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Dynamics of a multigroup SIR epidemic model with stochastic perturbation. (English) Zbl 1244.93154
Summary: We introduce stochasticity into a multigroup Susceptible, Infective, and Recovered (SIR) model. The stochasticity in the model is introduced by parameter perturbation, which is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number $\cal R_{0}$ is a threshold which completely determines the persistence or extinction of the disease. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the value of $\cal R_{0}$. If $\cal R_{0}\le 1$, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if $\cal R_{0}>1$, there is a stationary distribution, which means that the disease will prevail.

MSC:
93E03General theory of stochastic systems
93C73Perturbations in control systems
92D30Epidemiology
93A30Mathematical modelling of systems
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References:
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