Viral dynamics of HIV-1 with CTL immune response

Aiping Wang; Michael Y. Li

doi:10.3934/dcdsb.2020212

Article Contents

2021, Volume 26, Issue 4: 2257-2272. Doi: 10.3934/dcdsb.2020212

This issue Previous Article Traveling wave solutions to diffusive Holling-Tanner predator-prey models Next Article Positive solution branches of two-species competition model in open advective environments

Viral dynamics of HIV-1 with CTL immune response

Aiping Wang^1, and
Michael Y. Li^2, ,

1.
School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

^* Corresponding author: Michael Y. Li
^* Corresponding author: Michael Y. Li

Dedicated to Professor Sze-Bi Hsu on the occasion of his retirement.

Received: May 31, 2019

Revised: October 31, 2019

Early access: July 2020

Published: April 2021

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Abstract

In this paper, we investigate an in-host model for the viral dynamics of HIV-1 infection and its interaction with the CTL immune response. The model is sufficiently general to allow nonlinear forms for both viral infection and CTL response. Threshold parameters are identified that completely determine the global dynamics and outcomes of the virus-target cell-CTL interactions. Impacts of key parameter values for CTL functions and viral budding rate on the HIV-1 viral load and CD4 count are investigated using numerical simulations. Results support clinical evidence for important differences between HIV-1 nonprogressors and progressors.

Keywords:

Mathematics Subject Classification: Primary: 34C60, 34D23; Secondary: 92C60.

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Figure 1. Transfer-infection diagram of model (2). Solid lines indicate cell transfer and dotted lines indicated virus-cell or cell-cell interaction

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Figure 2. Graphs of functions $ F(v) $ and $ G(v) $ and a geometric demonstration of existence of chronic-infection equilibria $ P_1 $ and $ P_2 $

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Figure 3. Effects of CTL response parameter $ c $ on HIV-1 viral load and CD4 count

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Figure 4. Effects of CTL killing rate $ \alpha $ on HIV-1 viral load and CD4 count

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Figure 5. Effects of viral budding number $ N $ on HIV-1 viral load and CD4 count

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