摘要：In this paper we have proposed a stochastic model for studying the dynamics of tuberculosis (TB) by incorporating vaccination of newly born babies. The total population in this model is subdivided in to four compartments, namely susceptible $S ( t )$ , infected $I ( t )$ , vaccinated newborns $V ( t ) $ , and recovered $R ( t ) $ . First, the developed model is expressed and analyzed by the deterministic approach. Since this approach neglects the randomness of the dynamics of the process, it has great limitations in the modeling process. To avoid this kind of issues, we transform the deterministic approach into a stochastic one, which is known to play a significant role by providing additional degree of realism compared to the deterministic approach. The analysis of the model is done employing both approaches. The invariant region, positivity of the solution, equilibrium points and their stability are checked. According to the analysis, we came to realize that the basic reproduction number for the stochastic approach is smaller than the deterministic one. We have conducted various numerical experiments and obtained interesting simulation results which indicate that a combination of increased newborn vaccination and appropriate treatment of infected individuals have a great contribution in combating TB. It is worth mentioning that the simulation results confirm the conclusion drawn from the qualitative analysis of the model.
