Global stability analysis and optimal control problem arise from tuberculosis transmission model with monitored treatment

Putri Zahra Kamalia, Tiara Ayumi, Athaya Yumna Fathiyah, Dipo Aldila

Abstract


In this paper, we discussed a Tuberculosis model by incorporating monitored treatment intervention and applying optimal control theory to analyze the optimal intervention for TB. Optimal control strategy aims to minimize both the disease burden and the intervention cost. The optimal control problem is derived analytically using the Pontryagin Maximum Principle. Analysis of the model shows that disease-free equilibrium is globally asymptotically stable if the controlled reproduction number is smaller than one and unstable if it is larger than one. Our numerical experiments show that implementation of monitored treatment should be given in the early spread of TB to avoid high cost of intervention. Furthermore, a better quality of treatment will give a lower cost for TB prevention.

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Published: 2024-02-02

How to Cite this Article:

Putri Zahra Kamalia, Tiara Ayumi, Athaya Yumna Fathiyah, Dipo Aldila, Global stability analysis and optimal control problem arise from tuberculosis transmission model with monitored treatment, Commun. Math. Biol. Neurosci., 2024 (2024), Article ID 15

Copyright © 2024 Putri Zahra Kamalia, Tiara Ayumi, Athaya Yumna Fathiyah, Dipo Aldila. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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