Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics

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 ${\mathcal{R}}_0$ is calculated as ${\mathcal{R}}_0\approx 2.13$. Finally, the sensitivity indices of ${\mathcal{R}}_0$ 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.