Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 388, Issue 1, Pages 248-271Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2011.11.072
Keywords
SIR epidemic model; SEIR epidemic model; Ito's formula; Stochastic Lyapunov function; Exponential stability; Ergodic property
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Funding
- Key Laboratory for Applied Statistics of MOE (KLAS)
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In this paper, we include stochastic perturbations into SIR and SEIR epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number R-0. The long time behavior of the two stochastic systems is studied. Mainly, we utilize stochastic Lyapunov functions to show under some conditions, the solution has the ergodic property as R-0 > 1, while exponential stability as R-0 <= 1. At last, we make simulations to conform our analytical results. (C) 2011 Elsevier Inc. All rights reserved.
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