Mathematical analysis of an age-structured HIV model with intracellular delay

Yuan Yuan; Xianlong Fu

doi:10.3934/dcdsb.2021123

Article Contents

2022, Volume 27, Issue 4: 2077-2106. Doi: 10.3934/dcdsb.2021123

This issue Previous Article Global solvability to a singular chemotaxis-consumption model with fast and slow diffusion and logistic source Next Article Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms

Mathematical analysis of an age-structured HIV model with intracellular delay

Yuan Yuan and
Xianlong Fu^,

School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China

^* Corresponding author: Xianlong Fu, Email: xlfu@math.ecnu.edu.cn
^* Corresponding author: Xianlong Fu, Email: xlfu@math.ecnu.edu.cn

Received: November 2020

Revised: February 2021

Early access: April 2021

Published: April 2022

This work is supported by NSF of China (Nos. 11671142 and 11771075), Science and Technology Commission of Shanghai Municipality (STCSM) (grant No. 18dz2271000)

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Abstract

In this paper, we study an age-structured HIV model with intracellular delay, logistic growth and antiretrowviral therapy. We first rewrite the model as an abstract non-densely defined Cauchy problem and obtain the existence of the unique positive steady state. Then through the linearization arguments we investigate the asymptotic behavior of steady states by determining the distribution of eigenvalues. We obtain successfully the globally asymptotic stability for the null equilibrium and (locally) asymptotic stability for the positive equilibrium respectively. Moreover, we also prove that Hopf bifurcations occur around the positive equilibrium under some conditions. In addition, we address the persistence of the semi-flow by showing the existence of a global attractor. Finally, some numerical examples are provided to illustrate the main results.

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Mathematics Subject Classification: Primary: 92D30, 92D25; Secondary: 34D20, 34C60.

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Figure 1. Solutions of the system (3) go to the disease-free steady state, where "T" represents the uninfected T cells, "I" represents the infected T cells, "$ V_{I} $" represents the infectious viral

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Figure 2. The infection is persistent

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Figure 3. Solutions of the system (7) go to the positive steady state when $ \tau_1 = \tau_2 = 0.5 $

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Figure 4. The solutions oscillate periodically for $ \tau_1 = \tau_2 = 1 $

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