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GLOBAL PROPERTIES OF HIV DYNAMICS MODELS INCLUDING IMPAIRMENT OF B-CELL FUNCTIONS

A. M. Elaiw

http://orcid.org/0000-0001-5030-633X

Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: a_m_elaiw@yahoo.com

Corresponding author.

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S. F. 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

E-mail Address: safiya.f.sh@gmail.com

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, and

A. D. HOBINY

Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

E-mail Address: ahobany@kau.edu.sa

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https://doi.org/10.1142/S0218339020500011Cited by:3 (Source: Crossref)

Abstract

In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two equilibria, whose existence is characterized by means of the basic reproduction number $R_{0}$ . The global stability of each equilibrium is proven by using the Lyapunov method. The effects of impairment of B-cell functions and of antiviral treatment on the human immunodeficiency virus (HIV) dynamics are studied. We have shown that if the functions of B-cell are impaired, then the concentration of HIV increases in the plasma. Moreover, we have determined the minimal drug efficacy which is required to reduce the concentration of HIV particles to a lower level. We have shown that a more accurate computation of drug efficacy can be performed by using our proposed model. Our theoretical results are illustrated by means of numerical simulations.

Keywords:

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