## Main

The SARS-CoV-2 pandemic has been characterized by the appearance and spread of genetically distinct virus variants that are associated with faster spread than pre-existing lineages. In May 2021, the World Health Organization (WHO) announced a new variant of concern (VOC), designated Delta. Delta became the variant primarily responsible for a wave of transmission and mortality in India in early-to-mid 2021, replacing Alpha (Pango lineage B.1.1.7) and Kappa (Pango lineage B.1.617.1) in the process3,4. Studies indicate that Delta has increased transmissibility5, rates of hospitalization6 and immune evasion7 compared with Alpha8,9, the variant that was previously dominant in many countries. These phenotypes are attributed to a constellation of 30 mutations across the virus genome (Supplementary Table 2) compared to the Wuhan-Hu-1 reference sequence, including: the spike mutation P681R in the furin cleavage site, which is thought to increase the speed and efficiency with which the virus fuses with host cells10,11; mutation L452R in the receptor-binding domain, which is thought to reduce neutralization by antibodies12; and the nucleocapsid mutation R203M, which is thought to increase virion infectivity13. Delta disseminated rapidly from India to locations worldwide and has been detected in 174 countries as of 12 April 2022 (https://cov-lineages.org/global_report.html). Delta became the dominant lineage in the UK by mid-May 202114, and similar increases in frequency were observed worldwide (for example, ref. 15).

The emergence of Delta in the UK occurred in the context of a heterogeneous landscape of prior immunity (from infection and vaccination) and non-pharmaceutical interventions (NPIs). Here we examine virus genomes generated from a random sample of all COVID-19-positive tests with PCR with reverse transcription (RT–PCR) Ct values greater than 30, collected during community-based testing in England between 12 March 2021 and 15 June 2021. Our data include 52,992 Delta genomes from England with known dates and locations of sampling, representing more than 40% of all positive lateral flow and PCR tests in England during the study period (see Methods and details on case data at https://coronavirus.data.gov.uk/details/about-data; an estimated 27% of COVID-19 infections were detected during the study period16). Using these data, we evaluate the effectiveness of policies in reducing international importations and how they contributed to the establishment and local transmission dynamics of Delta in England. We then investigate, at a high spatial resolution, how human mobility contributed to context-specific growth of Delta in England.

## International importations of Delta

To provide a global context for the emergence of Delta in the UK, we first conducted a phylodynamic analysis by uniformly subsampling SARS-CoV-2 Delta genome sequences by collection date between 4 March 2021 and 15 June 2021 (n = 975). Details of the origin and spread of Delta within India are uncertain. A substantial increase in genomic surveillance across the country would probably facilitate the study of the emergence and expansion of Delta there, but is outside the scope of this work. To put the UK epidemic into context, we estimated the time of the most recent common ancestor (TMRCA) of Delta globally to be 19 October 2020 (95% highest posterior density (HPD) interval: 6 September 2020 to 29 November 2020). The relative frequency of Delta in India does not appear to increase substantially until March 2021 (Fig. 1), coinciding with a rapid expansion in case numbers there (Extended Data Fig. 1) and a decline in the relative frequency of genomes assigned to Kappa, a sibling lineage of Delta (https://www.gisaid.org/). Genomic surveillance in India revealed that several sub-lineages of Delta existed prior to its expansion in March17 (Fig. 1a,b). This standing diversity is consistent with undetected transmission of Delta in India between late 2020 and March 2021.

We evaluated the global dissemination of Delta from March 2021 by multiplying, for each country, estimated numbers of SARS-CoV-2 cases, relative frequencies of Delta, and relative numbers of outward international passengers (estimated exportation intensity (EEI);  Methods). The EEI of Delta increased rapidly during March 2021 and was highest around late April 2021, coinciding with its peak incidence in India (Extended Data Fig. 1). The subsequent rapid spread of Delta in the USA, Russia, UK, Mexico and elsewhere and its decline in India resulted in the former locations becoming main exporters of Delta by June 2021 (Extended Data Fig. 1), corroborating global trends in Delta phylogeography (Fig. 1a) and reported cases (Fig. 1b). Similar patterns of rapidly changing foci of international dissemination were observed for the initial wave of SARS-CoV-2 in 202018.

To evaluate the temporal dynamics of Delta importation into England and to reconstruct its subsequent local spread, we conducted a travel history-aware Bayesian phylogeographic analysis19 of 93,649 Delta sequences, from GISAID and COVID-19 Genomics UK Consortium (COG-UK), which accounts in part for the phylogenetic uncertainty inherent in SARS-CoV-2 phylogenies18. To render the analysis tractable, we split the full tree into three independent subtrees (Fig. 1a) prior to phylogeographic analysis. Virus genomes were generated from around 40–60% of all positive cases in England during the emergence of Delta between March and May 202120 (Fig. 1c) and combined with metadata on the locations (at the upper tier local authority (UTLA) level), enabling us to trace the introduction of the virus and characterize its spread at a high spatio-temporal resolution20.

We estimated a minimum of 1,458 (95% HPD 1,398–1,513) separate international introductions of Delta into England, with approximately half inferred to have originated from India (posterior mean 56.5%; 95% HPD 53.7%–59.1%). We found that the majority of Delta genomes in England can be traced back to introductions that are inferred to have occurred prior to the implementation of a mandatory hotel quarantine for people arriving from India on 23 April 2021 (posterior mean 84.3%; 95% HPD 77.8–90.4%). During this period, 90.0% of introductions are inferred to have originated from India (95% HPD 86.5–93.1%). These inferred importation dynamics closely match data on individual travel histories obtained from infected incoming international passengers (origin–destination travel histories are available for 1.4% of genomes; n = 770) (Fig. 2b and Extended Data Fig. 2).

The high variation in sampling intensity among countries (specifically, the higher sampling intensity in England than in other countries) means that the true number of importations into England is probably much larger than that inferred from phylogeographic analysis alone (Fig. 1b,c; see the related discussion in the context of the first wave in the UK18). For example, the AY.4 lineage (Fig. 1a) comprises 42,445 sequences and was probably imported to England many times. We investigated AY.4 by pairing genomic data with contact tracing data collated by Public Health England (now the UK Health Security Agency). During the study period we found 61 sequenced cases with AY.4 had a travel history from India and 140 had a travel history from elsewhere, similar to the time-varying importation dynamics seen across the entire dataset (Fig. 2a and Extended Data Fig. 2). Thus, sampling heterogeneity means that the number of importations estimated from phylogenetic analysis represents a lower bound on the true number18.

To investigate the importation of Delta into England specifically, and to cross-validate the results above using independent data, we use the estimated importation intensity (EII) of Delta to England over time18,21. The EII is a metric of Delta importation that represents trends in the number of Delta cases arriving in the country, irrespective of whether or not those cases result in local transmission. This is distinct from the phylogenetic analysis above, which better captures trends in the number of Delta introductions that did lead to forward transmission in England. The EII combines (1) weekly reported cases, (2) weekly prevalence of Delta genomes, and (3) weekly aggregate human mobility (inferred from mobile phone data) into England through direct connections (Fig. 2a; see refs. 18,21 for related approaches). The EII from India increased rapidly in April 2021 following the rise in cases in India, and remained high until the end of May 2021. EII correlates strongly with the inferred importations from genomic data but is weaker for imports from India after the implementation of hotel quarantine (Extended Data Fig. 3). We then estimate, from genomic data, the proportion of inferred importations that led to observed onward transmission in the community (defined as at least one ancestral node in England), stratified by location of origin in the three weeks pre- and post-implementation of hotel quarantine. We find that pre-quarantine, 37.7% (95% HPD 34.0%–41.7%) of importations from India led to observable onward transmission. After the implementation, the fraction of importations from India leading to observed onward transmission dropped to 26.9% (95% HPD 23.0%–30.2%) (Fig. 2c). For comparison, the proportion of introductions from other locations leading to onward transmission did not change during the two periods (around 50%) (Fig. 2c). The decrease in onward transmission is most apparent in importations associated with travel history, which suggest the trend is driven by the implementation of hotel quarantine and not temporal biases in lineage detection (Extended Data Fig. 3). Even though we observe that the implementation of hotel quarantine was effective in reducing onward transmission, substantial importation had already occurred before its implementation and additional introductions from other countries probably further accelerated the spread of Delta in England from May onwards (Fig. 2a).

There are several reasons why some importations led to onward transmission within England after the implementation of hotel quarantine for arriving travellers: (1) a separate terminal for arrivals from mandatory quarantine countries was not opened at the UK’s largest airport (London Heathrow) until 1 June 202122, so arriving passengers may have mixed with others before entering mandatory quarantine; (2) individuals may have become infectious and transmitted the virus only after leaving quarantine, either owing to an unusually long latent period or within-group transmission during the quarantine period; (3) individuals may have infected others on a connecting flight where the connecting airport did not require hotel quarantine; (4) there were exemptions to hotel quarantine that may have led to onward transmission in the community23.

## Lineage dynamics of Delta in England

Importations of Delta occurred on a background of relaxation of social distancing in England: on 12 April 2021, outdoor dining and non-essential retail reopened, and on 17 May 2021, restrictions on indoor dining and international travel were relaxed24. The relative frequency of Delta genomes in England increased rapidly during May and the number of reported COVID-19 cases subsequently increased25 (Fig. 1c). Initially, Delta transmission clusters were concentrated in the North West region of England and were commonly associated with returning travellers26. We sought to reconstruct the dispersal dynamics of independently imported Delta transmission lineages within England, in the context of changing NPIs.

We analysed all identified Delta transmission lineages in England and inferred their history of dissemination among subnational regions (UTLAs). Sequence sampling was highly representative of reported cases at the UTLA level (Extended Data Fig. 4), making possible the reconstruction of virus movements across England using continuous phylogeography approaches27. We observe high heterogeneity among UTLAs in the numbers of Delta introductions from other English regions (Fig. 3a), with Lancashire and Greater Manchester each receiving more than 2,000 estimated independent introductions and Torbay receiving only 9. The majority (n = 11,960) of Delta sequences in England belong to a single transmission lineage (lineage I) (Fig. 3d), which was sampled mostly in Greater Manchester and Lancashire, and we observe many short-range lineage movements among UTLAs in these areas (Fig. 3a). Greater London also received many Delta cases from elsewhere in England (Fig. 3a), as expected, given its population size and connectedness to other metropolitan areas21. Transmission lineages II and III each comprised 3,000–4,000 genomes; lineage II is distributed across multiple urban areas (especially in the North West), whereas the latter is focused in Greater London and the South East (Fig. 3d). We also highlight transmission lineage V (Fig. 3d), originally centred in Bedfordshire, the location of one of the first Delta outbreaks in England that was subject to surge testing28 (Extended Data Fig. 5).

In early May 2021, the number of virus lineage movements among locations accelerated (Fig. 3b and Extended Data Fig. 5), showing that increase in Delta frequency (Fig. 1c) was associated with regional dissemination. This spread occurred on the background of relaxing NPIs and increased mixing (between mid-January and June 2021, mobility in England increased from 20% to 70% of its pre-pandemic level, and estimated mean daily contacts increased29 from approximately 2 to 5). By contrast, the initial wave of SARS-CoV-2 introductions to the UK in spring 2020 occurred during a period of increasing travel and social restrictions18. In general, we find that as NPIs were progressively relaxed over time, long-range viral lineage movements comprised an increasing proportion of all movements (Fig. 3c).

For the seven largest Delta transmission lineages in England (I–VII) we observed approximately three times more exports from Greater Manchester than from Greater London. Further, we observe that Bolton, Blackburn, Salford, Bury and Greater Manchester had on average higher than expected numbers of exportations for their population sizes (Extended Data Fig. 6). This difference matches early epidemiological data: the largest and earliest Delta outbreaks were in North West England (on 21 May, Bolton had 452 cases per 100,000 population and Greater London had 21.6 cases per 100,000 population) (https://coronavirus.data.gov.uk/Methods). Introductions of Delta into other, smaller urban areas also spread rapidly (for example, transmission lineage V) (Fig. 3d) and were important for the propagation of the variant across England. We observe a spatial structure of the seven largest lineages; the frequency of viral movements declined with the distance away from the origin location but we also observe a second peak at around 260 km (similar to the distance between Greater London and Greater Manchester) (Extended Data Fig. 7). Although North West England was a focus of early Delta transmission, the Delta epidemic in England derived from many successful independent international importations. Each of the main Delta transmission lineages in England grew at a similar rate (Extended Data Fig. 8). By contrast, the Alpha variant expanded across the UK from a single origin in South East England21. The spatial expansion of Delta transmission lineages plateaued after early June, when most UTLAs had established Delta transmission and the relative frequency of Delta genomes in England had exceeded 90% (https://covid19.sanger.ac.uk/lineages/raw).

Although Scotland, Wales or Northern Ireland were not included here, case count data suggest that cities in England (https://coronavirus.data.gov.uk/details/download) were the main source of the expanding Delta epidemic in the UK; owing to this source-sink structure we do not anticipate that omitting these countries substantially affects our reconstruction of epidemic dynamics in England (of the Delta genomes available before 15 June 2021, 57,592 were from England, 9,738 were from Scotland, 1,067 were from Wales and 325 were from Northern Ireland).

## Factors contributing to the growth of Delta

Regional and international heterogeneity in incidence, vaccination and human mobility determine the dynamics of infectious diseases30, including those of SARS-CoV-218,31,32. We used a combination of epidemiological, aggregate human mobility and genomic data to test whether relaxation of NPIs, virus importations and vaccination rates correlate with local Delta growth rates. To do so, we developed a hierarchical Bayesian model to estimate the effect of these factors on the weekly relative growth of Delta (that is, the weekly change in the observed proportion of Delta genomes on a log odds scale33) at the UTLA level for England. Models for estimating the increase in transmissibility of new variants are typically based on increases in relative frequency1,33 but rarely take into account other potential confounding factors, such as variation in population behaviour, vaccination rates or numbers of independent virus introductions.

In general, growth rates varied widely across locations and weeks in England (Fig. 4a and Extended Data Fig. 10). Our model estimates that the most important tested predictor of the variation in growth of Delta (relative to Alpha) across UTLAs in England was within-UTLA mixing (that is, relative changes in weekly within-UTLA human mobility, compared with the pre-pandemic period) (Fig. 4a,b and Supplementary Tables 5 and 6). The importance of within-UTLA mobility as a factor during the emergence of a new variant (until Delta prevalence reached 85% (25%–75% quantiles: 78%–96%)) is unsurprising, as pre-emptive restrictions on movement and social mixing slow the emergence of new pathogens or variants34 (see counterfactual scenarios in Extended Data Fig. 10); the cost/benefit ratio of such restrictions will of course depend on the specific context of variant emergence. The relaxation of NPIs therefore increased both within- and among-region transmission (see Fig. 3c). Other European countries did not observe such a rapid increase in Delta relative frequency during May 2021 (https://www.gisaid.org/); possible reasons for this difference are (1) during this period, levels of mobility and mixing (both local and regional) were lower in those countries and/or (2) those countries potentially received fewer international importations of Delta (86,489 passengers flew from India to the UK between March and June, whereas 43,515 flew to Germany, and 16,688 flew to France, during the same period).

Model fit did not improve when including weekly numbers of independent viral introductions estimated from genomic data or vaccination rates (Supplementary Table 6). We refrained from translating estimates of the growth rate of Delta relative frequency into differences in the reproduction number, as this is sensitive to assumptions about the generation time of the variant, which is also influenced by NPIs and immunity35. Further studies should consider estimating the generation times of VOCs in specific contexts of immunity, NPIs and household structure36 to accurately translate relative growth rates into Rt.

## Discussion, limitations and future work

We find that growing epidemics of SARS-CoV-2 Delta worldwide led to a wave of importations of the VOC into England, initially from India, and later from other countries. These importations found fertile ground as they arrived in a context of easing social restrictions, and consequently expanded rapidly across England. Much transmission occurred in unvaccinated and younger populations (https://coronavirus.data.gov.uk/details/download), and high levels of Delta transmission within the UK led to onward dissemination of the variant to other countries (see for example, ref. 37). By pairing the phylogenetic results with contact tracing data we conclude that hotel quarantine measures were effective in reducing onward transmission of imported Delta cases in England. However, after 21 May 2021, we found that levels of local social mixing in England—and not numbers of importations—were associated with faster relative growth of Delta. At that point, the independently introduced transmission lineages grew at a similar pace; details of their geographic distribution and expansion will support future work defining the optimal spatial interventions to reduce transmission of VOCs in England.

Compared with the Alpha variant, which arose and spread from a single location in South East England18, the expansion of the Delta variant was predominantly owing to exports from the North West (Fig. 3). Analysis of the Alpha variant and of the first wave of SARS-CoV-2 in spring 2020 suggested that Greater London had a substantial role in spreading SARS-CoV-2 across England, as expected, given it is the largest city in England by far, and is highly connected by road, rail and air to other locations. However, Greater London was less important in the spread of Delta, even after Delta had become established there. This indicates the importance of founder effects; where a VOC first becomes established within a country may have a strong effect on subnational spatial dissemination, and this information is useful for planning localized interventions.

Furthermore, although there are intrinsic differences in transmissibility between VOCs, the role of NPIs and levels of immunity from prior infection or vaccination also affect their dynamics. After the start of the first UK national lockdown during the first wave of infections in 2020, lineage movements were severely curtailed and most lineages went extinct18; by contrast, the viral movement of Delta lineages increased after the relaxation of NPIs, accompanied with a subsequent rise in positive cases (Fig. 3). For the most recent VOC, Omicron, NPIs have remained relatively stable throughout England, and the increase in cases of the Omicron subvariant BA.2 in more rural areas in the South West in February and March 2022 has been speculated to be a result of lower infection rates there during the previous Omicron BA.1 wave38 (December 2021–January 2022). Therefore, the effect of seeding location, immunity from previous waves or vaccination and NPI changes all contribute to the large and continued spatial heterogeneity in the spread of VOCs.

The undetected genetic diversity and uneven sampling of Delta in India make the precise estimation of the number of importations to England difficult to achieve from genetic data alone27 (Extended Data Fig. 9). However, our phylogenetic estimates correlate strongly with estimates derived from independent data on case incidence, Delta prevalence and arriving travellers (EII) (Methods and Fig. 2c) during the period before quarantine policies were announced. Fortunately, additional contact tracing data from public health agencies enabled us to overcome the limitations inherent in the unevenly sampled global virus genomic dataset and provide additional confidence in our findings.

Our statistical analysis shows that higher Delta growth rates were positively associated with levels of local mixing in England. The existence and magnitude of future NPIs needed to reduce the healthcare burden of future VOCs to sustainable levels will depend on the local levels of population immunity (from vaccination and prior infection). Future work should focus on identifying the factors that are most conducive to spread in particular contexts (for example, high versus low NPI regimes and across levels of population immunity39) so that responses can be planned accordingly. This will require a better characterization of the distribution and variation of infectiousness over time, and an understanding of the virus generation time in different behavioural contexts40—for example, among individuals who are vaccinated or unvaccinated and/or those who have had previous exposure to SARS-CoV-2 (including knowledge of the lineage or variant). To do so effectively will require investments in large-scale and coordinated serological studies41, especially for VOCs with the ability to evade immunity.

Even though reporting of case numbers, virus genomic surveillance, sampling strategies and mobile phone penetration differ across the world, our estimates can still provide qualitative insights into the trends in the source locations and the rates of international importation. Including estimates of probable importations in disease surveillance programmes may help support public health decision making42, and further improvements in these estimates can be achieved when global health surveillance systems are more integrated, and investments in data generation and capacity are linked directly to paired genomic–epidemiological analytical pipelines.

The detail with which we document the spatial invasion process of Delta in England provides an opportunity to re-examine how more spatially targeted interventions can support COVID-19 control in the future. Our work highlights the relative importance of local (within country) behavioural and mobility changes in determining the speed at which Delta spread in England; such changes will probably be more important than international travel restrictions during the emergence of future variants. Globally coordinated data and analytical pipelines that capture heterogeneity in virus circulation, immunity and policy responses will be necessary to produce the insights necessary to curb the spread of emerging infectious diseases and new variants. However, they can only be successful when integrated into a public health framework that can respond and adapt rapidly to public health threats during their emergence.

## Methods

### Genomic data

International (non-UK) sequences were downloaded from GISAID on 15 September 2021 and combined with sequences from England taken as part of community surveillance (pillar 2) available from COG-UK as of September 2021. Each week, each of the pillar 2 testing laboratories selected a number of 96-well plates proportional to the fraction of all testing done at the laboratory, for sequencing. Even though the instruction was that these should be selected randomly, we cannot exclude the possibility of some level of error. However, at the scale at which the COG-UK consortium is operating, we do not anticipate that this affects the results of the study. Sequences were processed and aligned as part of the daily datapipe analysis managed by CLIMB on behalf of COG-UK. Duplicate and environmental sequences, as well as those with impossible or incomplete collection dates, were removed. All sequences were aligned to the reference Wuhan-Hu-1 (GenBank accession MN908947.3) with minimap2 and samples with less than 93% coverage were discarded. Scorpio (https://github.com/cov-lineages/scorpio) was run as part of Pangolin43, and sequences containing the Delta VOC constellation of mutations were kept for further analysis.

Problematic sites in the resulting alignment were masked prior to phylogenetic inference and isolates with known sequence artefacts were removed (see https://github.com/COG-UK/Delta-analysis for details). Additionally, mutations in the Delta VOC have caused widespread amplicon dropout of amplicon 72 in the commonly used ARTIC primer scheme (https://www.protocols.io/view/ncov-2019-sequencing-protocol-v3-locost-bh42j8ye) before the introduction of version 4 of the primer scheme. To avoid spurious phylogenetic associations based on differential treatment of amplicon dropout with COG-UK and across the globe, we masked sites 2142–21990, which represent the region solely covered by amplicon 72 and are not overlapped by neighbouring amplicons. Delta sequences from India were highly heterogeneous in space (Extended Data Fig. 9).

### Phylogenetic analyses

To provide an overview of the global expansion of Delta (Fig. 1a), we analysed a subset of 1,000 Delta genomes sampled evenly through time. To minimize the effect of incorrectly reported collection dates, we restricted our analysis to samples where the lag between sample collection date and GISAID submission date is less than four weeks. To further ensure only the highest quality samples were included, we built an maximum likelihood tree using iqtree244, rooted with Wuhan-Hu-1 (GenBank accession MN908947.3) as an outgroup, and used Treetime45 to remove tips lying beyond two interquartile ranges from the regression of time against root-to-tip distance. This analysis resulted in a final dataset of 975 samples. The temporal tree estimated by treetime was used as a starting tree in the following Bayesian analysis with slight modifications to randomly resolve polytomies. Two chains of 100 million states were run using BEAST v1.10.446 with sampling every 20,000 states. Both chains were combined with the first 10 million states removed for burnin. We used a HKY + 𝚪 substitution model47, a flexible Skygrid coalescent prior48 with grid points every two weeks45, and an asymmetric, discrete phylogeographic model with samples assigned to Indian, English and global locales. Preliminary analysis showed very little temporal signal in the data, which is unsurprising given the relatively slow evolutionary rate of SARS-CoV-2 and the short study period. Therefore, in all analyses the evolutionary rate was fixed to 7.5 × 10−4 substitutions per site, as estimated in ref. 18. Convergence was assessed using Tracer v1.749.

The goal of our phylogenetic analysis was to accurately and efficiently describe importation dynamics into England, without sacrificing the dense sampling needed to reconstruct internal spread at a high resolution. Owing to the large size of the required dataset, we followed a similar phylogenetic approach to that used in ref. 18. First, an approximately maximum likelihood phylogeny was built using a JC69 substitution model in FastTree50, and rooted on Wuhan-Hu-1 (GenBank accession MN908947.3), a high quality Pango lineage B sample from 2019-12-26, as an outgroup. Internal branches representing less than one substitution were collapsed to polytomies. This tree was then split into three subtrees of roughly equal size (Fig. 1a) (28,783, 28,715 and 36,151 tips). As above, Treetime45 was then used to remove temporal outliers, generate a starting time tree, and estimate the number of mutations along each branch. For subtree an empirical distribution of time trees was estimated independently using a recently implemented model in BEAST v1.1046 (commit:d1a45) which replaces the substitution model in classical analyses. In brief, in this approach the likelihood of the number of mutations along each branch was calculated from a Poisson distribution with mean equal to the evolutionary rate multiplied by the length of the branch in time51. In this approach, the standard topological tree search is constrained to operators that sample node heights and resolutions of polytomies present in the substitution tree.

For each subtree, 50 MCMC chains of 40 million iterations were run, sampling trees every 2 million states with the first 20 million states removed as burnin, resulting in datasets of 514–520 empirical trees. The analyses were run using a flexible Skygrid coalescent prior48 with grid points every two weeks45. Model convergence and proper statistical mixing were verified in Tracer v1.749.

The empirical trees sets estimated above were used to reconstruct importations into England under an asymmetric discrete phylogeographic model. Taxa were split into three locations: England, India and global, with the global state representing all countries other than England and India. We used the recently developed travel-aware phylogenetic model available in BEAST v1.1019 to better inform the transition rates in the reconstructed phylogeography. ‘Travel history’ nodes were placed 1 week before isolates from England with known travel history. Where such travel included both India and other countries, ambiguous non-UK states were used. We ran eight chains of 625,000 states, sampling every 2,250 states and with the first 62,500 states removed as burnin, resulting in a total of 1,998 trees sampled from the posterior distribution. Introductions were defined as nodes inferred to be in England with parents in either India or the catch-all global location. The date of importation was assumed to be half-way between such a node and its parent.

Following the importation analysis, the seven largest importations (those with >1,500 sequences, n = 25,983) were selected, as well as all importations with five or more sequences, from a representative tree from the posterior set with the same number of total importations as the posterior median. Within this analysis, only sequences with unambiguous postcode districts were used, resulting in a dataset of 25,139 sequences for the seven largest transmission lineages and 24,411 across 280 smaller lineages, which were extracted from the master COG-UK alignment, described in ‘Genomic data’ above. Within those postcode districts, we assigned random coordinates to each sequence, as the continuous phylogeographic analysis does not permit identical values. This was achieved using geographical data from52. We then reconstructed the geographic movement of nodes on a fixed tree (pruned from the overall maximum clade credibility (MCC) tree) in BEAST v.1.1046, using a relaxed random walk model53, and a Cauchy distribution to account for among-branch heterogeneity in dispersal velocity. Large lineages were inferred independently, and all small lineages were inferred in a single run, with the shared parameters for likelihood, precision, and covariance of coordinates, but independent estimates of diffusion rate and trait likelihood. Following this run, 22 small introductions were removed due to their chains not converging to the same posterior. An MCC tree was then generated using TreeAnnotator46 to summarize the posterior tree distribution for all lineages. Visualizations were madeusing a custom Python script. XML files were generated using beastgen.py (https://github.com/ViralVerity/beastgenpy) and can be found along with data processing and visualization scripts on GitHub.

For the export analyses we compare Greater London to Greater Manchester which consists of the UTLAs Salford, Trafford, Stockport, Oldham, Bolton, Tameside, Bury, Rochdale, Wigan and Manchester.

#### State-level incidence data from India

State-level COVID-19 case count data were extracted from https://api.covid19india.org/csv/latest/states.csv.

### Travel history data

Four sources of data were compiled to provide the travel history for laboratory-confirmed cases, depending on availability for each individual case: (1) public health passenger locator forms are required for entry into the UK; (2) routine public health contact tracing data including UK Health Security Agency Second Generation Surveillance System (SGSS)54, (3) COVID-19 test requests with reported travel associations and (4) responses to additional telephone interviews for cases.

### Covariate processing for statistical analyses

#### COVID-19 case count and vaccination data for the UK

COVID-19 case count data and cumulative vaccination data were downloaded by UTLA from 30 January 2020 to 28 July 2021 by specimen and dosage date, respectively, via https://coronavirus.data.gov.uk/details/download. These data include positive laboratory-based PCR tests and positive lateral flow tests, but do not include tests where the lateral flow test was positive and PCR follow-up tests were negative (further details at https://coronavirus.data.gov.uk/details/about-data). The COVID-19 case count at the UK country level was calculated by aggregating case data on the UTLA level. Additionally, to match the genomic data, the COVID-19 case count and vaccination data for some UTLAs were aggregated under an area code made up of these multiple UTLAs (see Supplementary Table 3). All entries with the recently discontinued area code E10000002 were assigned the new area code E06000060.

#### UK population data

UTLA-level 2020-mid-year population size estimates were downloaded from https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/datasets/populationestimatesforukenglandandwalesscotlandandnorthernireland. Population size data were used to calculate the proportion of the population that was partially or fully vaccinated in a location.

#### Global population data

Country-level population size estimates for the year 2021 were downloaded from https://data.worldbank.org/indicator/SP.POP.TOTL?name_desc=false.

#### Aggregated and anonymised human mobility data

We used the Google COVID-19 Aggregated Mobility Research Dataset31,55, which contains anonymized relative mobility flows aggregated over users who have turned on the ‘location history’ setting, which is turned off by default. This is similar to the data used to show how busy certain types of places are in Google Maps, helping identify when a local business tends to be the most crowded. The mobility flux is aggregated per week, between pairs of approximately 5 km2 cells worldwide, and for the purpose of this study further aggregated for LTLAs in the UK (https://geoportal.statistics.gov.uk/datasets/lower-tier-local-authority-to-upper-tier-local-authority-december-2016-lookup-in-england-and-wales/explore) and to the country level (https://gadm.org/) for all other countries for the time period of 29 October 2020 to 6 June 2021.

To produce this dataset, machine learning is applied to log data to automatically segment it into semantic trips. To provide strong privacy guarantees56, all trips were anonymized and aggregated using a differentially private mechanism to aggregate flows over time (see https://policies.google.com/technologies/anonymization). This research is done on the resulting heavily aggregated and differentially private data. No individual user data was ever manually inspected; only heavily aggregated flows of large populations were handled. All anonymized trips are processed in aggregate to extract their origin and destination location and time. For example, if users travelled from location a to location b within time interval t, the corresponding cell (a,b,t) in the tensor would be n ± err, where err is Laplacian noise. The automated Laplace mechanism adds random noise drawn from a zero-mean Laplacian distribution and yields (𝜖,δ)-differential privacy guarantee of 𝜖 = 0.66 and δ = 2.1 × 10−29 per metric. Specifically, for each week W and each location pair (A,B), we compute the number of unique users who took a trip from location A to location B during week W. To each of these metrics, we add Laplace noise from a zero-mean distribution of scale 1/0.66. We then remove all metrics for which the noisy number of users is lower than 100, following the process described56, and publish the rest. This yields that each metric we publish satisfies (ε,δ)-differential privacy with values defined above. The parameter 𝜖 controls the noise intensity in terms of its variance, while δ represents the deviation from pure 𝜖-privacy. The closer they are to zero, the stronger the privacy guarantees.

These results should be interpreted in light of several important limitations. First, the Google mobility data is limited to smartphone users who have opted into Google’s location history feature, which is off by default. These data may not be representative of the population as whole, and furthermore their representativeness may vary by location. Importantly, these limited data are only viewed through the lens of differential privacy algorithms, specifically designed to protect user anonymity and obscure fine detail. Moreover, comparisons across rather than within locations are only descriptive since these regions can differ in substantial ways.

#### Flight data

We used data from the International Air Transport Association (https://bluedot.global/) on the monthly number of confirmed passengers on flights (direct and indirect) from India to all other countries from January 2021 to June 2021.

#### Estimated importation intensity

We estimated the weekly importation intensity of the Delta variant for each destination location at the weekly level using the human mobility, GISAID and COG-UK genomic data and COVID-19 case data. An importation intensity value was calculated for each international movement by multiplying the proportion of Delta in the location of origin, the total number of new weekly reported COVID-19 cases and the movement intensity between each origin location and the destination location. We then aggregated all importation intensity values by week and destination location to obtain the EII.

#### Estimated exportation intensity

We estimated the exportation intensity of the Delta variant for each location of origin at the weekly level using aggregated human mobility, genomic and case count data. An exportation intensity value was calculated for each international movement by multiplying the proportion of Delta in the country of origin, the total number of new weekly reported cases and the movement intensity between the country of origin and the destination country. We then aggregated all importation intensity values by week and origin location to obtain the EEI.

#### Estimated local human mobility intensity

To obtain an estimate of the intensity of human mobility within a location, we calculated a ‘relative self-mobility’ value indicating the intensity of mobility within a location (where the origin and destination of the trips are the same) as a percent of the highest recorded of movement within this location in our mobility data during the time period from 22 March 2020 to 6 June 2021 using the human mobility data described above.

#### New Delta lineage introductions

Daily new lineage introductions into the UK by UTLA were obtained from the continuous phylogenetic analysis described above. The data were aggregated by week and UTLA.

### Statistical modelling of Delta growth

Data pre-processing: we kept data starting from the 13th (week commencing 28th March 2021) epidemiological week. These dates are referred to as baseline elsewhere in the main text. We excluded weeks after the first time 95% of samples were observed to be Delta in each UTLA because, after this point, we can no longer estimate the relative growth rates reliably since Delta is effectively fixed in the population. Finally, we kept only those UTLAs which had data on Delta for at least 9 weeks (which are not required to be consecutive). In the final dataset, we had 683 observations (across 64 UTLAs with approximately 11 weeks of non-missing data on average for each) (Supplementary Table 8).

#### Model

In what follows, we model the dynamics of Delta penetration within a UTLA. Here, we model how the number of Delta samples per UTLA (i), varies over time (t) (here measured in weeks). The background transmission conditions driving the observed number of Delta samples in a given UTLA may be similar to other UTLAs within the same region. We model this variation hierarchically and index variables at the UTLA level by i[j] to indicate that UTLA i is nested within (the overarching) NUTS1 unit j. We use a binomial sampling distribution to model the number of Delta samples $${Z}_{t}^{i[\,j]}$$,

$${Z}_{t}^{i[\,j]}\sim {\rm{b}}{\rm{i}}{\rm{n}}{\rm{o}}{\rm{m}}{\rm{i}}{\rm{a}}{\rm{l}}({Y}_{t}^{i[\,j]},{p}_{t}^{i[\,j]}),$$

where $${Y}_{t}^{i[\,j]}$$ is the total number of sequenced samples, and $$0\le {p}_{t}^{i[\,j]}\le 1$$ is the corresponding proportion of Delta samples in subregion i in week t. We then transform this probability, so that it is on the (unconstrained) logit scale:

$${{\boldsymbol{\varphi }}}_{t}^{i[\,j]}={\rm{l}}{\rm{o}}{\rm{g}}{\rm{i}}{\rm{t}}({p}_{t}^{i[\,j]}).$$

A key quantity of interest is the relative growth in the proportion of Delta on the logit (that is, log odds) scale, which we estimate weekly and is denoted by $${\rho }_{t}^{i[\,j]}$$, where

$${{\boldsymbol{\varphi }}}_{t}^{i[\,j]}={{\boldsymbol{\varphi }}}_{t-1}^{i[\,j]}+{{\boldsymbol{\rho }}}_{t-1}^{i[\,j]}.$$

Relative growth for each UTLA is modelled spatially as depending hierarchically on its containing region, j. It is also assumed to depend on UTLA-specific covariates:

$${{\boldsymbol{\rho }}}_{t}^{i[\,j]}={{\boldsymbol{\rho }}}_{t}^{j}+{\boldsymbol{\beta }}{\prime} {x}_{t}^{i[\,j]}+{\delta }_{t}^{i[\,j]},$$

where $${{\boldsymbol{\rho }}}_{t}^{j}$$ is a NUTS1-region-level growth trend, $${x}_{t}^{i[\,j]}$$ is a vector of covariates, and $${\delta }_{t}^{i[\,j]}$$ is a UTLA- and week-specific term representing the deviation from the region-level growth. To account for temporal autocorrelation in the relative growth rate, a given region’s relative growth is assumed to follow a random walk centred around its relative growth in the previous week:

$${{\boldsymbol{\rho }}}_{t}^{j}\,\sim \,{\rm{normal}}({{\boldsymbol{\rho }}}_{t-1}^{j},\,{{\boldsymbol{\sigma }}}_{2}).$$

To assess the importance of covariates, we compared the predictive performance of models which included different sets of covariates. All covariates were standardized by subtracting the mean and dividing by the standard deviation. Since the cumulative proportions vaccinated (considering either the cumulative proportion vaccinated with a 1st or 2nd dose) increased monotonically throughout the time period of observation, we included the UTLA-level mean of these variables in our regressions: that is, we used time-invariant regressors. We did so to avoid the risk of spurious association due to both Delta and proportions vaccinated growing coincidently. Covariates were chosen as important predictors if including them in the model improved the model fit on a hold-out set comprising the last two weeks of data for each UTLA. Our best model included within-UTLA mobility and time since baseline, which outperformed the model where we included no covariates (Supplementary Table 6). A model including the cumulative proportion vaccinated with a second dose, time since baseline and within-UTLA mobility also outperformed the no covariate model. However, the improvement in prediction accuracy was minimal, and this was the only model outperforming the no covariate model which included vaccinations, so we do not take this as strong evidence of the importance of vaccination in slowing Delta growth.

We estimated our model in a Bayesian framework and chose priors (Supplementary Table 9) so that a wide range of possible Delta proportions were possible yet were centred on low values in the absence of further information: our prior predictive distributions in Extended Data Fig. 11 illustrate these characteristics.

The computations were done using R and Stan using four parallel chains with 50,000 to 60,000 iterations (depending on the model), half of which were discarded as warm-up iterations; the chains were subsequently thinned by a factor of 10. In all cases, MCMC sampling was diagnosed as converged with $$\hat{R} < 1.01$$, and bulk and tail effective sample sizes >400 for all parameters. For 6 of 15 models used for model comparison (which included neither the no covariate model nor the best fit model), there remained 2 out of 4,410 parameters which had $$\hat{R} > 1.01$$ or had a tail effective sample size below 400; in all cases, the bulk effective sample sizes exceeded 400. In these models, the last two weeks were held-out from each UTLA to perform out of sample predictions, resulting in a smaller dataset, which likely explains the difficulty in obtaining convergence with 50,000 iterations.

Our model outputted two sets of key quantities: the weekly relative growth rate of Delta over time ($${{\boldsymbol{\rho }}}_{t}^{i[\,j]}$$) and the estimated ‘effect’ of a variable on Delta growth (β). To determine the implications of the effect sizes, we computed the estimated proportion of Delta samples when the covariates took factual versus counterfactual values. We considered counterfactual scenarios for within-UTLA mobility, holding all other covariates at their factual values. The counterfactual scenario we considered was:

• Minimum mobility (within-UTLA mobility = 0)

• Maximum mobility (within-UTLA mobility = 1)

The results of these counterfactual simulations are shown in Extended Data Fig. 10.

Simulation and model robustness: to test model parameter identifiability, we performed inference on simulated data. We fixed the parameters and simulated from the model to create hypothetical data (with 5 regions, each with 6 sub-regions (that is, UTLAs) and 15 time points). We then used these data to estimate the known parameters. We were reasonably able to recover our parameters, and the model converged with $$\hat{{R}}$$ < 1.01, bulk and tail effective sample sizes >400 after 20,000 iterations, discarding 10,000 warm-up iterations and thinning by a factor of 10 (Extended Data Fig. 12 and Supplementary Table 7).

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.