Mathematical modeling and optimal control of a deterministic SHATR model of HIV/AIDS with possibility of rehabilitation: a dynamic analysis

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Published: Aug 1, 2024
DOI: https://doi.org/10.5556/j.tkjm.55.2024.5109
Keywords:
Antiretroviral therapy (ART) basic reproduction number Lyapunov optimal control Pontryagin’s maximum principle

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Pankaj Singh Rana
National Institute of Technology Uttarakhand
Nitin Sharma
National Institute of Technology Uttarakhand, INDIA
https://orcid.org/0000-0001-5422-8869
Anupam Priyadarshi
Banaras Hindu University, Varanasi – 221005, INDIA

Abstract

In the present work, we developed a deterministic SHATR (Susceptible - HIV infected -AIDS infected - Antiretroviral Treatment - Recovered) compartment model for HIV/AIDS. This model considers the disease outbreak due to a lack of awareness and treatment. The steady states of the proposed model system are obtained and analyzed by using the nonlinear stability theory of differential equations. The basic reproduction number  is derived and explored to determine the stability and sensitivity index of some important relative parameters. Further, to know the global behavior of the model one parameter bifurcation study is discussed. Moreover, the optimal control theory has been applied to identify the optimal strategy by taking treatment and awareness for safe intercourse as control parameters. The control problem is solved analytically by using Pontryagin’s maximum principle. Finally, the model is simulated to describe the optimality under various assumptions and the stability of equilibrium points.

Article Details

How to Cite
Rana, P. S., Sharma, N., & Priyadarshi, A. (2024). Mathematical modeling and optimal control of a deterministic SHATR model of HIV/AIDS with possibility of rehabilitation: a dynamic analysis. Tamkang Journal of Mathematics, 55(3), 267–285. https://doi.org/10.5556/j.tkjm.55.2024.5109
Issue
Vol. 55 No. 3 (2024)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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