# 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
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.

### Share and Cite

##### ISRP Style

A. M. Elaiw, M. A. Alshaikh, Stability of a general discrete-time HIV dynamics model with three categories of infected CD4$^{+}$ T-cells and multiple time delays, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 264--282

##### AMA Style

Elaiw A. M., Alshaikh M. A., Stability of a general discrete-time HIV dynamics model with three categories of infected CD4$^{+}$ T-cells and multiple time delays. J Math Comput SCI-JM. (2020); 20(4):264--282

##### Chicago/Turabian Style

Elaiw, A. M., Alshaikh, M. A.. "Stability of a general discrete-time HIV dynamics model with three categories of infected CD4$^{+}$ T-cells and multiple time delays." Journal of Mathematics and Computer Science, 20, no. 4 (2020): 264--282

### Keywords

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

•  34D20
•  34D23
•  37N25
•  92B05

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