NSF Award
2436332
During the COVID-19 pandemic, it was observed that individuals did not always follow mitigation policies closely. Instead, they behaved according to their own objectives, where demographic and socioeconomic factors seemed to have influenced their responses to the set policies. Therefore, this project aims to improve the policymaking processes to mitigate the transmission of respiratory pathogens by incorporating the individuals’ decision-making and socio-demographic heterogeneities. To do this, the investigators propose to develop and study game theoretical mathematical models, as well as simulation tools and numerical approaches that can be adapted to specific public health problems of interest to practitioners and researchers. These tools will be made publicly available. This project will also involve interdisciplinary training for graduate students in applied mathematics, statistics, operations research, epidemiology, and quantitative biology.<br/><br/>To model many interacting agents, the investigators will develop and study extensions of mean field games (MFGs). First, they will focus on building multi-population MFGs and graphon games to incorporate socio-demographic heterogeneities while finding the Nash equilibrium responses of individuals under different disease mitigation policies (e.g., vaccination policies and non-pharmaceutical interventions). Furthermore, different equilibrium notions to incorporate altruism in the populations will be explored through the introduction of mixed multi-population MFGs that include both cooperative and non-cooperative individuals. Later, the investigators will focus on finding optimal mitigation policies by using Stackelberg MFGs that include the optimization of a regulator (e.g., a governmental institution). The extensions of Stackelberg MFGs that include heterogeneities in the mean field populations, altruistic behaviors, and possible state variables for the regulator will be developed and analyzed. Surveys and analyses of publicly available data will be conducted to calibrate and parameterize the mathematical models to capture real-life patterns. Finally, numerical approaches and simulation toolboxes will be implemented to solve large dimensional and more complex models, which will allow policymakers to adapt and parametrize our models according to their specific needs. <br/><br/>This award is co-funded by the NSF Division of Mathematical Sciences (DMS) and the CDC Coronavirus and Other Respiratory Viruses Division (CORVD).<br/><br/>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.
