Analysis of a CD4$^+$ T cell viral infection model with a class of saturated infection rate

This paper formulates and analyzes anHIV-1 infection model with saturated infection rate. We firstdiscuss the boundedness of the solution and the existence of theequilibrium. The local stability of the virus-free equilibrium andinfected equilibrium is established by analyzing the roots of thecharacteristic equations. Furthermore, we study the global stabilityof the virus-free equilibrium and infected equilibrium by usingsuitable Lyapunov function and LaSalle's invariance principle, andobtain sufficient conditions for the global stability of theinfected equilibrium. Finally, numerical simulations are presentedto illustrate the main results.