Cell-free infection and cell-cell transmission HIV-1 dynamics model with cure rate

Abstract

Direct cell-to-cell transmission of HIV-1 is found to be a more efficient means of virus propagation than virus-to-cell infection. In this paper, a mathematical model combining these two modes of viral infection with cure rate is investigated. Through calculation, the explicit expression of the basic reproduction number of the model is obtained. By analyzing the characteristic equations, the local stability of equilibria of the model is established. It is proven that the model is permanent if the chronic-infection equilibrium exists. By means of the second additive compound matrix theory, we show that the chronic-infection equilibrium is globally stable if the basic reproduction number is greater than one. By using Lyapunov function, a sufficient condition of global stability for the infection-free equilibrium is obtained if the basic reproduction number is less than one.