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Stochastic differential equation systems for an SIS epidemic model with vaccination and immigration

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  • Rahman Farnoosh
  • Mahmood Parsamanesh

Abstract

Two Itô stochastic differential equation (SDE) systems are constructed for a Susceptible-Infected-Susceptible epidemic model with temporary vaccination. A constant number of new members enter the population and total size of the population is variable. Some conditions for disease extinction in the stochastic models are established and compared with conditions in deterministic one. It is shown that the two stochastic models are equivalent in the sense that their solutions come from same distribution. In addition, the SDE models are simulated and the equivalence of the two stochastic models is confirmed by numerical examples. The probability distribution for extinction is also obtained numerically, provided there exists a probability for disease persistence whereas the expected duration of epidemic is acquired when extinction occurs with probability 1.

Suggested Citation

  • Rahman Farnoosh & Mahmood Parsamanesh, 2017. "Stochastic differential equation systems for an SIS epidemic model with vaccination and immigration," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8723-8736, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:17:p:8723-8736
    DOI: 10.1080/03610926.2016.1189571
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    Cited by:

    1. Parsamanesh, Mahmood & Erfanian, Majid, 2021. "Stability and bifurcations in a discrete-time SIVS model with saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.

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