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 \(\mathcal R_{0}\) 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 \(\mathcal R_{0}\). If \(\mathcal R_{0}\leq 1\), the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if \(\mathcal R_{0}>1\), there is a stationary distribution, which means that the disease will prevail.


93E03 Stochastic systems in control theory (general)
93C73 Perturbations in control/observation systems
92D30 Epidemiology
93A30 Mathematical modelling of systems (MSC2010)
Full Text: DOI


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