论文标题
具有分布式延迟和多维lévy的随机SIR流行模型的长期行为
The long-time behaviour of a stochastic SIR epidemic model with distributed delay and multidimensional Lévy jumps
论文作者
论文摘要
最近，诸如Covid-19及其变体之类的新兴流行病需要预测的数学模型来实施合适的响应，以限制其对社会的负面影响。 SIR（易感性感染）系统是一种直接的数学公式，可以模拟许多传染病的传播。本文报告了具有伽马分布延迟的SIR模型的扰动版本的新型理论和分析结果。值得注意的是，我们的流行模型由Itô-l'evy随机微分方程表示，以模拟突然和意外的外部现象。通过使用一些新的和改善的数学方法，我们研究了扰动延迟模型的长期特征。在此范围内，我们为两个有趣的渐近礼节提供了足够的条件：流行病的灭绝和持久性。最有趣的结果之一是，随机模型的动力学与白色噪声和L'evy跳跃的强度密切相关，这可以使我们能够很好地了解在某些意外情况下流行病的演变。我们的工作补充了一些先前研究的结果，并提供了一种新的方法来预测和分析流行病的动态行为，并以分布延迟。出于说明目的，提出了用于检查理论研究的数值示例
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system is a straightforward mathematical formulation to model the dissemination of many infectious diseases. The present paper reports novel theoretical and analytical results for a perturbed version of an SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by Itô-L'evy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic proprieties: extinction and persistence of the epidemic. One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and L'evy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study
