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An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors

Author

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  • Fatima Sulayman

    (School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
    These authors contributed equally to this work.)

  • Farah Aini Abdullah

    (School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
    These authors contributed equally to this work.)

  • Mohd Hafiz Mohd

    (School of Mathematical Sciences, Universiti Sains Malaysia (USM), Penang 11800, Malaysia
    These authors contributed equally to this work.)

Abstract

This study extends a deterministic mathematical model for the dynamics of tuberculosis transmission to examine the impact of an imperfect vaccine and other exogenous factors, such as re-infection among treated individuals and exogenous re-infection. The qualitative behaviors of the model are investigated, covering many distinct aspects of the transmission of the disease. The proposed model is observed to show a backward bifurcation, even when R v < 1 . As such, we assume that diminishing R v to less than unity is not effective for the elimination of tuberculosis. Furthermore, the results reveal that an imperfect tuberculosis vaccine is always effective at reducing the spread of infectious diseases within the population, though the general effect increases with the increase in effectiveness and coverage. In particular, it is shown that a limited portion of people being vaccinated at steady-state and vaccine efficacy assume a equivalent role in decreasing disease burden. From the numerical simulation, it is shown that using an imperfect vaccine lead to effective control of tuberculosis in a population, provided that the efficacy of the vaccine and its coverage are reasonably high.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:327-:d:494904
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    References listed on IDEAS

    as
    1. Ullah, Saif & Khan, Muhammad Altaf & Farooq, Muhammad & Gul, Taza, 2019. "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 181-199.
    2. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    3. Buonomo, Bruno & Della Marca, Rossella, 2019. "Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 97-114.
    4. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
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    Cited by:

    1. Qiuyun Li & Fengna Wang, 2023. "An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection," Mathematics, MDPI, vol. 11(11), pages 1-17, May.

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