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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Main Authors: Driss Kiouach, Lahcen Boulaasair
Format: Article
Language:English
Published: Wiley 2018-01-01
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.
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publishDate 2018-01-01
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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