Global stability analysis of a viral infection model in a critical case

Abstract

Recently, it has been proved that for the diffusive viral infection model with cell-to-cell infection, the virus-free steady state E0 is globally attractive when the basic reproduction number R0 < 1, and the virus is uniformly persistent if R0 > 1. However, the global stability analysis in the critical case of R0 = 1 is not given due to a technical difficulty. For the diffusive viral infection model including a single equation with diffusion term, global stability analysis in the critical case has been performed by constructing Lyapunov functions. Unfortunately, this method is not applicable for two or more equations with diffusion terms, which was left it as an open problem. The present study is devoted to solving this open problem and shows that E0 is globally asymptotically stable when R0 = 1 for three equations with diffusion terms by means of Gronwall's inequality, comparison theorem and the properties of semigroup.

Keywords

• reaction-diffusion equation model
• global attractor
• globally attractive
• asymptotical stability