Mathematical Analysis of TB Model with Vaccination and Saturated Incidence Rate. (4th December 2020)

• Record Type: Journal Article
• Authors: Mengistu, Ashenafi Kelemu; Witbooi, Peter J.
• Other Names: Jodar Lucas Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2020(2020)
• Publication Date: 2020-12-04
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2020/6669997
• Languages: English
• ISSNs: 1085-3375

Abstract

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 R 0 > 1 . The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.