Analyzing global stability of a viral model with general incidence rate and cytotoxic T lymphocytes immune response

Abstract

The global dynamics of a viral model with general incidence rate and CTL immune response is investigated. We derive the basic reproduction number for viral infection $R_{0}$ and the immune response reproduction number $R_\mathrm{CTL}$ for the viral infection model and establish the global dynamics completely determined by the values of $R_{0}$ and $R_\mathrm{CTL}$. By constructing Lyapunov functions and using LaSalle invariance principle, the disease-free equilibrium $E_{0}$ is globally asymptotically stable when the basic reproduction number for viral infection $R_{0}< 1$, and there exists a unique CTL-inactivated infection equilibrium $E_{1}$ which is globally stable and the infection becomes endemic with no sustained immune response when $R_\mathrm{CTL}\le 1<R_{0}$, and then, the CTL-activated infection equilibrium $E^{*}$ of the model exists and is also globally attractive when the immune response reproduction number $R_\mathrm{CTL}>1$.