随机SIQR传染病模型全局正解的渐近行为

Asymptotic Behavior of Global Positive Solution to Stochastic SIQR Epidemic Model

为了研究具有非单调发生率以及白噪声影响的随机SIQR传染病模型的动力学行为,使模型符合相应的生态学意义,证明SIQR动力学系统全局正解的存在唯一性,并通过构造适当的Lyapunov函数以及利用伊藤公式,分别讨论随机模型的解在无病平衡点和地方病平衡点附近的渐近行为,利用数值模拟的方法对随机系统解的渐近行为进行进一步分析并验证结论的正确性。结果表明:当基本再生数不大于1时,在一定的条件下,随机模型在无病平衡点附近具有渐近稳定性;当基本再生数大于1时,随机系统的解在确定性模型的地方病平衡点附近振荡。

To explore the dynamic behavior of the stochastic SIQR epidemic model with nonmonotonic incidence influenced by white noise,and make the model accord with the corresponding ecological significance,the existence and uniqueness of the global positive solution of the SIQR model were proved.By constructing appropriate Lyapunov functions and using It formula,the asymptotic behavior of solutions of stochastic model around disease-free equilibrium and endemic equilibrium were discussed respectively.The asymptotic behavior of the solution of the stochastic model was further analyzed by numerical simulation and the correctness of the conclusion was verified.The results show that when the basic regeneration number is not greater than1,the stochastic model has asymptotic stability around the disease-free equilibrium under certain conditions.When the basic regeneration number is greater than1,the solution of the stochastic system oscillates around the endemic equilibrium of the deterministic model.