A Stochastic Approach of Tuberculosis Model With Effects of Case Detection and Treatment

In this paper we are deriving and extending a non-linear deterministic mathematical model of tuberculosis with emphasis on case detection and treatment into its equivalent stochastic model. By revising the analysis in the deterministic method, different Equilibria in the model were found using convenient technique and analyzed their condition for stability and reproduction number were computed. Some dynamical behavior of the model and their approximations are illustrated through analytic and numerical simulation for both deterministic and stochastic model which shows strong oscillation for stochastic trajectory this lead to a narrow gap between the curves of deterministic and stochastic. This happened because of random white translated by a supplementary term added whose trajectories come to superimpose the deterministic trajectories. Some preliminary result shows that case detection play an important role towards eliminating the spread of TB.