Optimal control analysis of a tuberculosis model with drug-resistant population
Keywords:
Mathematical Model, Stability, Optimal Control, Tuberculosis, Drug-sensitive Tuberculosis, Drug-resistant Tuberculosis
Abstract
Tuberculosis (TB), caused by Mycobacterium tuberculosis, stands as one of the most infectious diseases globally, predominantly affecting the lungs (known as pulmonary tuberculosis). It manifests in two primary forms based on bacterial drug sensitivity: drug-sensitive TB (DS-TB) and drug-resistant TB (DR-TB). DS-TB remains susceptible to medication, whereas DR-TB has developed resistance. This study explores a mathematical model explaining the spread of tuberculosis within a drug-resistant population, proposing optimal control strategies to curb its dissemination through educational initiatives and enhancements in healthcare facilities. The stability analysis reveals that disease-free equilibrium points are locally asymptotically stable when R_0 < 1, while endemic equilibrium points prevail and are locally asymptotically stable if R_0 > 1. Additionally, sensitivity analysis identifies important parameters within the model. By using the Pontryagin Maximum Principle, control variables are integrated and numerically solved. Through simulations and cost assessments, we illustrate the efficacy of employing both control strategies concurrently, effectively reducing the populations susceptible to exposure, DS-TB, and DR-TB infections.References
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\newblock \emph{Analysis of tuberculosis model with saturated incidence rate and optimal control},
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\bibitem{13}
\newblock S. Liu, Y. Bi, Y. Liu,
\newblock \emph{Modeling and dynamic analysis of tuberculosis in mainland China from 1998 to 2017: The effect of DOTS strategy and further control},
\newblock Theoretical Biology and Medical Modelling, vol. 17, pp. 6, 2020.
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\newblock P. van den Driessche, and J. Watmough,
\newblock \emph{Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission},
\newblock Mathematical Biosciences, vol. 180, pp. 29--48, 2002.
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\newblock A. Kamput, and C. Dechsupa,
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\newblock S. Ullah, M. A. Khan, M. Farooq, T. Gul,
\newblock \emph{Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa Pakistan},
\newblock Mathematics and Computers in Simulation, vol. 165, pp. 181--199, 2019.
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\newblock \emph{A co-infection model of malaria and cholera diseases with optimal control},
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\newblock K. O. Okosun,
\newblock \emph{Optimal control analysis of hepatitis C virus with acute and chronic stages in the presence of treatment and infected immigrants},
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\newblock G. T. Tilahun, O. D. Makinde, D. Malonza,
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\newblock M. Farman, C. Alfiniyah, A. Shehzad,
\newblock \emph{Modelling and analysis tuberculosis (TB) model with hybrid fractional operator},
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\bibitem{20}
\newblock E. Idriss, E. El-Hassan, T. Mouhcine,
\newblock \emph{Global existence of weak solutions to a three-dimensional fractional model in magneto-elastic interactions},
\newblock Boundary Value Problems, vol. 2017, pp. 122, 2017.
\bibitem{21}
\newblock S. Panda, S. Palei, M. V. S. Samartha, B. Jena, S. Saxena,,
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Published
2025-01-31
How to Cite
Alfiniyah, C., Windarto, Permatasari , N. A., Farman, M., Millah, N., & Ahmadin. (2025). Optimal control analysis of a tuberculosis model with drug-resistant population. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2292
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Section
Research Articles
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