TY - JOUR
T1 - Analysis of a Kind of Stochastic Dynamics Model with Nonlinear Function
AU - Li , Zhimin
AU - Zhang , Tailei
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 523
EP - 546
PY - 2022
DA - 2022/06
SN - 3
DO - http://doi.org/10.12150/jnma.2021.523
UR - https://global-sci.org/intro/article_detail/jnma/20682.html
KW - Nonlinear incidence, Stochastic differential equation, Stationary
distribution, Permanence, Extinction.
AB - <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>