This paper considers a general stochastic SIR epidemic model driven by a multidimensional Lévy jump process with heavy-tailed increments and possible correlation between noise components. In this framework, we derive new sufficient conditions for disease extinction and persistence in the mean. Our method differs from previous approaches by the use of Kunita’s inequality instead of the Burkholder–Davis–Gundy inequality for continuous processes, and allows for the treatment of infinite Lévy measures by the definition of new threshold \(\mathcal {\bar{R}}_0\). An SIR model driven by a tempered stable process is presented as an example of application with the ability to model sudden disease outbreak, illustrated by numerical simulations. The results show that persistence and extinction are dependent not only on the variance of the processes increments, but also on the shapes of their distributions.

本文考虑由多维Lévy跳跃过程驱动的一般随机SIR流行模型，该过程具有重尾增量和噪声分量之间的可能相关性。在此框架中，我们得出了疾病灭绝和持续存在的新的充分条件。我们的方法与以前的方法不同，在连续过程中使用Kunita不等式而不是Burkholder-Davis-Gundy不等式，并且通过定义新阈值\（\ mathcal {\ bar {R} } _0 \）。作为一个应用实例，提出了一种由钢化稳定过程驱动的SIR模型，该模型具有对突发疾病进行建模的能力，并通过数值模拟进行了说明。结果表明，持久性和消亡不仅取决于过程增量的方差，还取决于其分布的形状。