Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 244, Issue -, Pages 118-131Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2014.06.100
Keywords
Stochastic SIR epidemic model; Stationary distribution; Ito formula; Extinction
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Funding
- National Natural Science Foundation of China [11271260, 11071164]
- Innovation Program of Shanghai Municipal Education Commission [13ZZ116]
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In this paper, the dynamics of a SIR epidemic model is investigated. First, we show that the system admits a unique positive global solution starting from the positive initial value. Then, when R-0 > 1, we show that the stochastic model has a stationary distribution under certain parametric restrictions. In particular, we show that random effects may lead the disease to extinction in scenarios where the deterministic model predicts persistence. When R-0 <= 1, a result on fluctuation of the solution around the disease-free equilibrium of deterministic system is established under suitable conditions. Finally, numerical simulations are carried out to illustrate the theoretical results. (C) 2014 Elsevier Inc. All rights reserved.
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