THE ASYMPTOTIC BEHAVIORS OF A STOCHASTIC SOCIAL EPIDEMIC MODEL WITH MULTI-PERTURBATION

Xunyang Wang; Qingshan Yang; Haifeng Huo

doi:10.11948/2018.272

2018 Volume 8 Issue 1

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Xunyang Wang, Qingshan Yang, Haifeng Huo. THE ASYMPTOTIC BEHAVIORS OF A STOCHASTIC SOCIAL EPIDEMIC MODEL WITH MULTI-PERTURBATION[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 272-295. doi: 10.11948/2018.272

Citation:

Xunyang Wang, Qingshan Yang, Haifeng Huo. THE ASYMPTOTIC BEHAVIORS OF A STOCHASTIC SOCIAL EPIDEMIC MODEL WITH MULTI-PERTURBATION[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 272-295. doi: 10.11948/2018.272

THE ASYMPTOTIC BEHAVIORS OF A STOCHASTIC SOCIAL EPIDEMIC MODEL WITH MULTI-PERTURBATION

1 Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China;
2 College of Electrical and Information engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China;
3 School of mathematics and statistics, Northeast Normal University, Changchun, Jilin, 130024, China

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Abstract

Abstract

Alcohol abuse is a major social problem, which is often called social epidemic, for the some similarities to the classical infectious diseases. In this paper, we formulated a new stochastic alcoholism model based on the deterministic model proposed in[24], with the mortalities of all populations as well as the contact infected coefficient are all perturbed. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. Finally, we carry out numerical simulations to support our theoretical results.
- Stochastic differential equation /
- Ergodic /
- positive recurrence /
- stochastic Lyapunov functional
MSC: 92D25

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References

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