Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination

Yanan Zhao and Daqing Jiang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R0 is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease‐related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease‐free equilibrium of the corresponding deterministic model, whereas, if R0 > 1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

Date: 2013
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https://doi.org/10.1155/2013/517439

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:517439

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