Estimating rates of SARS-CoV-2 lineage spread using graph spectra from genetic sequence data

The modern enormous scale of viral genomic data, as exemplified by SARS-CoV-2, presents unique opportunities for epidemic inference and real-time monitoring. A key challenge is to wade through the extremely large stream of sequence data in order to identify small subsets of sequences that may represent rapid population growth of newly emerged lineages. To address this challenge, we developed a new approach that combines techniques in graph theory and machine learning. We represent distances between small subsets of sequences as graph Laplacians and identify from them features of rapid population growth. From early sequence data collected in the US and the UK between 2021 and mid-2022, we identified two features-genetic diversity and graph connectivity-that allow us to reliably estimate growth rates of newly emerged lineages. To test our model, we used data collected from mid-2022 to end-2024 and accurately inferred the growth rates of lineages that appeared during this period. Furthermore, we demonstrate that for data collected in 2023 when the sequencing efforts were relatively high (thousands of sequences per day) in the US and the UK, our model correctly identified the most rapidly expanding lineages when they were still at low frequencies. Overall, our work provides a scalable and adaptable tool to estimate the growth rate of newly emerged SARS-CoV-2 lineages.