A stochastic TB model for a crowded environment

Abstract

We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation.We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing thebasic reproductionnumber andprove the stabilityof thedisease-free equilibriumwhen it is below unity or slightly higher than unity and the perturbation is small. Ourmain theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.