| Volume 8, Number 1, 2018, Pages 272-295 DOI：10.11948/2018.272 |
| The asymptotic behaviors of a stochastic social epidemics model with multi-perturbation |
| Xunyang Wang,Qingshan Yang,Haifeng Huo |
| Keywords:Stochastic differential equation, Ergodic, positive recurrence, stochastic Lyapunov functional. |
| 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 \cite{Wangxy}, 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. |
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