@article{Yang2025, 
author = {Jing Yang and Shaojuan Ma and Dongmei Wei},
title = {Dynamical analysis of SIR model with Gamma distribution delay driven by Lévy noise and switching},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {3158-3176},
keywords = {SIR model, distributed delay, Markov switching, Lévy noise, stationary distribution},
url = {https://www.sciopen.com/article/10.3934/era.2025138},
doi = {10.3934/era.2025138},
abstract = {Considering the distributed time delay and the stochastic change of environment, this research primarily studied the dynamical behavior of the gamma-distributed delay SIR model driven by Lévy noise and Markov chain. First, it is proved that there is a unique global positive solution for stochastic model. Second, by constructing appropriate stochastic Lyapunov functions that account for regime switching, we derive a sufficient condition,              R      s        >  1, indicating the existence of a stationary distribution. This suggests the disease will persist over a long period. Finally, numerical simulations confirm the theoretical findings.}
}