一类具有对偶扰动的随机SIR传染病模型的动力学特征
Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation
摘要：
本文提出了一个带有两种不同扰动的SIR传染病模型：白噪声和Lévy噪声。我们致力于发展一种数学方法来获得扰动模型的渐近性质。利用比较定理、互斥可能性引理和随机微分系统的一些新技巧，讨论了疾病的均值持续性、遍历性和灭绝性。最后，对不同扰动进行了数值模拟，验证了理论分析的正确性.
英文摘要：
This paper presents an SIR epidemic model with two different types of perturbations: white and Lévy noises. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. We use the comparison theorem, mutually exclusive possibilities lemma, and some new techniques of the stochastic differential systems to discuss the following characteristics: persistence in the mean, ergodicity, and extinction of the disease. Finally, numerical simulations about different perturbations are realized to confirm the obtained theoretical results.
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