A STOCHASTIC DIFFERENTIAL EQUATION (SDE) BASED MODEL FOR THE SPREAD OF TUBERCULOSIS

Abstract

Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. In this work, a deterministic and stochastic model of the transmission dynamics of Tuberculosis is developed and analyzed. The models involve the Susceptible, Exposed, Infectious and Recovered individuals. We computed the basic reproduction number and showed that for, the disease-free equilibrium is globally asymptotically stable. The resulting deterministic model was transformed into an equivalent stochastic model resulting in stochastic differential equation. The drift coefficient, the covariance matrix and the diffusion matrix were determined using the method proposed by Allen et al. (2008).