Analysis of a Mathematical Model on The Spread and Control of Tuberculosis in Deneba Town, Ethiopia

Most of mathematical modeling dealing disease curable by optimally: In this study, a non-linear deterministic model was developed to study the spread and control of Tuberculosis in the community of Deneba town in Ethiopia. The whole population of Deneba town were divided into five compartments namely, Susceptible class under fourteen, Susceptible class equal and above fourteen, Exposed class, Infected class and Recovered class was represented byS₁, S₂, E, I and Rrespectively. The basic reproduction number of the dynamical systemR₀is calculated bywhich depends on ten parameters. And also the numerical value of the basic reproduction number based on the real data collected from Deneba townR₀ = 2.981008273 > 1. This in principle implies that the disease spreads in the community of Deneba town. Basically we found two equilibrium points namely disease free equilibrium point and endemic equilibrium point. As a result, the disease free equilibrium point is unstable and the endemic equilibrium point is stable. To control the spread of Tuberculosis, the basic reproduction number should be less than one. Therefore, this finding identify the control parameter β₂ is the contact rate of susceptible class equal and above fourteen with infected class,β₂ = 0.068511865 Thus, the basic reproduction number is less than one, the contact rate must be less than 0.068511865. The effect of the remaining control parameters was discussed in detail in the subsection.