一类随机SEIAQR腮腺炎传染病模型的动力学分析

Dynamic analysis on an SEIAQR mumps infection model with stochastic effects

为探究现实环境中随机因素对腮腺炎传播的影响,研究了一类具有随机效应的SEIAQR腮腺炎传染病模型。首先凭借停时理论证明了随机模型全局正解的存在唯一性,并通过构造Lyapunov函数并引入It8公式,分析了随机模型的解在相应确定性模型的无病平衡点和地方病平衡点附近的震荡行为;然后探究了随机模型解的平均持续性以及疾病灭绝的充分条件;最后通过数值模拟添加了噪声对模型的影响。结果显示:随机模型在确定性模型的平衡点附近扰动,扰动程度和噪声强度呈正相关,充分大的噪声会使疾病灭绝。

To explore the influence of random factors on the spread of mumps in real environment,an SEIAQR mumps infection model with stochastic effects is studied.Firstly,the existence and uniqueness of global positive solutions of stochastic models are proven by means of the stop-time theory.Secondly,the oscillating behavior of the solutions of the random model near the disease-free equilibrium point and the endemic equilibrium point of the corresponding deterministic model is analyzed by constructing the Lyapunov function and It formula.Then the sufficient conditions for the mean duration of the random model solution and the extinction of the disease are explored.Finally,the influence of noise on the model is added into the numerical simulations.The results show that the stochastic model vibrates near the equilibrium point of the deterministic model,and the disturbance degree with the noise intensity positively correlates.The sufficiently loud noise makes the disease extinct.