Stochastic modeling of nonlinear epidemiology
Stochastic modeling of nonlinear epidemiology
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DOI：
10.1016/j.jtbi.2004.11.033
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发表时间：
2005-06-21
影响因子：
2
通讯作者：
Bokka, S
中科院分区：
文献类型：
--
作者：
Chen, WY;Bokka, S
本文的目标是利用现代随机算法来分析、建模和模拟传染病的传播。该方法使得绕过过去大多数流行病过程随机分析工作中强加的简化线性假设成为可能。传染病通常通过感染者与易感者的接触传播；因此，这些过程本质上是非线性的。根据 Kermack 和 McKendrick 的经典模型，即 SIR 模型，三类人群涉及两种类型的过程：易感者 (S) 向感染者 (I) 的转化和感染者向去除者 (R) 的转化。 SIR 过程的主方程是通过考虑互斥事件、围绕特定状态的概率总体平衡来制定的。本方法的有效性主要归因于它能够通过非线性主方程的系统规模展开的方法推导随机变量的均值、方差和协方差的控制方程。同时单独求解这些方程和与流感流行数据相关的比率，不仅可以得到有关三个人群的平均值的信息，还可以得到有关流行病固有的这些人群的最小不确定性的信息。流行病期间三类不同人群的随机路径，即它们的均值和围绕这些均值的波动，也通过从主方程导出的算法以及事件驱动的蒙特卡罗算法进行了独立的数值模拟。主方程和蒙特卡罗算法得到了相同的结果。 (c) 2005 Elsevier Ltd. 保留所有权利。
The objectives of this paper to analyse, model and simulate the spread of an infections disease by resorting to modern stochastic algorithms. The approach renders it possible to circumvent the simplifying assumption of linearity imposed in the majority of the past works on stochastic analysis of epidemic processes. Infectious diseases are often transmitted through contacts of those infected with those susceptible; hence the processes are inherently nonlinear. According to the classical model of Kermack and McKendrick, or the SIR model, three classes of populations are involved in two types of processes: conversion of susceptibles (S) to infectives (I) and conversion of infectives to removed (R). The master equations of the SIR process have been formulated through the probabilistic population balance around a particular state by considering the mutually exclusive events. The efficacy of the present methodology is mainly attributable to its ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equations. Solving these equations simultaneously alone with rates associated influenza epidemic data yields information concerning not only the means of the three populations but also the minimal uncertainties of these populations inherent in the epidemic. The stochastic pathways of the three different classes of populations during an epidemic, i.e. their means and the fluctuations around these means, have also been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. The master equation and Monte Carlo algorithms have given rise to the identical results. (c) 2005 Elsevier Ltd. All rights reserved.