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An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection

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  • Qiuyun Li

    (Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China)

  • Fengna Wang

    (Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China)

Abstract

As tuberculosis (TB) patients do not have lifetime immunity, environmental transmission is one of the key reasons why TB has not been entirely eradicated. In this study, an SVEIRB model of recurrent TB considering environmental transmission was developed to explore the transmission kinetics of recurrent TB in the setting of environmental transmission, exogenous infection, and prophylaxis. A more thorough explanation of the effect of environmental transmission on recurrent TB can be found in the model’s underlying regeneration numbers. The global stability of disease-free and local equilibrium points can be discussed by looking at the relevant characteristic equations. The Lyapunov functions and the LaSalle invariance principle are used to show that the local equilibrium point is globally stable, and TB will persist if the basic reproduction number is larger. Conversely, the disease will disappear if the basic reproduction number is less than one. The impact of environmental transmission on the spread of tuberculosis was further demonstrated by numerical simulations, which also demonstrated that vaccination and reducing the presence of the virus in the environment are both efficient approaches to control the disease’s spread.

Suggested Citation

  • Qiuyun Li & Fengna Wang, 2023. "An Epidemiological Model for Tuberculosis Considering Environmental Transmission and Reinfection," Mathematics, MDPI, vol. 11(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2423-:d:1154131
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    References listed on IDEAS

    as
    1. Sharomi, Oluwaseun Y. & Safi, Mohammad A. & Gumel, Abba B. & Gerberry, David J., 2017. "Exogenous re-infection does not always cause backward bifurcation in TB transmission dynamics," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 322-335.
    2. 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.
    3. 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.
    4. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2014. "Global stability of an SIR model with two susceptible groups on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 42-50.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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