论文标题
开发新技术，以获取具有3维lévy过程的随机SIR流行模型的阈值
Developing new techniques for obtaining the threshold of a stochastic SIR epidemic model with 3-dimensional Lévy process
论文作者
论文摘要
本文考虑了由多维lévy跳跃过程驱动的经典SIR流行模型。我们奉献开发一种数学方法来获得扰动模型的渐近特性。我们的方法与以前的方法不同，通过使用比较定理，相互排斥的可能性引理以及随机差异系统的一些新技术。在此框架中，我们得出阈值，该阈值可以确定独特的恒定固定分布或流行病的灭绝。实现了有关不同扰动的数值模拟，以确认所获得的理论结果。
This paper considers the classical SIR epidemic model driven by a multidimensional Lévy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from previous approaches by the use of the comparison theorem, mutually exclusive possibilities lemma, and some new techniques of the stochastic differential systems. In this framework, we derive the threshold which can determine the existence of a unique ergodic stationary distribution or the extinction of the epidemic. Numerical simulations about different perturbations are realized to confirm the obtained theoretical results.
