Global dynamics of a class of HIV-1 infection models with latently infected cells

Abstract

Abstract. In this paper, the global dynamics of a class of HIV-1 infection models with different infection rates and latently infected cells are investigated. We first modify the basic virus infection model and propose two models with bilinear infection rate and saturation infection rate, respectively, which take HIV-1 latency into consideration, and then study a model with a general nonlinear infection rate. By using proper Lyapunov functions and LaSalle's invariance principle, it is proved that in the first two models, if the basic reproduction ratio is less than unity, each of the infection-free equilibria is globally asymptotically stable; if the basic reproduction ratio is greater than unity, each of the chronic-infection equilibria is globally asymptotically stable. For the last model with general nonlinear infection rate, we obtain sufficient conditions for the global stability of both the infection-free and chronic-infection equilibria of the model.

Effect of cellular reservoirs and delays on the global dynamics of HIV

“…Most of the mathematical models presented in the literature have focused on modeling the interaction between three main compartments: uninfected CD4 + T cells (s), infected cells (y), and free HIV particles (p). Other models have differentiated between latent and active infected cells by introducing a new variable (w) for the latently infected cells [32][33][34][35][36][37]. In [38], an HIV mathematical model has been presented by considering three types of infected cells: latently infected cells (w), short-lived productively infected cells (y), and long-lived productively infected cells (u) as follows:…”

Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission

“…It is shown that if N < N crit , then the uninfected steady state is the only steady state in the nonnegative orthant and this steady state is stable; while if N > N crit , then the uninfected steady state is unstable and the endemically infected steady state can be either stable, or unstable and surrounded by a stable limit cycle. Recently, Wang et al [36] studied the following HIV-1 infection model with the mass-action infection rate and latent cells,…”

Modeling the dynamics of viral infections in presence of latently infected cells

“…where is an overall drug efficacy. Furthermore, the model (1) includes the class of HIV infection models for different rates of infection and latently infected cells as investigated in Wang et al [26] .…”