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Quantifying Uncertainty in Epidemiological Models

机译：流行病学模型中的不确定性量化

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摘要

Modern epidemiology has made use of a number of mathematical models, including ordinary differential equation (ODE) based models and agent based models (ABMs) to describe the dynamics of how a disease may spread within a population and enable the rational design of strategies for intervention that effectively contain the spread of the disease. Although such predictions are of fundamental importance in preventing the next global pandemic, there is a significant gap in trusting the outcomes/predictions solely based on such models. Hence, there is a need to develop approaches such that mathematical models can be calibrated against historical data. In addition, there is a need to develop rigorous uncertainty quantification approaches that can provide insights into when a model will fail and characterize the confidence in the (possibly multiple) model outcomes/predictions, when such retrospective analysis cannot be performed. In this paper, we outline an approach to develop uncertainty quantification approaches for epidemiological models using formal methods and model checking. By specifying the outcomes expected from a model in a suitable spatio-temporal logic, we use probabilistic model checking methods to quantify the probability with which the epidemiological model satisfies a given behavioral specification. We argue that statistical model checking methods can solve the uncertainty quantification problem for complex epidemiological models.
机译：现代流行病学已经利用了许多数学模型，包括基于普通微分方程（ODE）的模型和基于代理的模型（ABM）来描述疾病在人群中的传播动态，并能够合理设计干预策略有效地控制了疾病的传播。尽管这样的预测对于防止下一次全球大流行具有根本的重要性，但是在完全基于这种模型的结果/预测的信任上仍然存在很大差距。因此，需要开发一些方法，使得可以针对历史数据校准数学模型。另外，需要开发严格的不确定性量化方法，这些方法可以提供何时模型失败的见解，以及在无法执行此类回顾性分析时表征（可能为多个）模型结果/预测的置信度的特征。在本文中，我们概述了一种使用形式化方法和模型检查为流行病学模型开发不确定性量化方法的方法。通过以合适的时空逻辑指定模型的预期结果，我们使用概率模型检查方法来量化流行病模型满足给定行为规范的概率。我们认为统计模型检查方法可以解决复杂的流行病学模型的不确定性量化问题。

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