A Stochastic Differential Equation SIS Epidemic Model

A. Gray, D. Greenhalgh, L. Hu, X. Mao, J. Pan
2011 SIAM Journal on Applied Mathematics  
In this paper we extend the classical SIS epidemic model from a deterministic framework to a stochastic one, and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). We then prove that this SDE has a unique global positive solution I(t) and establish conditions for extinction and persistence of I(t). We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions
more » ... or its mean and variance. The results are illustrated by computer simulations, including two examples based on real life diseases.
doi:10.1137/10081856x fatcat:3jywhi3655hp5f5xrvbhwuqwxy