Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation

We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant distribution which is ergod...

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Bibliographic Details
Main Authors: Yuguo Lin, Daqing Jiang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/917389
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Summary:We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant distribution which is ergodic if ℛ0>1. This is the same situation as the corresponding deterministic case. When the intensity of white noise is large, white noise controls this system. This means that the disease will extinct exponentially regardless of the magnitude of ℛ0.
ISSN:1085-3375
1687-0409