Dynamic behavior of a stochastic SIQS epidemic model with Lévy jumps.

*(English)*Zbl 1398.37096Summary: In this paper, we propose a stochastic SIQS epidemic model with Lévy jumps and investigate sufficient conditions of the extinction and persistence of the disease. Then, we analyze the asymptotic behavior of the solution of the model around the endemic equilibrium of the corresponding deterministic model. We find that Lévy jumps can suppress the disease outbreak. Numerical simulations are carried out and approve our results.

##### MSC:

37N25 | Dynamical systems in biology |

37H10 | Generation, random and stochastic difference and differential equations |

92D25 | Population dynamics (general) |

34F05 | Ordinary differential equations and systems with randomness |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

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\textit{X.-B. Zhang} et al., Nonlinear Dyn. 93, No. 3, 1481--1493 (2018; Zbl 1398.37096)

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