Mathematical Biosciences Institute, The Ohio State University, United States.
J Theor Biol. 2013 May 7;324:84-102. doi: 10.1016/j.jtbi.2012.12.021. Epub 2013 Jan 16.
Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.
霍乱和许多水源性疾病都表现出多种感染的特征时间尺度或途径，可以将其建模为直接和间接传播。水源性疾病的一个主要公共卫生问题是了解传播方式，以改善控制和预防策略。一个重要的流行病学问题是：给定暴发的数据，我们能否确定直接与环境/水源传播途径的作用和相对重要性？我们研究了在没有噪声数据的理想情况下（结构可识别性）和存在噪声的更现实情况下（实际可识别性），是否可以识别水源性疾病传播动力学微分方程模型的参数。我们使用微分代数方法和几种数值方法，特别强调了传输率的可识别性。为了在实际的公共卫生环境中研究这些问题，我们将模型应用于安哥拉最近的一次霍乱暴发（2006 年）。我们的结果表明，模型参数（包括水和人与人之间的传播途径）在全局结构上是可识别的，尽管当环境传播时间尺度较快时，它们变得不可识别。即使在可识别的水动力学范围内，当考虑到噪声数据时，也只能实际估计水传输参数的组合。这使得水源传播参数难以估计，从而导致基本繁殖数（R0）等重要流行病学参数的估计不准确。然而，环境水源中病原体持续时间的测量或水中病原体浓度的测量可以提高模型的可识别性，并允许更准确地估计水源传播途径参数以及 R0。安哥拉暴发的参数估计表明，需要两种传播途径来解释观察到的霍乱动态。这些结果强调了在检查水源性疾病时纳入环境数据的重要性。
