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Mathematical Analysis of TB Model with Vaccination and Saturated Incidence Rate

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  • Ashenafi Kelemu Mengistu
  • Peter J. Witbooi

Abstract

The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, it is proved that if the basic reproduction number is less than unity, then the disease‐free equilibrium point is globally asymptotically stable. The Routh‐Hurwitz criterion is used to prove the local stability of the endemic equilibrium when R0 > 1. The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.

Suggested Citation

  • Ashenafi Kelemu Mengistu & Peter J. Witbooi, 2020. "Mathematical Analysis of TB Model with Vaccination and Saturated Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlaaa:v:2020:y:2020:i:1:n:6669997
    DOI: 10.1155/2020/6669997
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    References listed on IDEAS

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    1. Sibaliwe Maku Vyambwera & Peter Witbooi, 2018. "A Stochastic TB Model for a Crowded Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    2. Sibaliwe Maku Vyambwera & Peter Witbooi, 2018. "A Stochastic TB Model for a Crowded Environment," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-8, June.
    3. Yu Zhao & Mingtao Li & Sanling Yuan, 2017. "Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model," IJERPH, MDPI, vol. 14(10), pages 1-14, October.
    4. 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.
    5. 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).
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    Cited by:

    1. Akın, E. & Yeni, G. & Konur, D. & Işık, S.R. & Işık, M.R., 2026. "An SEIR model on time scales with discrete applications to tuberculosis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 72-103.

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