Modeling the simple epidemic with deterministic differential equations and random initial conditions
Modeling the simple epidemic with deterministic differential equations and random initial conditions
复制标题
DOI：
10.1016/j.mbs.2005.02.004
复制
发表时间：
2005-06-01
影响因子：
4.3
通讯作者：
West, RW
中科院分区：
文献类型：
--
作者：
Kegan, B;West, RW
在一个简单的流行病中，种群的唯一转变是从易感到感染，总种群规模在任何时候都是固定的。研究了随机初始条件对确定性简单传染病模型的影响。通过假设易感人群的初始比例服从贝塔分布，我们定义了一个描述流行病期间任何时候人群中易感人群比例的分布。该分布的均值和方差作为超几何函数导出，并研究了这些函数的行为。最后，我们定义了一个分布来描述直到给定比例的人口保持易感的时间。一种方法来寻找这种分布的分位数的开发和使用，使置信声明的时间，直到一个给定的人口比例是敏感的。(c)2005年爱思唯尔公司All rights reserved.
In a simple epidemic the only transition in the population is from susceptible to infected and the total population size is fixed for all time. This paper investigates the effect of random initial conditions on the deterministic model for the simple epidemic. By assuming a Beta distribution on the initial proportion of susceptibles, we define a distribution that describes the proportion of susceptibles in a population at any time during an epidemic. The mean and variance for this distribution are derived as hypergeometric functions, and the behavior of these functions is investigated. Lastly, we define a distribution to describe the time until a given proportion of the population remains susceptible. A method for finding the quantiles of this distribution is developed and used to make confidence statements regarding the time until a given proportion of the population is susceptible. (c) 2005 Elsevier Inc. All rights reserved.