@Article{JNMA-3-523,
author = {Li , Zhimin and Zhang , Tailei},
title = {Analysis of a Kind of Stochastic Dynamics Model with Nonlinear Function},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2022},
volume = {3},
number = {4},
pages = {523--546},
abstract = {<p style="text-align: justify;">In this paper, we establish stochastic differential equations on the
basis of a nonlinear deterministic model and study the global dynamics. For
the deterministic model, we show that the basic reproduction number $\mathfrak{R}_0$ determines whether there is an endemic outbreak or not: if $\mathfrak{R}_0&lt;1,$ the disease
dies out; while if $\mathfrak{R}_0&gt;1,$ the disease persists. For the stochastic model, we
provide analytic results regarding the stochastic boundedness, perturbation,
permanence and extinction. Finally, some numerical examples are carried out
to confirm the analytical results. One of the most interesting findings is that
stochastic fluctuations introduced in our stochastic model can suppress disease outbreak, which can provide us some useful control strategies to regulate
disease dynamics.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2021.523},
url = {http://global-sci.org/intro/article_detail/jnma/20682.html}
}