@article{He2025, 
author = {Shuantu He and Zhongyi Xiang},
title = {Dynamics of stochastic SIQS model based on nonlinear incidence: disease extinction and stationary distribution under degenerate diffusion},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {7},
pages = {4259-4283},
keywords = {stochastic SIQS model, nonlinear incidence rate, degenerate diffusion, extinction, stationary distribution},
url = {https://www.sciopen.com/article/10.3934/era.2025193},
doi = {10.3934/era.2025193},
abstract = {This paper investigated the dynamical behaviors of the SIQS (susceptible, infected, isolated, and again susceptible) infectious disease model with nonlinear incidence rate and degenerate diffusion in a stochastic environment. By introducing nonlinear contagion rate, the model was able to more realistically reflect the complexity of real-world disease transmission, including the effects of social behavior, medical resource constraints, and public health interventions. It was proved that the infectious disease will be extinct when        R    0    s    <  1. Furthermore, by utilizing Markov semigroup theory, we obtained that there existed stationary distribution for the system when        R    0    s    >  1. Numerical simulations were conducted by introducing three different forms of nonlinear incidence rates (standard incidence, non-monotonic incidence, Beddington-DeAngelis incidence) to verify our results.}
}