CAREER: Designing Optimal Sampling Strategies for Epidemiological Models

新出现的传染病是我们世界不可避免的一部分。数学模型可以为科学理解这些复杂和不断变化的系统以及公共卫生政策提供信息。特别是，机械模型，即描述驱动动态、真实世界系统的关键过程的数学模型，以及经验数据，可以用于评估不同控制策略的有效性，或测试关于潜在生物学的不同假设。新冠肺炎疫情既突显了机械化模型的重要性，也突显了实施这些模型为政策提供信息所面临的挑战。其中一个跨学科的挑战是，现有数据与为这些模型提供信息并减少模型产出和预测中的不确定性所需的数据之间存在不匹配。模型与数据的不匹配可能导致关于哪种控制政策在实现特定目标方面最有效的错误结论。该项目旨在创建一种方法，为给定的数学模型找到最具成本效益的数据收集方法，以便该模型产生可靠的输出和不确定性测量。将这些方法应用于新冠肺炎、寨卡病毒和埃博拉病毒等最近的案例研究，可以为应对未来大流行的适当应对措施提供信息，并提高对未来大流行的准备。这些方法也将适用于生态学和生理学领域，在这些领域，整合建模和实证研究的总体目标对取得进展至关重要。作为研究目标的一部分，是一项针对本科生的新教育计划，该计划在STEM具有未被认识到的潜力。一系列教学模块将使用协作和基于探究的方法，让学生学习数学建模、编码和可视化的基础知识。参与者将通过使用与拟议项目相关的流行病学模型来磨练这些技能，并将利用他们作为具有不同背景的新手建模师的创造力和独特视角在公众中推广模型素养。解决模型数据不匹配问题的一种方法是首先评估模型的实际可识别性，即在给定特定数据集的情况下，从数据中毫不含糊地估计模型参数的能力。从一个实际无法识别的模型得出的结论可能并不可靠。此外，确定流行病学模型实际可识别性的常用方法依赖于简单的似然模型(与给定模型参数的观察数据的概率成正比的函数)，这些模型对流行病学数据做出不切实际的假设，而实际上这些数据高度相关且复杂。对真实似然模型的较差近似可能会导致对模型输出中的不确定性的不准确估计。使用适当的可辨识性度量和改进的(但易于处理的)似然模型，控制理论可用于在有限的公共卫生资源的约束下得出数据抽样策略，从而使模型实际上是可辨认的。方法是找到联合最小化可识别性度量和采样策略成本的采样协议。这些新方法将使用合成数据进行测试，并应用于最近的疫情，以确定哪些数据采样策略足以减少模型参数估计中的不确定性，从而减少模型输出中的不确定性。该奖项由MPS数学科学部门(DMS)通过数学生物学计划和环境生物学部门通过人口和社区生态(PCE)集群共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Emerging infectious diseases are an inevitable part of our world. Mathematical models can inform scientific understanding of these complex and ever-changing systems, as well as public health policy. In particular, mechanistic models, mathematical models that describe the key processes that drive dynamic, real-world systems, along with empirical data, can be useful for assessing the efficacy of different control strategies, or testing different hypotheses about the underlying biology. The COVID-19 pandemic has underscored both the importance of mechanistic models and the challenges of implementing these models to inform policy. One of these challenges, which spans disciplines, arises when there is a mismatch between the data available and the data required to inform these models and reduce uncertainty in model outputs and predictions. A model-data mismatch could lead to erroneous conclusions about which control policies will be most effective at achieving a particular goal. This project aims to create a methodology that finds the most cost-effective approach to data collection for a given mathematical model, such that the model produces reliable outputs and measures of uncertainty. Applying these methods to recent case studies like COVID-19, Zika, and Ebola can inform appropriate responses to, and improve preparedness for, future pandemics. These methods will also be applicable to areas of ecology and physiology, where the overarching goal of integrating modeling and empirical studies is critical to progress. Integral to the research objectives is a new education program targeting undergraduate students, with unrecognized potential in STEM. A series of educational modules will engage students in the fundamentals of mathematical modeling, coding, and visualization, using a collaborative and inquiry-based approach. Participants will hone these skills by working with epidemiological models related to the proposed project, and will use their creativity and unique perspectives as novice modelers with diverse backgrounds to promote model literacy in the general public.One way to address the problem of a model-data mismatch is first to evaluate the practical identifiability of a model, that is, the ability to estimate model parameters unambiguously from data, given a particular data set. Conclusions derived from a practically unidentifiable model may not be robust. Furthermore, commonly used methods to determine practical identifiability of epidemiological models rely on simple likelihood models (functions proportional to the probability of observed data given the model parameters) that make unrealistic assumptions about epidemiological data, which in reality are highly correlated and complex. A poor approximation to the true likelihood model can lead to inaccurate estimates of uncertainty in model outputs. Using appropriate identifiability metrics and improved (yet tractable) likelihood models, control theory can be leveraged to derive data sampling strategies, constrained by finite public health resources, that render a model practically identifiable. The approach is to find sampling protocols that jointly minimize the identifiability metric and the cost of the sampling strategy. These new methods will be tested using synthetic data, and applied to recent outbreaks to determine what data sampling strategies would have been sufficient to reduce the uncertainty in model parameter estimates, and therefore, reduce uncertainty in model outputs.This award is jointly funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and the BIO Division of Environmental Biology through the Population and Community Ecology (PCE) Cluster.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.