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随机SIS传染病模型中给定时间感染人数的闭式概率分布。

Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model.

作者信息

Otunuga Olusegun Michael

机构信息

Department of Mathematics, Marshall University, One John Marshall Drive, Huntington, WV, USA.

出版信息

Heliyon. 2019 Sep 23;5(9):e02499. doi: 10.1016/j.heliyon.2019.e02499. eCollection 2019 Sep.

DOI:10.1016/j.heliyon.2019.e02499
PMID:31687591
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6819802/
Abstract

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to a generalized Laguerre differential equation. The properties of the distribution, together with the effect of noise intensity, are analyzed. The distribution is demonstrated using parameter values relevant to the transmission dynamics of influenza in the United States.

摘要

我们研究某些疾病传播率的外部波动效应，以及这些波动如何随时间影响感染个体数量的分布。为此，我们在确定性SIS模型的传播率中引入随机噪声，并研究感染数量随时间如何变化。这项工作的目标是推导并分析所得随机SIS流行病模型中给定时间感染数量的封闭形式概率分布。利用福克 - 普朗克方程，我们将控制感染数量的微分方程简化为广义拉盖尔微分方程。分析了该分布的性质以及噪声强度的影响。使用与美国流感传播动态相关的参数值展示了该分布。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/9037b69d748c/gr014.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/9037b69d748c/gr014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/7b1178850e5a/gr001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/1d585bc22019/gr002.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/a4c240d44c6c/gr005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/69de8387be14/gr006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/ca656c5982ca/gr007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/4325932323e7/gr008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/8bd4e045e69f/gr009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/3ce8fcc91c67/gr010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/496ae3467ca1/gr011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/9a6ecece40fb/gr012.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/459f/6819802/9037b69d748c/gr014.jpg

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3
Stochastic fluctuations of the transmission rate in the susceptible-infected-susceptible epidemic model.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011919. doi: 10.1103/PhysRevE.86.011919. Epub 2012 Jul 23.