Survival and Stationary Distribution in a Stochastic SIS Model
The dynamics of a stochastic SIS epidemic model is investigated. First, we show that the system admits a unique positive global solution starting from the positive initial value. Then, the long-term asymptotic behavior of the model is studied: when R0≤1, we show how the solution spirals around the d...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/592821 |
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| Summary: | The dynamics of a stochastic SIS epidemic model is investigated. First, we
show that the system admits a unique positive global solution starting from the positive initial
value. Then, the long-term asymptotic behavior of the model is studied: when R0≤1, we show how the solution spirals around the disease-free equilibrium of deterministic system under some
conditions; when R0>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. Finally, numerical
simulations are carried out to illustrate the theoretical results. |
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| ISSN: | 1026-0226 1607-887X |