A novel approach to forecasting reproduction numbers of spatiotemporal stochastic epidemic spread using a PDE-based model and real-time infection data.

The COVID-19 pandemic highlighted the need for improved epidemic spread forecasting, a critical precursor for developing optimal control measures for spread mitigation. Well-recognized shortcomings in computing basic and effective reproduction numbers ( , )-fundamental metrics for forecasting-underscore the need for new methods for estimating them from available data. We present a novel computational framework for estimating reproduction numbers from empirical spread data. The framework is derived from a mechanistic, spatiotemporal, Partial Differential Equation (PDE) model of epidemic spread utilizing mathematical results from PDE epidemic models. Forecasts of spatiotemporal effective reproduction number using the framework are found to be in excellent agreement with COVID-19 spread trends for Hamilton County, Ohio, USA, for three distinct periods. Furthermore, the forecasts are shown to align with corresponding reproduction numbers computed independently using the Wallinga-Teunis and Cori retrospective methods used in epidemiology. In summary, the results establish the validity of the framework and indicate applicability to future epidemics-especially for regions such as counties and for timeframes extending in weeks-even during dynamic phases when obtainable real-time infection spread data will likely be sparse.