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Individual models of infectious diseases or trajectories coming from different simulations may vary considerably, making it challenging for public communication and supporting policy-making. Therefore, it is common in public health to first create a consensus across multiple models and simulations through ensembling. However, current methods are limited to mean and median ensembles that perform aggregation of scale (cases, hospitalizations, deaths) along the time axis, which often misrepresents the underlying trajectories -- e.g., they underrepresent the peak. Instead, we wish to create an ensemble that represents aggregation simultaneously over both time and scale and thus better preserves the properties of the trajectories. This is particularly useful for public health where time-series have a sequence of meaningful local trends that are ordered, e.g., a surge to an increase to a peak to a decrease. We propose a novel alignment method DTW+SBA, which combines a representation of local trends along with dynamic time warping barycenter averaging. We prove key properties of this method that ensure appropriate alignment based on local trends. We demonstrate on real multi-model outputs that our approach preserves the properties of underlying trajectories. We also show that our alignment leads to a more sensible clustering of epidemic trajectories. 

During the COVID-19 pandemic, a major driver of new surges has been the emergence of new variants. When a new variant emerges in one or more countries, other nations monitor its spread in preparation for its potential arrival. The impact of the new variant and the timings of epidemic peaks in a country highly depend on when the variant arrives. The current methods for predicting the spread of new variants rely on statistical modeling, however, these methods work only when the new variant has already arrived in the region of interest and has a significant prevalence. Can we predict when a variant existing elsewhere will arrive in a given region? To address this question, we propose a variant-dynamics-informed Graph Neural Network (GNN) approach. First, we derive the dynamics of variant prevalence across pairs of regions (countries) that apply to a large class of epidemic models. The dynamics motivate the introduction of certain features in the GNN. We demonstrate that our proposed dynamics-informed GNN outperforms all the baselines, including the currently pervasive framework of Physics-Informed Neural Networks (PINNs). To advance research in this area, we introduce a benchmarking tool to assess a user-defined model's prediction performance across 87 countries and 36 variants.