MathSys CDT, Mathematics Institute, University of Warwick, Coventry, United Kingdom.
Zeeman Institute (SBIDER), University of Warwick, Coventry, United Kingdom.
PLoS Comput Biol. 2020 Mar 16;16(3):e1006869. doi: 10.1371/journal.pcbi.1006869. eCollection 2020 Mar.
Complex, highly-computational, individual-based models are abundant in epidemiology. For epidemics such as macro-parasitic diseases, detailed modelling of human behaviour and pathogen life-cycle are required in order to produce accurate results. This can often lead to models that are computationally-expensive to analyse and perform model fitting, and often require many simulation runs in order to build up sufficient statistics. Emulation can provide a more computationally-efficient output of the individual-based model, by approximating it using a statistical model. Previous work has used Gaussian processes (GPs) in order to achieve this, but these can not deal with multi-modal, heavy-tailed, or discrete distributions. Here, we introduce the concept of a mixture density network (MDN) in its application in the emulation of epidemiological models. MDNs incorporate both a mixture model and a neural network to provide a flexible tool for emulating a variety of models and outputs. We develop an MDN emulation methodology and demonstrate its use on a number of simple models incorporating both normal, gamma and beta distribution outputs. We then explore its use on the stochastic SIR model to predict the final size distribution and infection dynamics. MDNs have the potential to faithfully reproduce multiple outputs of an individual-based model and allow for rapid analysis from a range of users. As such, an open-access library of the method has been released alongside this manuscript.
复杂的、高度计算的、基于个体的模型在流行病学中非常丰富。对于宏观寄生虫病等传染病，需要详细建模人类行为和病原体生命周期，才能得出准确的结果。这通常会导致分析和进行模型拟合的计算成本很高的模型，并且通常需要进行多次模拟运行才能建立足够的统计数据。通过使用统计模型来近似模拟，可以为基于个体的模型提供更具计算效率的输出。先前的工作已经使用高斯过程（GPs）来实现这一目标，但这些方法不能处理多峰、重尾或离散分布。在这里，我们介绍了混合密度网络（MDN）的概念，并将其应用于流行病学模型的仿真中。MDN 结合了混合模型和神经网络，为模拟各种模型和输出提供了灵活的工具。我们开发了一种 MDN 仿真方法，并在包含正态、伽马和贝塔分布输出的一些简单模型上演示了其使用。然后，我们探索了它在随机 SIR 模型中的使用，以预测最终规模分布和感染动态。MDN 有可能忠实地再现基于个体的模型的多个输出，并允许来自不同用户的快速分析。因此，在本文档旁边发布了该方法的一个开放访问库。
