The Stochastic Model

Recent research has revealed a surge in the application of Stochastic Differential Equations (SDEs) in the modeling of infectious diseases. Factors emanating from this surge has been the ability of stochastic differential equations to lay one of the most imperative fundamental differences in the asymptotic dynamics of the deterministic and stochastic epidemic models [1]. These fundamental differences include the convergence of the sample path of stochastic models to the disease-free state and that of the deterministic model to the endemic equilibrium. Stochastic phenomenon occurs naturally in our environment, and when small number of reacting molecules is involved in the modeling system, deterministic models become inappropriate [2]. Stochastic models have properties which include the probability of an outbreak, the quasistationary probability distribution, the final size distribution of an epidemic and the expected duration of an epidemic that makes it unique from others [3]. Stochastic Processes can have moments and covariance function associated with them, which are functions of time, as do random variables