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This paper considers a general stochastic SIR epidemic model driven by amultidimensional Levy jump process with heavy tailed increments and possiblecorrelation between noise components. In this framework, we derive newsufficient conditions for disease extinction and persistence in the mean. Ourmethod differs from previous approaches by the use of Kunita's inequalityinstead of the Burkholder-Davis-Gundy inequality for continuous processes, andallows for the treatment of infinite Levy measures by the definition of newthreshold values. An SIR model driven by a tempered stable process is presentedas an example of application with the ability to model sudden disease outbreak,illustrated by numerical simulations. The results show that persistence andextinction are dependent not only on the variance of the processes increments,but also on the shapes of their distributions.

Stochastic SIR Levy jump model with heavy tailed increments