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Dynamics of stochastically perturbed SIS epidemic model with vaccination. (English) Zbl 1288.92027

Summary: 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 \(R_0\) 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 the value of \(R_0\). If \(R_0\leq 1\), the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if \(R_0>1\), there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

MSC:

92D30 Epidemiology
92C60 Medical epidemiology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92-08 Computational methods for problems pertaining to biology
68U20 Simulation (MSC2010)
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