Global Stability of a Viral Infection Model with Defectively Infected Cells and Latent Age

Abstract

The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells. The existence of steady states is determined by the basic reproduction number of virus. With the Lyapunov’s direct method, they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter. To achieve it, a novel procedure is proposed. Its novelties are two-folded. On one hand, the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities. On the other hand, for the infection steady state, a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative (semi-)definite or not. This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states. Moreover, the procedure is expected to be applicable for other similar models.

Keywords

Viral infection model / Basic reproduction number / Equilibrium / Global stability / Lyapunov direct method / Age structure