<i>HIV</i> dynamics in a periodic environment with general transmission rates

Mohammed H. Alharbi; Mohammed H. Alharbi

doi:10.3934/math.20241512

AIMS Mathematics

2024, Volume 9, Issue 11: 31393-31413. doi: 10.3934/math.20241512

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HIV dynamics in a periodic environment with general transmission rates

Mohammed H. Alharbi ^,

Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia

Received: 02 September 2024 Revised: 14 October 2024 Accepted: 29 October 2024 Published: 05 November 2024
MSC : 34K13, 34K20, 34D23

In the current study, we present a mathematical model for human immunodeficiency virus type-1 (HIV-1) transmission, incorporating Cytotoxic T-Lymphocyte immune impairment within a seasonal environment. The model divides the infected cell compartment into two sub-compartments: latently infected cells and productively infected cells. Additionally, we consider three possible routes of infection, allowing HIV to spread among susceptible cells via direct contact with the virus, latently infected cells, or productively infected cells. The system is analyzed, and the basic reproduction number is derived using an integral operator. We demonstrate that the HIV-free periodic trajectory is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, while HIV persists when $ \mathcal{R}_0 > 1 $. Several numerical simulations are provided to validate the theoretical results.
- HIV transmission,
- three infection routes,
- periodic environment,
- periodic trajectory,
- integral operator,
- uniform persistence
Citation: Mohammed H. Alharbi. HIV dynamics in a periodic environment with general transmission rates[J]. AIMS Mathematics, 2024, 9(11): 31393-31413. doi: 10.3934/math.20241512

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Abstract

In the current study, we present a mathematical model for human immunodeficiency virus type-1 (HIV-1) transmission, incorporating Cytotoxic T-Lymphocyte immune impairment within a seasonal environment. The model divides the infected cell compartment into two sub-compartments: latently infected cells and productively infected cells. Additionally, we consider three possible routes of infection, allowing HIV to spread among susceptible cells via direct contact with the virus, latently infected cells, or productively infected cells. The system is analyzed, and the basic reproduction number is derived using an integral operator. We demonstrate that the HIV-free periodic trajectory is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, while HIV persists when $ \mathcal{R}_0 > 1 $. Several numerical simulations are provided to validate the theoretical results.

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