Threshold dynamics of a stochastic SIVS model with saturated incidence and Lévy jumps

Advances in Difference Equations

Yuanlin Ma¹  Xingwang Yu² 

[1] School of Economics, Zhengzhou University of Aeronautics;School of Management Engineering, Zhengzhou University of Aeronautics;

关键词: Threshold dynamics;    Persistence in mean;    Extinction;    Lévy jumps;   

DOI  :  10.1186/s13662-020-02723-9

来源: DOAJ

【 摘 要 】

Abstract In this paper, we propose and analyze a stochastic SIVS model with saturated incidence and Lévy jumps. We first prove the existence of a global positive solution of the model. Then, with the help of semimartingale convergence theorem, we obtain a stochastic threshold of the model that completely determines the extinction and persistence of the epidemic. At last, we further study the threshold dynamics of a stochastic SIRS model with saturated or bilinear incidence by a similar method and carry out some numerical simulations to demonstrate our theoretical results. Comparing with the method given by Zhou and Zhang (Physica A 446:204–216, 2016), we find that the method used in this paper is simple and effective.

【 授权许可】

Unknown