Stability Analysis of an In-Host Viral Model with Cure of Infected Cells and Humoral Immunity

Abstract

An in-host viral model with cure of infected cells and humoral immunity is studied. We prove that the stability is completely determined by the basic reproductive number $R_0$ and show that the infection-free equilibrium $E_0$ is globally asymptotically stable if and only if $R_0\le 1$. Moreover, if $R_0>1$, the infection equilibrium is locally asymptotically stable when the time delay $\tau$ is small and it loses stability as the length of the time delay increases past a critical value ${\tau }_0$. Finally, we confirm our analysis by providing several numerical examples.