Sensitivity and optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation

Volume 26, Issue 1, pp 90--100 http://dx.doi.org/10.22436/jmcs.026.01.08

Publication Date: October 14, 2021 Submission Date: August 12, 2020 Revision Date: July 30, 2021 Accteptance Date: August 26, 2021

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Authors

U. Habibah - Department of Mathematics and member of Research Group of Biomathematics, Brawijaya University, Jl. Veteran Malang, Indonesia. Trisilowati - Department of Mathematics and member of Research Group of Biomathematics, Brawijaya University, Jl. Veteran Malang, Indonesia. Y. L. Pradana - Undergraduate student of the Department of Mathematics, Brawijaya University, Jl. Veteran Malang, Indonesia.

Abstract

We study optimal control analysis of HIV/AIDS model with two different stages of infection subpopulation. There are two controls, antiretroviral (ARV) treatment is given to HIV-infected subpopulation, and HAART (highly active antiretroviral treatment) is given to full-blown AIDS subpopulation. Before that, we analyze the sensitivity of parameters which can be used to determine the most parameter take effect in the spread of HIV virus. We apply the sensitivity analysis to all the parameters appear in the reproduction number. Furthermore, we apply optimal control theory to minimize HIV-infected and full-blown AIDS subpopulation, and the cost related to the implementation of control strategies using the Pontryagin's Minimum Principle. We prove an existence of a optimal control pair. Numerical solution is conducted by solving the optimally system using the sweep backward and forward method. The results show that giving control pair in the model can decrease the infected and the full-blown AIDS subpopulations significantly.

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Keywords

• Optimal control
• HIV/AIDS model
• Pontryagin's minimum principle

MSC

•  46C05
•  46C99
•  25D15
•  26D10

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