Dynamics of a stochastic periodic SIRS model with time delay. (English) Zbl 1461.92119
Summary: Dynamical behaviors of a stochastic periodic SIRS epidemic model with time delay are investigated. By constructing suitable Lyapunov functions and applying Itô’s formula, the existence of the global positive solution and the property of stochastically ultimate boundedness of model (1.1) are proved. Moreover, the extinction and the persistence of the disease are established. The results are verified by numerical simulations.
MSC:
| 92D30 | Epidemiology |
| 34K13 | Periodic solutions to functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
Keywords:
stochastic periodic model; delay; extinction; stochastically ultimate boundedness; persistenceReferences:
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