Exploring Tuberculosis: A Theoretical Framework for Infection Regulation and Eradication

Abstract

In this paper we explored the study of tuberculosis, throughout human history, tuberculosis (TB) has been a persistent challenge due to its severe consequences for society. It is an infectious disease transmitted by Mycobacterium tuberculosis (MT),more than 150 million years ago, it was thought to have originated from the genus Mycobacterium. Our theoretical framework presents methods for regulating and eradicating tuberculosis infections. This has led to the compartmentalization of the model population and the analytical solution of the ensuing model equations. To validate the outcomes of the theoretical approach, a numerical simulation has been deployed. This model carried out six compartment stage, susceptible, latent for a short time period and latent for long time period, infected in hospital, random infected at public place and the recovered class. In this model we examined Disease free equilibrium points (DFEP), Basic reproduction number R_0. Positive boundaries solution is used to describe the infection at particular stage. If R_0<1, the DFE is locally asymptotically stable, using Jacobian matrix we explored the negative Eigen values. Lyapunov function is used to examined the global stability of endemic equilibrium. We used Carrying out a simulation using random data in a selected region,using random values in MATLAB, to simulate the result of the model.