具有阶段结构与随机扰动的酗酒模型

A binge drinking model with two stages structure and random perturbation

研究一类具有阶段结构与随机扰动的酗酒模型,分析饮酒平衡点附近的随机扰动.通过建立Lyapunov函数及应用伊藤公式,证明饮酒平衡点附近的随机全局渐近稳定性.当确定性模型基本再生数R_0>1,随机模型的解是平均持续的,说明饮酒行为持续存在.另外,饮酒的传播率,自然死亡率及复发率对饮酒平衡点附近的随机全局渐近稳定性起着决定性作用.

A binge drinking model with two stages and random perturbation is introduced.The random fluctuation around the alcohol-present equilibrium of deterministic binge drinking model is studied.The stochastic asymptotical stability of the alcohol-present equilibrium is proved by constructing Lyapunov function and applying Ito′s formula.If the deterministic basic production number R_01,there is a stationary distribution,which means that the binge drinking will prevail.In addition,it is noted that transmission coefficient,the natural death rate and the relapse rate play a crucial role for the stochastic asymptotical stability of the model.