratio, is established and the global stability of the equilibria is discussed. Moreover, in the absence of the above-mentioned monotonicity property, estimations for the sizes of the domains of attraction are given. Biological significance of the results and possible extensions of the model are also discussed.