@article{Chen2025, 
author = {Jia Chen and Yuming Chen and Qimin Zhang},
title = {Ergodic stationary distribution and extinction of stochastic pertussis model with immune and Markov switching},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {2736-2761},
keywords = {stochastic pertussis model, Markov switching, ergodic stationary distribution},
url = {https://www.sciopen.com/article/10.3934/era.2025121},
doi = {10.3934/era.2025121},
abstract = {Temperature, humidity, and other environmental factors can influence the spread of diseases. To investigate the impact of environmental perturbations and state changes on pertussis, this study established a random pertussis model with immunity and Markov switching. This stochastic model presented a global positive solution. Subsequently, using Itô's lemma and Lyapunov function, we concluded that the disease will become extinct. Then, a critical value              R              0        e   was introduced. It was established that the stochastic model with Markov switching has an ergodic stationary distribution when              R              0        e    >  1, which implies that this infectious disease will persist and remain prevalent. Some examples are presented to further substantiate our theoretical conclusions.}
}