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Since its emergence in late 2019, SARS-CoV-2 has diversified into a large number of lineages and caused multiple waves of infection globally. Novel lineages have the potential to spread rapidly and internationally if they have higher intrinsic transmissibility and/or can evade host immune responses, as has been seen with the Alpha, Delta, and Omicron variants of concern. They can also cause increased mortality and morbidity if they have increased virulence, as was seen for Alpha and Delta. Phylogenetic methods provide the "gold standard" for representing the global diversity of SARS-CoV-2 and to identify newly emerging lineages. However, these methods are computationally expensive, struggle when datasets get too large, and require manual curation to designate new lineages. These challenges provide a motivation to develop complementary methods that can incorporate all of the genetic data available without down-sampling to extract meaningful information rapidly and with minimal curation. In this paper, we demonstrate the utility of using algorithmic approaches based on word-statistics to represent whole sequences, bringing speed, scalability, and interpretability to the construction of genetic topologies. While not serving as a substitute for current phylogenetic analyses, the proposed methods can be used as a complementary, and fully automatable, approach to identify and confirm new emerging variants., Competing Interests: Competing interests statement:The authors declare no competing interest.

Persistent SARS-CoV-2 infections may act as viral reservoirs that could seed future outbreaks 1-5 , give rise to highly divergent lineages 6-8 and contribute to cases with post-acute COVID-19 sequelae (long COVID) 9,10 . However, the population prevalence of persistent infections, their viral load kinetics and evolutionary dynamics over the course of infections remain largely unknown. Here, using viral sequence data collected as part of a national infection survey, we identified 381 individuals with SARS-CoV-2 RNA at high titre persisting for at least 30 days, of which 54 had viral RNA persisting at least 60 days. We refer to these as 'persistent infections' as available evidence suggests that they represent ongoing viral replication, although the persistence of non-replicating RNA cannot be ruled out in all. Individuals with persistent infection had more than 50% higher odds of self-reporting long COVID than individuals with non-persistent infection. We estimate that 0.1-0.5% of infections may become persistent with typically rebounding high viral loads and last for at least 60 days. In some individuals, we identified many viral amino acid substitutions, indicating periods of strong positive selection, whereas others had no consensus change in the sequences for prolonged periods, consistent with weak selection. Substitutions included mutations that are lineage defining for SARS-CoV-2 variants, at target sites for monoclonal antibodies and/or are commonly found in immunocompromised people 11-14 . This work has profound implications for understanding and characterizing SARS-CoV-2 infection, epidemiology and evolution., (© 2024. The Author(s).)