MPOPHC: A Novel Mean-Field Game Modeling Framework with Interdependent Health Policies and Public Opinions Feedback Loop for Real-Time Public Health Decision Support

Mathematical models, particularly ones that characterize key epidemiological mechanisms such as transmission, enable public health policymakers to estimate epidemic risks, quantify uncertainties, and evaluate policy implications throughout epidemics. This project aims to address deficiencies in current mechanistic modeling paradigms by further integrating the often-neglected feedback loop among various public health policies (such as vaccination and non-pharmaceutical interventions), dynamic public opinions toward these policies during different phases of an epidemic, and critical outcomes such as hospitalization and death. This project establishes a detailed, integrated system encompassing policy, opinion, and epidemic dynamics, supported by robust mathematical methodologies and novel computational opinion mining approaches. This system will serve as a resource for developing, evaluating, and adjusting public health policies. The methodology developed can be applied to mechanistic models beyond the scope of this project, contributing to the broader field of mathematical epidemiology. Additionally, this project seeks to train the next generation of multidisciplinary modeling and public health teams, ensuring more precise situational awareness and policy support, ultimately enabling our society to stay ahead of the curve in future epidemics. This project aims to develop and deliver innovative mathematical models for the co-evolution of public opinions and epidemic dynamics within the framework of mean field games (MFGs), resulting in an integrated system of epidemic MFG equations. The MFG approach captures the complex feedback among public health policies, dynamic public opinions, and epidemic outcomes that are not well captured by the commonly used susceptible-exposed-infected-recovered (SEIR)-type compartment and agent-based models. MFGs will significantly enhance our ability to track the coupled public opinion-epidemic system under spatially and temporally heterogeneous health policies. Additionally, this project will develop robust convexification numerical methods with guaranteed global convergence to accurately infer critical parameters (e.g., transmission coefficient, recovery rate, ...) from observed data, treating these as coefficient inverse problems. Furthermore, advanced natural language processing techniques, including content analysis and sentiment analysis, will be developed to characterize real-time public opinion and estimate compliance with various health policies across time and space. The integrated MFG system will be simulated under various scenarios, such as different public health policies and varying compliance, to predict future epidemic outcomes for policy decision support. This award is jointly funded by the NSF Division of Mathematical Sciences (DMS) through the Mathematical Biology program and Division of Environment Biology (DEB). This project was also co-funded in collaboration with the CDC.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.