一类截尾稳定过程驱动的SIS传染病模型

doi:10.3969/j.issn.1000-5641.2019.01.001

华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (1): 1-12,38.doi: 10.3969/j.issn.1000-5641.2019.01.001

• 数学 • 下一篇

一类截尾稳定过程驱动的SIS传染病模型

张振中, 张权, 杨红倩, 张恩华

东华大学应用数学系, 上海 201620

收稿日期:2017-12-08 出版日期:2019-01-25 发布日期:2019-01-24
作者简介:张振中,男,副教授,研究方向为随机分析及其应用.E-mail:zzzhang@dhu.edu.cn.
基金资助:
教育部人文社会科学研究规划基金（17YJA910004）

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

摘要/Abstract

摘要： 考虑一类由谱正α-稳定过程驱动的SIS（易感-感染-易感）模型.首先证明了全局正解的存在唯一性；其次，利用Khasminskii引理和Lyapunov方法，得到了平稳分布存在唯一性的条件，并证明了模型的指数遍历性；最后，给出了模型灭绝的条件.

关键词: 谱正α-稳定过程, 平稳分布, 指数遍历性, 灭绝性

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

中图分类号:

O211.63

张振中, 张权, 杨红倩, 张恩华. 一类截尾稳定过程驱动的SIS传染病模型[J]. 华东师范大学学报(自然科学版), 2019, 2019(1): 1-12,38.

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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一类截尾稳定过程驱动的SIS传染病模型

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

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