Exploring HIV Dynamics and an Optimal Control Strategy

Salah Alsahafi and Stephen Woodcock
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Salah Alsahafi: School of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia
Stephen Woodcock: School of Mathematical and Physical Sciences, University of Technology Sydney, 15 Broadway, Ultimo, NSW 2007, Australia

Mathematics, 2022, vol. 10, issue 5, 1-26

Abstract: In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Based on this study, an optimal strategy is proposed to decrease the number of infected cells. Finally, some numerical simulations are presented to illustrate the theoretical findings.

Keywords: HIV; general incidence rate; local and global stability; Lyapunov theory; LaSalle’s invariance principle; sensitivity analysis; optimal strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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