Global Stability of an Infection Model with Crowley-Martin Functional Response and Latently Infected Cells

This paper exhibits a dynamics model with Crowley-Martin functional response infection rate. We consider nonnegativity of solutions, local asymptotic stability, and global asymptotic stability of the uninfected and infected equilibria. Lyapunov functions are constructed to establish the global asymptotic stability. We have proven that if the basic reproduction number
$R_{0}$
is less than unity, then the disease-free equilibrium of the model is globally asymptotically stable, and if
$R_{0} > 1$
, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamics are completely determined by
$R_{0}$
.