Stationary distribution of an SIR epidemic model with three correlated Brownian motions and general Levy measure

Exhaustive surveys have been previously done on the long-time behavior of illness systems with Le??vy motion. All of these works have considered a Le??vy???Ito?? decomposition associated with independent white noises and a specific Le??vy measure. This setting is very particular and ignores an important class of dependent Le??vy noises with a general infinite measure (finite or infinite). In this paper, we adopt this general framework and we treat a novel correlated stochastic SIRE system. By presuming some assumptions, we demonstrate the ergodic characteristic of our system. To numerically probe the advantage of our proposed framework, we implement Rosinski???s algorithm for tempered stable distributions. We conclude that tempered tails have a strong effect on the long-term dynamics of the system and abruptly alter its behavior.

Automated summary

This paper investigates the long-term behavior of illness systems with Levy motion, specifically focusing on a general framework that includes correlated Levy noises. By treating a novel correlated stochastic SIRE system and implementing Rosinski's algorithm for tempered stable distributions, the study demonstrates the ergodic characteristics and the strong effect of tempered tails on the system's long-term dynamics.