# Global dynamics of delayed HIV infection models including impairment of B-cell functions

Volume 20, Issue 2, pp 161--188
Publication Date: November 08, 2019 Submission Date: June 18, 2019 Revision Date: August 26, 2019 Accteptance Date: September 16, 2019
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### Authors

Ahmed Elaiw - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. Safiya Alshehaiween - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Taibah University, P. O. Box 344, Medina 42353, Saudi Arabia. Aatef Hobiny - Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, 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. Numerical simulations illustrate the theoretical results.

### Keywords

• HIV dynamics
• global stability
• Lyapunov function
• B-cell impairment
• latent reservoirs
• time delay

•  34D20
•  34D23
•  37N25
•  92B05

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