  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.
