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

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

doi:10.3969/j.issn.1000-5641.2019.01.001

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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 Sciences), 2019, (1): 1-12, 38. doi: 10.3969/j.issn.1000-5641.2019.01.001

Citation:

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 Sciences), 2019, (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

doi: 10.3969/j.issn.1000-5641.2019.01.001

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

Received Date: 2017-12-08
Publish Date: 2019-01-25

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.
- spectrally positive α-stable processes,
- stationary distribution,
- exponential ergodicity,
- extinction

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References(19)

References

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