Global dynamics for a class of age-infection HIV models with nonlinear infection rate

Abstract

In this paper, we study the global stability of a class of HIV viral infection models with continuous age-structure using the direct Lyapunov method. In each of the cases where the incidence rates are given by nonlinear infection rate F (T )G(V ), Holling type II functional response and Crowley-Martin functional response, we define the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on technical materials and necessary arguments, including relative compactness of the orbit and uniform persistence of system, by reformulating the system as a system of Volterra integral equations. We further investigate global behaviors of HIV viral infection models with Holling type II functional response and Crowley-Martin functional response through numerical simulations.

Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells

“…For example, an HIV‐1 infection model with age‐structured infected cells to account for the mechanism of AZT (Zidovudine) treatment of HIV infection was proposed in , and the cost‐effectiveness of treatments with combined therapies involving reverse transcriptase, protease, and entry/fusion inhibitors could also be evaluated by age‐structured models . These age‐structured within‐host virus models with the consideration of age‐dependent infected cell death rates and viral production rates have attracted many recent investigations, see, for example, the models in the literatures .…”

“…Georgescu and Hsieh and Wang et al. considered a nonlinear infection rate in the form of , where is the contact rate function dependent on susceptible cell density T and represents the force of infection by virus at density V . Korobeinikov assumed the incidence rate to be a more general form .…”

Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

“…Following Theorem 2 of Van den Driessche and Watmough [17], we have the following result on the local stability of E 0 : Theorem 1: The disease free equilibrium 0 E of the system (7)- (12) is locally asymptotically stable if 0 1 < R and unstable if 0 1. > R…”

“…Elaiw and Almuallem [16] to investigate the qualitative behaviors of three HIV dynamical models with two types of co circulating target cells. Wang et al [17] has been studied the global stability of HIV viral infection model with continuous agestructure using the direct lyapunov method. Shen et al [18] to analyze the mathematical model of global dynamics with two lyapunov functions are constructed to prove the global stability of disease free and endemic equilibria.…”

Analysis of an SVEIR model with age-dependence vaccination, latency and relapse

“…There is growing interest in the dynamics of epidemic model with age structure (see, e.g., [1,2,4,11,13,14,16,17,[23][24][25][26]28] and references cited therein). In general, the average age at which individuals become infected is largely determined by the prevalence of infection in the population.…”