BIFURCATION AND STABILITY ANALYSIS OF THE DYNAMICS OF TUBERCULOSIS MODEL INCORPORATING, VACCINATION, SCREENING AND TREATMENT

Copyright © 2014 Nyerere, Luboobi and Gyekye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract: In this paper, a deterministic Tuberculosis (TB) model is formulated with the aim of assessing the effects of vaccination, screening and treatment on the transmission of TB infections. The analysis of the model shows that its dynamics are completely determined by the effective reproduction number, Reff. If Reff < 1 the disease-free equilibrium exists and is locally and globally asymptotically stable whereas an endemic equilibrium exists if Reff> 1 and is globally asymptotically stable, the disease persistence occurs. Furthermore, when the effective reproduction number is equal to one, that is Reff = 1, a backward bifurcation occurs. Numerical results are presented for the justifications of theoretical results