Stability of a general discrete-time HIV dynamics model with three categories of infected CD4\(^{+}\) T-cells and multiple time delays

Volume 20, Issue 4, pp 264--282 http://dx.doi.org/10.22436/jmcs.020.04.01

Publication Date: February 19, 2020 Submission Date: July 12, 2019 Revision Date: October 14, 2019 Accteptance Date: December 09, 2019

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Authors

A. M. Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. M. A. Alshaikh - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Taif University, P. O. Box 888, Taif 21974, Saudi Arabia.

Abstract

In this paper, we construct delayed HIV dynamics models with impairment of B-cell functions. Two forms of the incidence rate have been considered, bilinear and general. Three types of infected cells and five-time delays have been incorporated into the models. The well-posedness of the models is justified. The models admit two equilibria which are determined by the basic reproduction number \(R_{0}\). The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations.

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Keywords

• HIV infection
• latent reservoirs
• time delay
• global stability
• Lyapunov function
• discrete time model

MSC

•  34D20
•  34D23
•  37N25
•  92B05

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