MATHEMATICAL MODELLING OF TUBERCULOSIS TRANSMISSION DYNAMICS

Abstract

In this study, a mathematical modeling of Tuberculosis (TB) infection was developed by incorporating vaccination, isolation and treatment. The Basic reproductive number was computed using the next generation matrix method. Analysis of the model at disease free equilibrium state shows that whenever the basic reproductive number is less than unity at the disease free equilibrium state and locally and globally asymptotically stable whenever the basic reproductive number is greater than unity. The equilibrium states of the model were analysed, including the Disease-Free and Endemic Equilibria, were determined and analyzed for stability using the basic reproduction number (R₀) derived via the next generation matrix method. Numerical simulations were performed using MAPLE software, our results shows that increasing vaccination coverage, maintaining effective isolation of infectious individuals, and improving treatment rates significantly reduce the prevalence of TB over time.