Modeling the Impact of Screening on the Dynamics of Tuberculosis Transmission in Ethiopia

Abstract Tuberculosis (TB) is a chronic respiratory infectious disease caused by the pathogen Mycobacterium tuberculosis. Infected people can spread TB germs from their mouth when they cough or sneeze. In this study, we have proposed and analyzed a mathematical model to examine the impact of awareness regarding TB transmission and treatment effects for a disease transmitted by contact in a constant population. We determined the six equilibriums using a system of nonlinear ordinary differential equations. The well-posedness of the proposed infection model is then analytically studied by showing properties such as the existence, uniqueness, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of the model is also discussed after computing the basic reproduction number. The disease-free equilibrium point of the model was seen locally and globally and it was stable for R 0 < 1 but unstable for R 0 > 1. The sensitivity analysis and model simulation was also studied to supplement the analytical outcomes. As a result high awareness creation of TB transmission through community and high treatment rate of infectious classes have high impacts of Tuberculosis disease Transmission.