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Preprint in English | medRxiv | ID: ppmedrxiv-22281255


We derive and introduce the angular reproduction number, {Omega}, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number, R, and the generation time distribution, w. Predominant approaches for tracking the dynamics of pathogen spread either infer R or the epidemic growth rate r. However, R is easily biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. Moreover, R and r may disagree on the relative transmissibility of two epidemics or variants (i.e., rA > rB does not imply RA > RB for variants A and B). We find that {Omega} responds meaningfully to mismatches in w while maintaining most of the interpretability of R. Additionally, we prove that {Omega} > 1 if and only if R > 1 and that {Omega} agrees with r on the relative transmissibility of pathogens. Estimating {Omega} is no harder than inferring R, uses existing software, and requires no generation time measurement. These advantages come at the expense of selecting one free parameter. We propose {Omega} as a useful statistic for tracking and comparing the spread of infectious diseases that may better reflect the impact of interventions when those interventions concurrently change both R and w or alter the relative risk of co-circulating pathogens.

Preprint in English | medRxiv | ID: ppmedrxiv-21267606


The Delta variant of concern of SARS-CoV-2 has spread globally causing large outbreaks and resurgences of COVID-19 cases1-3. The emergence of Delta in the UK occurred on the background of a heterogeneous landscape of immunity and relaxation of non-pharmaceutical interventions4,5. Here we analyse 52,992 Delta genomes from England in combination with 93,649 global genomes to reconstruct the emergence of Delta, and quantify its introduction to and regional dissemination across England, in the context of changing travel and social restrictions. Through analysis of human movement, contact tracing, and virus genomic data, we find that the focus of geographic expansion of Delta shifted from India to a more global pattern in early May 2021. In England, Delta lineages were introduced >1,000 times and spread nationally as non-pharmaceutical interventions were relaxed. We find that hotel quarantine for travellers from India reduced onward transmission from importations; however the transmission chains that later dominated the Delta wave in England had been already seeded before restrictions were introduced. In England, increasing inter-regional travel drove Deltas nationwide dissemination, with some cities receiving >2,000 observable lineage introductions from other regions. Subsequently, increased levels of local population mixing, not the number of importations, was associated with faster relative growth of Delta. Among US states, we find that regions that previously experienced large waves also had faster Delta growth rates, and a model including interactions between immunity and human behaviour could accurately predict the rise of Delta there. Deltas invasion dynamics depended on fine scale spatial heterogeneity in immunity and contact patterns and our findings will inform optimal spatial interventions to reduce transmission of current and future VOCs such as Omicron.