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Exploring a Mathematical Model with Saturated Treatment for the Co-Dynamics of Tuberculosis and Diabetes

Author

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  • Saburi Rasheed

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

  • Olaniyi S. Iyiola

    (Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA)

  • Segun I. Oke

    (Department of Physics, Chemistry and Mathematics, Alabama A&M University, Huntsville, AL 35811, USA)

  • Bruce A. Wade

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

Abstract

In this research, we present a deterministic epidemiological mathematical model that delves into the intricate dynamics of the coexistence of tuberculosis and diabetes. Our comprehensive analysis explores the interplay and the influence of diabetes on tuberculosis incidence within a human population segregated into diabetic and non-diabetic groups. The model incorporates a saturated incidence rate and treatment regimen for latent tuberculosis infections, offering insights into their impact on tuberculosis control. The theoretical findings reveal the emergence of a phenomenon known as backward bifurcation, attributed to exogenous reinfection and saturated treatment. Additionally, our study employs both local and global sensitivity analyses to identify pivotal parameters crucial to the spread of tuberculosis within the population. This investigation contributes valuable insights to the understanding of the complex relationship between tuberculosis and diabetes, offering a foundation for more effective disease control strategies.

Suggested Citation

  • Saburi Rasheed & Olaniyi S. Iyiola & Segun I. Oke & Bruce A. Wade, 2024. "Exploring a Mathematical Model with Saturated Treatment for the Co-Dynamics of Tuberculosis and Diabetes," Mathematics, MDPI, vol. 12(23), pages 1-28, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3765-:d:1532634
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    References listed on IDEAS

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    4. Christie Y Jeon & Megan B Murray, 2008. "Diabetes Mellitus Increases the Risk of Active Tuberculosis: A Systematic Review of 13 Observational Studies," PLOS Medicine, Public Library of Science, vol. 5(7), pages 1-11, July.
    5. 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.
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