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The asymptotic behaviors of a stochastic social epidemics model with multi-perturbation
Keywords:Stochastic differential equations; Ergodic; Positive recurrence; Stochastic Lyapunov functional
      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 [13], with the mortalities of all populations as well as the contact infected coefficient are 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 the corresponding theoretical results.