library.bib

@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2019},
    url = {https://www.R-project.org/},
  }

@Manual{cmdstanr,
    title = {cmdstanr: R Interface to 'CmdStan'},
    author = {Jonah Gabry and Rok Češnovar},
    year = {2021},
    note = {https://mc-stan.org/cmdstanr, https://discourse.mc-stan.org},
  }

@Manual{stan,
    title = {Stan Modeling Language Users Guide and Reference Manual, 2.28.1},
    author = {Stan Development Team},
    year = {2021},
    note = {https://mc-stan.org},
  }

@Manual{scoringutils,
  title = {scoringutils: A collection of proper scoring rules and metrics to assess predictions},
  author = {Nikos Bosse},
  year = {2020},
  note = {R package version 0.0.0.9000},
  url = {https://github.com/epiforecasts/scoringutils}
}

@Article{betancourt_2017,
  title={Diagnosing biased inference with divergences},
  author={Betancourt, Michael},
  year={2017},
  volume={4},
  journal={Stan Case Studies},
  url={https://mc-stan.org/users/documentation/case-studies/divergences_and_bias.html}
}

@Article{forecast.vocs,
  title = {forecast.vocs: Forecast case and sequence notifications using variant of concern strain dynamics},
  author = {Sam Abbott},
  journal = {Zenodo},
  year = {2021},
  doi = {10.5281/zenodo.5559016},
  }

  @Misc{loo,
    title = {loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models},
    author = {Aki Vehtari and Jonah Gabry and Mans Magnusson and Yuling Yao and Paul-Christian Bürkner and Topi Paananen and Andrew Gelman},
    year = {2020},
    note = {R package version 2.4.1},
    url = {https://mc-stan.org/loo/},
  }

  @Article{loo-paper,
    title = {Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC},
    author = {Aki Vehtari and Andrew Gelman and Jonah Gabry},
    year = {2017},
    journal = {Statistics and Computing},
    volume = {27},
    issue = {5},
    pages = {1413--1432},
    doi = {10.1007/s11222-016-9696-4},
  }

@Article{pearson-omicron,
  title={Bounding the levels of transmissibility \& immune evasion of the Omicron
variant in South Africa},
  author={Carl A. B. Pearson and Sheetal P. Silal and Michael W.Z. Li and Jonathan Dushoff and Benjamin M. Bolker and Sam Abbott and Cari van Schalkwyk and Nicholas G. Davies and Rosanna C. Barnard and W. John Edmunds and Jeremy Bingham and Gesine Meyer-Rath and Lise Jamieson and Allison Glass and Nicole Wolter and Nevashan Govender and Wendy S. Stevens and Lesley Scott and Koleka Mlisana and Harry Moultrie and Juliet R. C. Pulliam},
  year={2021},
  url={https://www.sacmcepidemicexplorer.co.za/downloads/Pearson_etal_Omicron.pdf}
}

@Article{golding-omicron,
  title={Analyses to predict the efficacy and waning of vaccines and previous infection against transmission and clinical outcomes of SARS-CoV-2 variants},
  author={Nick Golding},
  year={2021},
  url={https://github.com/goldingn/neuts2efficacy}
}

@Article{brandal-omicron-incubation,
   author = "Brandal, Lin T. and MacDonald, Emily and Veneti, Lamprini and Ravlo, Tine and Lange, Heidi and Naseer, Umaer and Feruglio, Siri and Bragstad, Karoline and Hungnes, Olav and Ødeskaug, Liz E. and Hagen, Frode and Hanch-Hansen, Kristian E. and Lind, Andreas and Watle, Sara Viksmoen and Taxt, Arne M. and Johansen, Mia and Vold, Line and Aavitsland, Preben and Nygård, Karin and Madslien, Elisabeth H.",
   title = "Outbreak caused by the SARS-CoV-2 Omicron variant in Norway, November to December 2021",
   journal = "Eurosurveillance",
   year = "2021",
   volume = "26",
   number = "50",
   eid = 2101147,
   pages = "",
   url = "https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2021.26.50.2101147",
   doi = "https://doi.org/10.2807/1560-7917.ES.2021.26.50.2101147"
}

@Article{ferguson-omicron-transmission,
  author = "Neil Ferguson, Azra Ghani, Anne Cori, Alexandra Hogan, Wes Hinsley, Erik Volz",
  title = "Report 49 - Growth, population distribution and immune escape of Omicron in England",
  year = {2021},
  url = {https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-49-Omicron/}
}

@Article{si-south-korea,
  author = {Kim, Dasom and Jo, Jisoo and Lim, Jun-Sik and Ryu, Sukhyun},
  title = {Serial interval and basic reproduction number of SARS-CoV-2 Omicron variant in South Korea},
  elocation-id = {2021.12.25.21268301},
  year = {2021},
  doi = {10.1101/2021.12.25.21268301},
  URL = {https://www.medrxiv.org/content/early/2021/12/25/2021.12.25.21268301},
  eprint = {https://www.medrxiv.org/content/early/2021/12/25/2021.12.25.21268301.full.pdf},
  journal = {medRxiv}
}

@article{park2019,
  title = {A Practical Generation-Interval-Based Approach to Inferring the Strength of Epidemics from Their Speed},
  author = {Park, Sang Woo and Champredon, David and Weitz, Joshua S. and Dushoff, Jonathan},
  year = {2019},
  month = jun,
  journal = {Epidemics},
  volume = {27},
  pages = {12--18},
  issn = {1755-4365},
  doi = {10.1016/j.epidem.2018.12.002},
  abstract = {Infectious disease outbreaks are often characterized by the reproduction number R and exponential rate of growth r. R provides information about outbreak control and predicted final size, but estimating R is difficult, while r can often be estimated directly from incidence data. These quantities are linked by the generation interval \textendash{} the time between when an individual is infected by an infector, and when that infector was infected. It is often infeasible to obtain the exact shape of a generation-interval distribution, and to understand how this shape affects estimates of R. We show that estimating generation interval mean and variance provides insight into the relationship between R and r. We use examples based on Ebola, rabies and measles to explore approximations based on gamma-distributed generation intervals, and find that use of these simple approximations are often sufficient to capture the r\textendash R relationship and provide robust estimates of R.},
  langid = {english},
  keywords = {Basic reproduction number,Generation interval,Infectious disease modeling}
}

@article{park2020,
  title = {Reconciling Early-Outbreak Estimates of the Basic Reproductive Number and Its Uncertainty: Framework and Applications to the Novel Coronavirus ({{SARS-CoV-2}}) Outbreak},
  shorttitle = {Reconciling Early-Outbreak Estimates of the Basic Reproductive Number and Its Uncertainty},
  author = {Park, Sang Woo and Bolker, Benjamin M. and Champredon, David and Earn, David J. D. and Li, Michael and Weitz, Joshua S. and Grenfell, Bryan T. and Dushoff, Jonathan},
  year = {2020},
  month = jul,
  journal = {Journal of The Royal Society Interface},
  volume = {17},
  number = {168},
  pages = {20200144},
  publisher = {{Royal Society}},
  doi = {10.1098/rsif.2020.0144},
  abstract = {A novel coronavirus (SARS-CoV-2) emerged as a global threat in December 2019. As the epidemic progresses, disease modellers continue to focus on estimating the basic reproductive number {$\mathscr{R}$}0 R 0 \textemdash the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modelling approaches and resulting estimates of {$\mathscr{R}$}0 R 0  during the beginning of the outbreak vary widely, despite relying on similar data sources. Here, we present a statistical framework for comparing and combining different estimates of {$\mathscr{R}$}0 R 0  across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate, the mean generation interval and the generation-interval dispersion. We apply our framework to early estimates of {$\mathscr{R}$}0 R 0  for the SARS-CoV-2 outbreak, showing that many {$\mathscr{R}$}0 R 0  estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of {$\mathscr{R}$}0 R 0 , including the shape of the generation-interval distribution, in efforts to estimate {$\mathscr{R}$}0 R 0  at the outset of an epidemic.},
  keywords = {basic reproductive number,Bayesian multilevel model,COVID-19,generation interval,novel coronavirus,SARS-CoV-2}
}

@misc{hart2021,
  title = {Generation Time of the {{Alpha}} and {{Delta SARS-CoV-2}} Variants},
  author = {Hart, W. S. and Miller, E. and Andrews, N. J. and Waight, P. and Maini, P. K. and Funk, S. and Thompson, R. N.},
  year = {2021},
  month = oct,
  pages = {2021.10.21.21265216},
  institution = {{Cold Spring Harbor Laboratory Press}},
  issn = {2126-5216},
  doi = {10.1101/2021.10.21.21265216},
  abstract = {Background In May 2021, the Delta SARS-CoV-2 variant became dominant in the UK. This variant is associated with increased transmissibility compared to the Alpha variant that was previously dominant. To understand ongoing transmission and interventions, a key question is whether the Delta variant generation time (the time between infections in infector- infectee pairs) is typically shorter\textendash i.e., transmissions are happening more quickly\textendash or whether infected individuals simply generate more infections. Methods We analysed transmission data from a UK Health Security Agency household study. By fitting a mathematical transmission model to the data, we estimated the generation times for the Alpha and Delta variants. Results The mean intrinsic generation time (the generation time if there had been a constant supply of susceptibles throughout infection) was shorter for the Delta variant (4{$\cdot$}6 days, 95\% CrI 4{$\cdot$}0-5{$\cdot$}4 days) than the Alpha variant (5{$\cdot$}5 days, 95\% CrI 4{$\cdot$}6-6{$\cdot$}4 days), although within uncertainty ranges. However, there was a larger difference in the realised mean household generation time between the Delta (3{$\cdot$}2 days, 95\% CrI 2{$\cdot$}4-4{$\cdot$}2 days) and Alpha (4{$\cdot$}5 days, 95\% CrI 3{$\cdot$}7-5{$\cdot$}4 days) variants. This is because higher transmissibility led to faster susceptible depletion in households, in addition to the reduced intrinsic generation time. Conclusions The Delta variant transmits more quickly than previously circulating variants. This has implications for interventions such as contact tracing, testing and isolation, which are less effective if the virus is transmitted quickly. Epidemiological models of interventions should be updated to include the shorter generation time of the Delta variant.},
  copyright = {\textcopyright{} 2021, Posted by Cold Spring Harbor Laboratory. This pre-print is available under a Creative Commons License (Attribution-NonCommercial 4.0 International), CC BY-NC 4.0, as described at http://creativecommons.org/licenses/by-nc/4.0/},
  langid = {english}
}

@software{abbott_Real-time_estimation_of_2021,
author = {Abbott, Sam and Sherratt, Katharine and Funk, Sebastian},
doi = {10.5281/zenodo.5799135},
month = {12},
title = {{Real-time estimation of the time-varying transmission advantage of Omicron in England using S-Gene Target Status as a Proxy}},
url = {https://github.com/epiforecasts/omicron-sgtf-forecast},
version = {1.0.0},
year = {2021}
}

@article{volz2021,
  title = {Assessing Transmissibility of {{SARS-CoV-2}} Lineage {{B}}.1.1.7 in {{England}}},
  author = {Volz, Erik and Mishra, Swapnil and Chand, Meera and Barrett, Jeffrey C. and Johnson, Robert and Geidelberg, Lily and Hinsley, Wes R. and Laydon, Daniel J. and Dabrera, Gavin and O'Toole, {\'A}ine and Amato, Robert and {Ragonnet-Cronin}, Manon and Harrison, Ian and Jackson, Ben and Ariani, Cristina V. and Boyd, Olivia and Loman, Nicholas J. and McCrone, John T. and Gon{\c c}alves, S{\'o}nia and Jorgensen, David and Myers, Richard and Hill, Verity and Jackson, David K. and Gaythorpe, Katy and Groves, Natalie and Sillitoe, John and Kwiatkowski, Dominic P. and Flaxman, Seth and Ratmann, Oliver and Bhatt, Samir and Hopkins, Susan and Gandy, Axel and Rambaut, Andrew and Ferguson, Neil M.},
  year = {2021},
  month = may,
  journal = {Nature},
  volume = {593},
  number = {7858},
  pages = {266--269},
  publisher = {{Nature Publishing Group}},
  issn = {1476-4687},
  doi = {10.1038/s41586-021-03470-x},
  abstract = {The SARS-CoV-2 lineage B.1.1.7, designated variant of concern (VOC) 202012/01 by Public Health England1, was first identified in the UK in late summer to early autumn 20202. Whole-genome SARS-CoV-2 sequence data collected from community-based diagnostic testing for COVID-19 show an extremely rapid expansion of the B.1.1.7 lineage during autumn 2020, suggesting that it has a selective advantage. Here we show that changes in VOC frequency inferred from genetic data correspond closely to changes inferred by S gene target failures (SGTF) in community-based diagnostic PCR testing. Analysis of trends in SGTF and non-SGTF case numbers in local areas across England shows that B.1.1.7 has higher transmissibility than non-VOC lineages, even if it has a different latent period or generation time. The SGTF data indicate a transient shift in the age composition of reported cases, with cases of B.1.1.7 including a larger share of under 20-year-olds than non-VOC cases. We estimated time-varying reproduction numbers for B.1.1.7 and co-circulating lineages using SGTF and genomic data. The best-supported models did not indicate a substantial difference in VOC transmissibility among different age groups, but all analyses agreed that B.1.1.7 has a substantial transmission advantage over other lineages, with a 50\% to 100\% higher reproduction number.},
  copyright = {2021 The Author(s), under exclusive licence to Springer Nature Limited},
  langid = {english},
  keywords = {Population genetics,SARS-CoV-2,Viral infection},
  annotation = {Bandiera\_abtest: a Cg\_type: Nature Research Journals Primary\_atype: Research Subject\_term: Population genetics;SARS-CoV-2;Viral infection Subject\_term\_id: population-genetics;sars-cov-2;viral-infection}
}