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A stochastic differential equation SIS epidemic model. (English) Zbl 1263.34068
Authors’ abstract: In this paper we extend the classical susceptible-infected-susceptible 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 for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34F05ODE with randomness
60H10Stochastic ordinary differential equations
92D25Population dynamics (general)
92D30Epidemiology