Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (1): 1-12,38.doi: 10.3969/j.issn.1000-5641.2019.01.001

• Mathematics •     Next Articles

An SIS epidemic model driven by a class of truncated stable processes

ZHANG Zhen-zhong, ZHANG Quan, YANG Hong-qian, ZHANG En-hua   

  1. Department of Applied Mathematics, Donghua University, Shanghai 201620, China
  • Received:2017-12-08 Online:2019-01-25 Published:2019-01-24

Abstract: A susceptible-infected-susceptible (SIS) epidemic model driven by spectrally positive α-stable processes is considered. Firstly, the uniqueness and the existence of the global positive solution are proved. Next, by using Khasminskii's lemma and the Lyapunov method, conditions for the existence of a unique stationary distribution are given. In addition, the model is shown to be exponentially ergodic. Finally, conditions for extinction of the model are given.

Key words: spectrally positive α-stable processes, stationary distribution, exponential ergodicity, extinction

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