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建模与人类行为的经济模型之间的差距。COVID-19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与人类行为变化之间的相互依赖关系。在数学生物学和经济学领域分别取得了令人兴奋的进展。 该项目采取了一种融合的方法，结合人类如何应对和做出决定，作为一种流行病的展开，使用两个学科的关键思想和方法。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（MPS）数学科学处（DMS）和社会、行为和经济科学局（SBE）社会和经济科学处（SES）共同资助。经济（博弈论）模型的个人决策集成到一个连续时间马尔可夫链框架的疾病和接触动力学。在这种方法下，流行病和接触网络率受到个体最优代理行为的影响，而个体最优代理行为又取决于代理的（不可观察的）社会经济成本。基于可能性的推理方法，以适应时间不均匀的速率参数推导，大大扩展了现有模型的灵活性和现实性，同时严格的算法参数估计和不确定性量化。贝叶斯数据增强用于通过潜变量对不可观测的量以及缺失数据进行概率解释。使用信息理论标准的模型选择同时量化了从行为模型中获得的拟合改善，并防止过拟合。基于学习到的模型参数，对提出的模型进行测试，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知识价值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.