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Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine

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  • Driss Kiouach
  • Lahcen Boulaasair

Abstract

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.

Suggested Citation

  • Driss Kiouach & Lahcen Boulaasair, 2018. "Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-11, July.
    • Handle: RePEc:hin:jnljam:1291402
    DOI: 10.1155/2018/1291402
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    Cited by:

    1. Gamboa, M. & López-García, M. & Lopez-Herrero, M.J., 2024. "On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine," Applied Mathematics and Computation, Elsevier, vol. 468(C).

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