Acta mathematica scientia, Series B >
STOCHASTIC SIRS MODEL DRIVEN BY LÉVY NOISE
Received date: 2015-04-07
Revised date: 2015-07-29
Online 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).
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
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 . DOI: 10.1016/S0252-9602(16)30036-4
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