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

Abstract

Human immunodeficiency virus (HIV) can infect various types of cell populations such as CD4 + T cells and macrophages. The heterogeneity of these target cells implies different birth, death, infection rates, and so on. To investigate the within-host dynamics of HIV which can infect n different types of target cells, a theoretical model with infection-age structure for each type of target cells and a general nonlinear incidence rate is proposed in this manuscript. The model, in the form of a hyperbolic system of partial differential equations (PDE) for infected target cells coupled with several ordinary differential equations, is shown to be biologically reasonable with the establishment of existence, positivity, and boundedness of solutions. Although the PDE form poses novel challenges to theoretical investigation, rigorous analysis is performed to show the uniform persistence of the virus when the basic reproduction number is greater than one. Furthermore, by constructing suitable Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than unity, while the positive steady state is globally asymptotically stable when the basic reproduction number is greater than one.

Asymptotic analysis of a vector-borne disease model with the age of infection

“…Thereafter, Korobeinikov et al [27,28] used a very general form f (S, I) for the incidence rate. For more other nonlinear incidence rates, we refer readers to [5,10,11,17,34,44,56].…”

An Age-Structured Model of HIV Latent Infection with Two Transmission Routes: Analysis and Optimal Control

“…Models with age structure have been used in studying viral dynamics because many within-host processes, such as viral production by infected cells, may rely on the time after infection, i.e., the age of infection [31][32][33][34][35][36][37][38][39][40][41]. For example, Rong et al [42] studied age of infection models with combination therapy including reverse transcriptase inhibitor (RTI), protease inhibitor (PI), and entry/fusion inhibitor.…”

Analysis and control of an age-structured HIV-1 epidemic model with different transmission mechanisms

“…Here x i (t) and y i (t, a) denote the amount of target uninfected CD4 + cells and infected cells, respectively. h i is the incidence rate function satisfying some conditions (see assumptions from (H1) to (H4) [5]). The authors showed that if the therapy is 100% effective, then applying the drug at late infectious stage results in a faster decay of viremia.…”

“…The other parameters are obtained from the literature and are listed in Table 1. We choose production rates of CD4 + lymphoblasts and macrophages as λ i = 1 ml/day, i = 1, 2, respectively and the viral production rate for macrophage as p 2 (a) = 0.1 exp(-3 × 0.00028a) in [5]. The basic reproduction number is obtained, R 0 = 0.4417 < 1, which implies that the virus-free steady state E 0 is globally asymptotically stable by Theorem 2.2 and Theorem 3.1 (see Figure 1).…”

“…Mathematical models [3][4][5][6][7][8][9] have been used to investigate the within-host viral dynamics to explore the effects of drug treatment. In order to discover the effects of drug treatment applied to the infectives at different infection stages, Lloyd [3] proposed a within-host model with multiple infection stages and find that treatment at initial infection stage is much more sensitive than treatment at other stages.…”