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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/592821 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567669306425344 |
|---|---|
| author | Yanli Zhou Weiguo Zhang Sanling Yuan |
| author_facet | Yanli Zhou Weiguo Zhang Sanling Yuan |
| author_sort | Yanli Zhou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a6db2e3272824eaea6a94c4bad4971e3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a6db2e3272824eaea6a94c4bad4971e32025-02-03T01:00:50ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/592821592821Survival and Stationary Distribution in a Stochastic SIS ModelYanli Zhou0Weiguo Zhang1Sanling Yuan2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThe 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.http://dx.doi.org/10.1155/2013/592821 |
| spellingShingle | Yanli Zhou Weiguo Zhang Sanling Yuan Survival and Stationary Distribution in a Stochastic SIS Model Discrete Dynamics in Nature and Society |
| title | Survival and Stationary Distribution in a Stochastic SIS Model |
| title_full | Survival and Stationary Distribution in a Stochastic SIS Model |
| title_fullStr | Survival and Stationary Distribution in a Stochastic SIS Model |
| title_full_unstemmed | Survival and Stationary Distribution in a Stochastic SIS Model |
| title_short | Survival and Stationary Distribution in a Stochastic SIS Model |
| title_sort | survival and stationary distribution in a stochastic sis model |
| url | http://dx.doi.org/10.1155/2013/592821 |
| work_keys_str_mv | AT yanlizhou survivalandstationarydistributioninastochasticsismodel AT weiguozhang survivalandstationarydistributioninastochasticsismodel AT sanlingyuan survivalandstationarydistributioninastochasticsismodel |