Analysis and Dynamics of Tuberculosis Outbreak: A Mathematical Modelling Approach

Abstract

Tuberculosis (TB) is an infectious disease caused by mycobacterium disease which causes major ill health in humans. Control strategies like vaccines, early detention, treatment and isolation are required to minimize or eradicate this deadly pandemic disease. This article presents a novel mathematical modelling approach to tuberculosis disease using Vaccinated-Susceptible- Latent-Mild-Chronic-Isolated-Treated model. We examined if the epidemiology model is well posed and then obtained two equilibria points (disease free and endemic equilibrium). We also showed that TB disease free equilibrium is locally and globally asymptotically stable if 𝑅଴ < 1. We solved the model analytically using Homotopy Perturbation Method (HPM) and the graphical representations and interpretations of various effects of the model parameters in order to measure the impact for effective disease control are presented. The findings show that infected populations will be reduced when the isolation and treatment rates and their effectiveness are high.