STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE

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

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (3): 740-752.doi: 10.1016/S0252-9602(16)30036-4

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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).

Abstract

Abstract:

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.

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

CLC Number:

92D25

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

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