Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain.
Comput Math Methods Med. 2012;2012:742086. doi: 10.1155/2012/742086. Epub 2012 Aug 15.
Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model.
基于常微分方程的数学模型是研究流行病学中涉及的过程的有用工具。许多模型认为参数是确定性变量。但在实践中，传播参数存在很大的可变性，无法准确确定它们，因此需要引入随机性。本文将多项式混沌方法应用于基于常微分方程的具有随机系数的流行病学数学模型。考虑到模型传播参数的可变性，该方法允许我们获得辅助微分方程组，然后对其进行数值积分，以获得输出随机过程的一阶和二阶矩。还进行了基于多项式混沌方法的敏感性分析，以确定哪些参数对结果的影响最大。作为一个例子，我们将应用这种方法来研究肥胖症流行模型。
