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本文引用的文献

1
Global properties of infectious disease models with nonlinear incidence.具有非线性发病率的传染病模型的全局性质
Bull Math Biol. 2007 Aug;69(6):1871-86. doi: 10.1007/s11538-007-9196-y. Epub 2007 Apr 19.
2
Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission.具有非线性传播的SIR和SIRS流行病模型的李雅普诺夫函数与全局稳定性
Bull Math Biol. 2006 Apr;68(3):615-26. doi: 10.1007/s11538-005-9037-9. Epub 2006 Mar 29.
3
The reinfection threshold.再感染阈值。
J Theor Biol. 2005 Sep 7;236(1):111-3. doi: 10.1016/j.jtbi.2005.03.001. Epub 2005 Apr 18.
4
Global stability for the SEIR model in epidemiology.流行病学中SEIR模型的全局稳定性
Math Biosci. 1995 Feb;125(2):155-64. doi: 10.1016/0025-5564(95)92756-5.

关于具有饱和发生率的随机 SEIR 传染病模型的平稳分布的注释。

A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate.

机构信息

School of Mathematics, Changchun Normal University, Changchun, 130032, China.

School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China.

出版信息

Sci Rep. 2017 Jun 21;7(1):3996. doi: 10.1038/s41598-017-03858-8.

DOI:10.1038/s41598-017-03858-8
PMID:28638046
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5479838/
Abstract

The stochastic SEIR infectious diseases model with saturated incidence rate is studied in this paper. By constructing appropriate Lyapunov functions, we show that there is a stationary distribution for the system and the ergodicity holds provided [Formula: see text] > 1. In particular, we improve the results obtained by previous studies greatly, condition in our Theorem is more concise and elegant.

摘要

本文研究了具有饱和发生率的随机 SEIR 传染病模型。通过构造适当的李雅普诺夫函数，我们证明了系统存在一个平稳分布，并且在[Formula: see text] > 1 时系统具有遍历性。特别地，我们大大改进了前人研究的结果，我们定理中的条件更加简洁和优美。