Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 71, Issue 3, Pages 876-902Publisher
SIAM PUBLICATIONS
DOI: 10.1137/10081856X
Keywords
susceptible-infected-susceptible model; Brownian motion; stochastic differential equations; extinction; persistence; basic reproduction number; stationary distribution; gonorrhea; pneumococcus
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Funding
- Scottish Government
- British Council Shanghai
- Chinese Scholarship Council
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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.
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