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

doi:10.3969/j.issn.1000-5641.2019.01.001

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

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

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

Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Received:2017-12-08 Online:2019-01-25 Published:2019-01-24

Abstract

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

CLC Number:

O211.63

ZHANG Zhen-zhong, ZHANG Quan, YANG Hong-qian, ZHANG En-hua. An SIS epidemic model driven by a class of truncated stable processes[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(1): 1-12,38.

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

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