Mathematical Model of the Role of Vaccination and Treatment on the Transmission Dynamics of Tuberculosis

In this study the role of vaccination of new born babies against tuberculosis and treatment of both latently and activity infected individuals in controlling the spread of tuberculosis was mathematically modelled based on the standard SEIR model. The disease - free equilibrium state of the model was established and its stability analyzed using the Routh-Hurwitz theorem. The result of the analysis of the stability of the disease-free equilibrium state shows that tuberculosis can totally be eradicated if effort is made to ensure that the sum of the rate of recovery of the latent class, the rate at which latently infected individuals become actively infected and the rate of natural death , must have a lower bound.