Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics. (23rd December 2019)

• Record Type: Journal Article
• Authors: Kelemu Mengistu, Ashenafi; Witbooi, Peter J.
• Other Names: Ashrafi Ali R. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2019(2019)
• Publication Date: 2019-12-23
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2019/7463167
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : In this study, we develop and analyze a deterministic mathematical model for tuberculosis (TB) transmission dynamics. The model includes vaccination for newborns and treatment for both high-risk latent and active TB patients. The stability of disease-free equilibrium point is discussed in detail. In the numerical simulation, the model parameters are estimated using reported TB incidence data in Ethiopia from the years 2003 to 2017, and R 0 is calculated as R 0 ≈ 2.13 . Finally, the sensitivity indices of R 0 with respect to the model parameters are performed, and their corresponding graphical results are presented. Our results quantify the positive influence of vaccination and the treatment for high-risk latent and active TB patients on the control of tuberculosis.