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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Modelling of HIV Pathogens' Impact on the AIDS Disease Transmission with Optimal Control Analysis

Journal of Applied Nonlinear Dynamics 13(3) (2024) 571--582 | DOI:10.5890/JAND.2024.09.012

Abdisa Shiferaw Melese$^{1}$, Legesse Lemecha Obsu$^{1}$, Eshetu Dadi Gurmu$^{2}$

$^{1}$ Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia

$^{2}$ Department of Mathematics, Samara University, Afar, Ethiopia

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Abstract

HIV is a viral pathogen that weakens a human's immune organ, making it vulnerable to infectious diseases. This study focuses on a nonlinear deterministic mathematical model for the impact of HIV pathogens on AIDS disease transmission with optimal control analysis. Equilibrium points and basic reproduction number are computed. The qualitative analysis of the model revealed the scenario for both HIV-free and endemic equilibrium points. The local stability of the equilibrium is established via the Routh-Hurwitz criteria, while the global stability of the equilibrium is justified by using a Lyapunov function. Also, the normalized sensitivity analysis is performed. We extended the proposed model into an optimal control problem by incorporating four control variables, namely, a safer sex programme, a preventive measure, a condom usage programme, and medical care. Furthermore the optimal control is found by minimizing the number of HIV/AIDS individuals. Finally, the numerical simulations show agreement with the analytical results.

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