Year: 2021
Author: Zhimin Li, Tailei Zhang
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 4 : pp. 523–546
Abstract
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 $\mathfrak{R}_0<1,$ the disease dies out; while if $\mathfrak{R}_0>1,$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.523
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 4 : pp. 523–546
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Nonlinear incidence Stochastic differential equation Stationary distribution Permanence Extinction.