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Mathematical Model Dynamics of Drug‐Resistant Tuberculosis and Its Optimal Control Analysis

Author

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  • Mohammed Hasen Galete
  • Mohammed Yiha Dawed
  • Legesse Lemecha Obsu

Abstract

This study presents a mathematical model to understand and control the spread of drug‐resistant tuberculosis (DR‐TB). A system of nonlinear ordinary differential equations is developed to represent the transmission dynamics, incorporating prevention and treatment strategies. Well‐posedness, positivity, and boundedness of solution of the model are explained. The basic reproduction number is derived, and stability analysis of fixed point reveals that the disease‐free equilibrium is globally asymptotically stable when R0

Suggested Citation

  • Mohammed Hasen Galete & Mohammed Yiha Dawed & Legesse Lemecha Obsu, 2025. "Mathematical Model Dynamics of Drug‐Resistant Tuberculosis and Its Optimal Control Analysis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:4101918
    DOI: 10.1155/jama/4101918
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    References listed on IDEAS

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    1. Ashenafi Kelemu Mengistu & Peter J. Witbooi, 2019. "Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-9, December.
    2. Ashenafi Kelemu Mengistu & Peter J. Witbooi & Elena Braverman, 2023. "Cost-Effectiveness Analysis of the Optimal Control Strategies for Multidrug-Resistant Tuberculosis Transmission in Ethiopia," International Journal of Differential Equations, Hindawi, vol. 2023, pages 1-15, September.
    3. Ashenafi Kelemu Mengistu & Peter J. Witbooi, 2019. "Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
    4. Fatima Sulayman & Farah Aini Abdullah & Mohd Hafiz Mohd, 2021. "An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    5. Chih-Wen Chang & Zohaib Ali Qureshi & Sania Qureshi & Asif Ali Shaikh & Muhammad Yaqoob Shahani, 2024. "Real-Data-Based Study on Divorce Dynamics and Elimination Strategies Using Nonlinear Differential Equations," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
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