For EDITORS

For READERS

All Issues

Vol.15, 2025
Vol.14, 2024
Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 9, Number 2, 2019, Pages 440-451                                                                DOI:10.11948/2156-907X.20160269
Threshold dynamics of the stochastic epidemic model with jump-diffusion infection force
Dianli Zhao,Sanling Yuan
Keywords:Stochastic epidemic model, jump-diffusion infection force, the threshold, extinction.
Abstract:
      This paper formulates a stochastic SIR epidemic model by supposing that the infection force is perturbed by Brown motion and L\'{e}vy jumps. The globally positive and bounded solution is proved firstly by constructing the suitable Lyapunov function. Then, a stochastic basic reproduction number $R_0^{L}$ is derived, which is less than that for the deterministic model and the stochastic model driven by Brown motion. Analytical results show that the disease will die out if $R_0^{L}<1$, and $R_0^{L}>1$ is the necessary and sufficient condition for persistence of the disease. Theoretical results and numerical simulations indicate that the effects of L\'{e}vy jumps may lead to extinction of the disease while the deterministic model and the stochastic model driven by Brown motion both predict persistence. Additionally, the method developed in this paper can be used to investigate a class of related stochastic models driven by L\'{e}vy noise.
PDF      Download reader