Integrating epidemiological modeling and time-series forecasting to optimize pandemic patient allocation

This paper addresses the challenge of allocating patients to healthcare facilities with limited capacities during infectious disease outbreaks. The method is based on a hierarchical time-series model to forecast hospital bed demand and a mixed-integer nonlinear mathematical model for allocating patients among a set of regions to minimize disease spread. Our contributions include (1) a new hierarchical time-series model for forecasting hospital bed demand to enhance regional predictive accuracy, (2) a mathematical model that integrates the forecasting model with a Susceptible, Infected, Recovered (SIR) epidemic model to capture metapopulation dynamics and the impact of patient allocation on disease spread across regions, and (3) a sensitivity analysis to assess the importance of the optimization and forecasting parameters on allocation performance. The proposed approach is illustrated with a real-data case study from the COVID-19 pandemic in Florida which demonstrates that forecasting performance depends strongly on regional hospital capacity. The hierarchical model performs better in high-capacity regions, while the univariate model is more effective in regions with sparse bed availability. At the state level, both models yield comparable objective function values, but they lead to markedly different spatial distributions of unmet demand. The sensitivity analysis enables us to study the contributions of individual factors and shows that decision-making frequency plays a more critical role. Based on these findings, monthly decision intervals are recommended and forecasting model selection should be tailored to regional capacity. The results highlight the practical effectiveness of the proposed approach and its ability to capture trade-offs in patient allocation strategies. By explicitly modeling the additional disease transmissions resulting from patient reallocations across counties, the proposed framework offers actionable insights to support healthcare preparedness and operational decision-making during pandemics.