STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

doi:10.1016/S0252-9602(16)30036-4

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 740-752.doi: 10.1016/S0252-9602(16)30036-4

STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

张向华¹, 陈芙², 王克³, 杜红⁴

1. College of Science, Heilongjiang University of Science and Technology, Harbin 150022, China;
2. College of Humanities and Law, Northeast Agricultural University, Harbin 150030, China;
3. Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China;
4. College of Science, Heilongjiang University of Science and Technology, Harbin 150022, China

收稿日期:2015-04-07 修回日期:2015-07-29 出版日期:2016-06-25 发布日期:2016-06-25
作者简介:Xianghua ZHANG,E-mail:hljzhangxianghua@163.com;Fu CHEN,E-mail:10658249@qq.com;Ke WANG,E-mail:wangke@hitwh.edu.cn;Hong DU,E-mail:dohong2003@sohu.com
基金资助:
This research was partially supported by the Natural Science Foundation of Heilongjiang Province (A201420), Educational Reform Project of Heilongjiang Province (JG2013010482), Foundation of Heilongjiang Province Educational Committee (12541696) and the Natural Science Foundation of China (11401136, 11301112, 11301207, 11501148).

STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

Xianghua ZHANG¹, Fu CHEN², Ke WANG³, Hong DU⁴

1. College of Science, Heilongjiang University of Science and Technology, Harbin 150022, China;
2. College of Humanities and Law, Northeast Agricultural University, Harbin 150030, China;
3. Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China;
4. College of Science, Heilongjiang University of Science and Technology, Harbin 150022, China

Received:2015-04-07 Revised:2015-07-29 Online:2016-06-25 Published:2016-06-25
Supported by:
This research was partially supported by the Natural Science Foundation of Heilongjiang Province (A201420), Educational Reform Project of Heilongjiang Province (JG2013010482), Foundation of Heilongjiang Province Educational Committee (12541696) and the Natural Science Foundation of China (11401136, 11301112, 11301207, 11501148).

摘要/Abstract

摘要：

The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.

关键词: jumps, stochastically stable, SIRS model, network virus

Abstract:

Key words: jumps, stochastically stable, SIRS model, network virus

中图分类号:

92D25

张向华, 陈芙, 王克, 杜红. STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE[J]. 数学物理学报(英文版), 2016, 36(3): 740-752.

Xianghua ZHANG, Fu CHEN, Ke WANG, Hong DU. STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE[J]. Acta mathematica scientia,Series B, 2016, 36(3): 740-752.

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STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

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