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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 . 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, Hindawi, vol. 2020, pages 1-10, December.
    • Handle: RePEc:hin:jnlaaa:6669997
    DOI: 10.1155/2020/6669997
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