Dynamical Analysis Within-Host and Between-Host for HIV\AIDS with the Application of Optimal Control Strategy

Dynamical analysis within-host and between-host for an HIV\AIDS

  • Ahmed Ali Mohsen Ministry of Education, Rusafa/1, Baghdad, Iraq
  • Raid Kamel Naji Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: HIV\AIDS, AIDS within-host body, AIDS between-host individuals, Stability, Optimal control

Abstract

The aims of this paper is investigating the spread of AIDS both within-host, through the contact between healthy cells with free virus inside the body, and between-host, through sexual contact among individuals and external sources of infectious. The outbreak of AIDS is described by a mathematical model consisting of two stages. The first stage describes the within-host spread of AIDS and is represented by the first three equations. While the second stage describes the between-host spread of AIDS and represented by the last four equations. The existence, uniqueness and boundedness of the solution of the model are discussed and all possible equilibrium points are determined. The local asymptotic stability (LAS) of the model is studied, while suitable Lyapunov functions are used to investigate the global asymptotic stability (GAS) of the model. Optimal control strategy is used to control the outbreak of AIDS. Finally, a numerical simulation is carried out to confirm the analytical results and understand the effects of varying the parameters on the spread of disease.

Published
2020-05-28
How to Cite
Mohsen, A. A., & Naji, R. K. (2020). Dynamical Analysis Within-Host and Between-Host for HIV\AIDS with the Application of Optimal Control Strategy: Dynamical analysis within-host and between-host for an HIV\AIDS. Iraqi Journal of Science, 61(5), 1173-1189. https://doi.org/10.24996/ijs.2020.61.5.25
Section
Mathematics

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