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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| 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. |
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| ISSN: | 1085-3375 1687-0409 |