RAISE: IHBEM: Equilibrium, Network Formation, and Infectious-Disease Spread: Bridging the Divide between Mathematical Biology and Economics

该项目将弥合流行病过程的数学和统计模型与人类行为的经济模型之间的差距。新冠肺炎大流行表明，需要一套新的数学模型和相应的推理工具，以更好地理解传染病传播和不断变化的人类行为之间的相互依存关系。数学生物学和经济学分别取得了令人振奋的进展。这个项目采取了一种融合的方法，利用两个学科的关键想法和方法，纳入了人类如何在疫情展开时做出反应和决策。这对于实现可靠的预测和有效的实时政策至关重要。该项目由数学和物理科学局的数学科学部(DMS)和社会、行为和经济科学局(SBE)的社会和经济科学部(SES)共同资助。在这个项目中，个体决策的经济(博弈论)模型被集成到疾病和接触动力学的连续时间马尔可夫链框架中。在这种方法下，流行病和接触网络比率受到个体最优代理人行为的影响，而最优代理人行为又取决于代理人(不可观测的)社会经济成本。推导出了适应时间非齐次利率参数的基于似然的推理方法，极大地扩展了现有模型的灵活性和现实性，以及用于参数估计和不确定性量化的严格算法。贝叶斯数据扩充用于通过潜在变量对不可观测的数据量以及丢失的数据进行概率解释。使用信息论标准的模型选择同时量化了从行为模型中获得的适合度的改善，并防止过度适配。根据学习到的模型参数，测试建议的模型，评估可能的爆发情景，并通过模拟研究和限制行为分析比较替代政策的影响。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。

This project will bridge the gap between mathematical and statistical modeling of epidemic processes and economic models of human behavior. The COVID-19 pandemic has demonstrated the need for a new suite of mathematical models and corresponding inference tools to better understand the interdependence between the spread of infectious disease and changing human behaviors. Exciting progress has been made separately in mathematical biology and in economics. This project takes a convergent approach, incorporating how humans respond and make decisions as an epidemic unfolds, using key ideas and methodologies from both disciplines. This is critical to enable reliable forecasting and effective, real-time policy. This project is funded jointly by the Division of Mathematical Sciences (DMS) in the Directorate of Mathematical and Physical Sciences (MPS) and the Division of Social and Economic Sciences (SES) in the Directorate of Social, Behavioral, and Economic Sciences (SBE).In this project, an economic (game-theoretic) model of individual decision-making is integrated into a continuous-time Markov chain framework for disease and contact dynamics. Under this approach, epidemic and contact network rates are affected by individually optimal agent behavior, which in turn depend on agents' (unobservable) social-economic costs. Likelihood-based inference methods to accommodate time-inhomogeneous rate parameters are derived, considerably extending the flexibility and realism of existing models, alongside rigorous algorithms for parameter estimation and uncertainty quantification. Bayesian data augmentation is used to account probabilistically for unobservable quantities as well as missing data via latent variables. Model selection using information-theoretic criteria simultaneously quantifies the improvement in fit reaped from behavioral models and guards against overfitting. Based on learned model parameters, proposed models are tested, possible outbreak scenarios are evaluated, and the impacts of alternative policies are compared via simulation studies and analyses of limiting behaviors.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.