EpiGF: Epidemic Prediction and Inference with Generating Functions

Epidemics are persistent threats to human health, yet epidemiological data are always limited and generally delayed, hindering prevention and control measures. Improving real-time epidemic information and performing robust short-term forecasts would enhance our ability to limit the impact of epidemics. One key limitation of most current approaches is that they capture either the biology of the transmission process or statistical trends in the epidemiological data, but rarely both. The investigators will develop a novel approach that characterizes transmission chains as branching processes, enabling mathematical approaches to link the transmission biology directly to the reported epidemiological data. In a pilot project, they showed that this approach could make quality real-time influenza hospitalization forecasts. Here, they will develop these methods to link transmission across jurisdictions and incorporate multiple epidemiological outcomes (e.g., cases and wastewater testing data). They will evaluate these methods extensively using influenza and COVID-19 data to assess their robustness for situational awareness and forecasting in the United States. This work will improve scientific understanding of the transmission of infectious disease as well as the ability to model transmission in real-time, providing new open tools and training materials to improve preparedness and response. To further validate these approaches compared to other methods and to maximize their utility, the investigators will deliver real-time analyses to state, territorial, and local health departments and the Centers for Disease Control and Prevention. Current infectious disease models rely on complex compartmental structures to capture underlying transmission dynamics, providing a valuable tool to assess spread potential, project impacts, and identify drivers. However, they are challenging to fit to real-time epidemiological data, necessitating simplification or fitting approaches which do not efficiently search parameter space. To overcome current tradeoffs between mechanistic model complexity and efficient inference, the investigators will develop an epidemic analytics framework, EpiGF, that uses probability generating functions to model transmission as a branching process, simultaneously incorporating mechanistic detail and enabling efficient fitting to varied and noisy data. The EpiGF framework will produce robust inference, integrating multiple observed outcomes and mobility data to strengthen inference to estimate the time-varying reproduction number. The investigators will also develop methods to project epidemic trajectories into the future to forecast changes in incidence, leveraging joint estimation of uncertainty in trajectories and observations, and inference on acquired immunity from the underlying infection dynamics. The novel mathematical framework for spatiotemporal epidemic analytics will have specific, advantageous, and practical applications in public health areas where current models have substantial limitations. This framework will facilitate efficient inference on detailed mechanistic infection processes with complex epidemiological observations, addressing the greatest deficiency of existing mechanistic frameworks. As a novel approach to these problems, the EpiGF framework offers transformative analytics for critical health threats such as influenza, COVID-19, and Disease X. This work will also advance the technical foundations of PGF-based inference and make PGFs more accessible for other systems modeled by multitype branching processes. 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.