Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine
We consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution t...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/1291402 |
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| author | Driss Kiouach Lahcen Boulaasair |
| author_facet | Driss Kiouach Lahcen Boulaasair |
| author_sort | Driss Kiouach |
| collection | DOAJ |
| description | We consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Third, we study the extinction of the disease. Finally, numerical simulations are given to support the analytical results. |
| format | Article |
| id | doaj-art-3698f769a52d48b8bf13b580e7dd169b |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3698f769a52d48b8bf13b580e7dd169b2025-08-20T02:08:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/12914021291402Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect VaccineDriss Kiouach0Lahcen Boulaasair1MSTI (Modelling, Systems and Technologies of Information) Team, High School of Technology, Ibn Zohr University, Agadir, MoroccoMSTI (Modelling, Systems and Technologies of Information) Team, High School of Technology, Ibn Zohr University, Agadir, MoroccoWe consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Third, we study the extinction of the disease. Finally, numerical simulations are given to support the analytical results.http://dx.doi.org/10.1155/2018/1291402 |
| spellingShingle | Driss Kiouach Lahcen Boulaasair Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine Journal of Applied Mathematics |
| title | Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine |
| title_full | Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine |
| title_fullStr | Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine |
| title_full_unstemmed | Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine |
| title_short | Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine |
| title_sort | stationary distribution and dynamic behaviour of a stochastic sivr epidemic model with imperfect vaccine |
| url | http://dx.doi.org/10.1155/2018/1291402 |
| work_keys_str_mv | AT drisskiouach stationarydistributionanddynamicbehaviourofastochasticsivrepidemicmodelwithimperfectvaccine AT lahcenboulaasair stationarydistributionanddynamicbehaviourofastochasticsivrepidemicmodelwithimperfectvaccine |