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Analysis of tuberculosis model with saturated incidence rate and optimal control

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  • Baba, Isa Abdullahi
  • Abdulkadir, Rabiu Aliyu
  • Esmaili, Parvaneh

Abstract

We study a basic tuberculosis model using saturated incidence rate. Incorporated in the model is the therapeutic treatments given to infected individuals. Global stability of both the disease-free equilibrium and the endemic equilibrium are determined by a threshold quantity, the basic reproduction ratio R0. We also prove that when R0≤1, the DFE is globally asymptotically stable and the disease dies out. When R0>1, the unique endemic equilibrium exists, is globally asymptotically stable, and epidemic occurs. Optimal control is applied to the model, to show how the use of optimal control strategy will reduce the number of infectious individuals. The result is supported by numerical computations. The significance of δ (the parameter that measures the psychological or inhibitory effect), and the optimal control functions u1(t) and u2(t), are also shown numerically.

Suggested Citation

  • Baba, Isa Abdullahi & Abdulkadir, Rabiu Aliyu & Esmaili, Parvaneh, 2020. "Analysis of tuberculosis model with saturated incidence rate and optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119318175
    DOI: 10.1016/j.physa.2019.123237
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    References listed on IDEAS

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    1. Bilgen Kaymakamzade & Evren Hincal, 2018. "Two-strain epidemic model with two vaccinations and two time delayed," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 695-709, December.
    2. Baba, Isa Abdullahi & Hincal, Evren, 2018. "A model for influenza with vaccination and awareness," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 49-55.
    3. Baba, Isa Abdullahi & Kaymakamzade, Bilgen & Hincal, Evren, 2018. "Two-strain epidemic model with two vaccinations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 342-348.
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    Cited by:

    1. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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