International Journal of Differential Equations · 2019 · 38 citations · 15 references
Veterinary MedicineInfectious DiseasesEpidemiologyStochastic ModelingStochastic ProcessesDisease IncidenceDisease ModelingDisease SpreadInfectious Disease DynamicsStochastic Differential EquationsTransmission DynamicsEpidemic ModelsEpidemic Population DynamicsEpidemic SpreadingInfectious Disease ModelsMathematical Modeling Of EpidemicsNonlinear Incidence FunctionsStochastic Disease ModelsStochastic Epidemic Models
We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.
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