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

Jinliang Wang; Jiying Lang; Yuming Chen

doi:10.3934/dcdsb.2017186

Article Contents

2017, Volume 22, Issue 10: 3721-3747. Doi: 10.3934/dcdsb.2017186

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

1.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
2.
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5 Canada

* Corresponding author: Yuming Chen
* Corresponding author: Yuming Chen

Received: October 2016

Revised: May 2017

Published: September 2017

The research of Wang is supported partially by the National Natural Science Foundation of China (No. 11226255 and No. 11201128), the Science and Technology Innovation Team in Higher Education Institutions of Heilongjiang Province (No. 2014TD005); while that of Chen is supported by NSERC.

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Abstract

In this paper, we are concerned with an age-structured HIV infection model incorporating latency and cell-to-cell transmission. The model is a hybrid system consisting of coupled ordinary differential equations and partial differential equations. First, we address the relative compactness and persistence of the solution semi-flow, and the existence of a global attractor. Then, applying the approach of Lyapunov functionals, we establish the global stability of the infection-free equilibrium and the infection equilibrium, which is completely determined by the basic reproduction number.

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Mathematics Subject Classification: Primary:92D30;Secondary:35B35, 35Q92, 37C75.

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Figure 1. Transfer diagram for model (1.4)

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Figure 2. The distributions of infected cells and latent cells with parameter (8.3)

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Figure 3. Evolutions of infected cells and latent cells with parameter (8.3) except that h = 1

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Figure 4. Evolutions of infected cells and latent cells with parameter (8.4)

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Table 1. Biological meanings of parameters (1.4) and (1.5)

Parameter	Meaning
$h$	Constant recruitment rate of uninfected CD4⁺ T cells
$d$	Death rate of uninfected CD4⁺ T cells
$\beta$	Infection rate of CD4⁺ T cells by infectious virus
$\beta_1$	Infection rate of CD4⁺ T cells by latently infected T cells
$\beta_2$	Infection rate of CD4⁺ T cells by infectious T cells
$q_1(a)$	Infectivity of a latently infected T cell with latency age $a$
$q_2(b)$	Infectivity of an infectious T cell with infection age $b$
$\theta_1(a)$	Sum of death rate and activation rate $\xi(a)$
	of latently infected T cells with latency age $a$
$\theta_2(b)$	Death rate of infectious T cells with infection age $b$
$p(b)$	Viral production rate of an infectious T cell with infection age $b$
$c$	Clearance rate of virions
$\xi(a)$	Activation rate of latently infected T cells with latency age $a$

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