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@misc{ons_infections,
	title = {Coronavirus (COVID-19) Infection Survey: England - Office for National Statistics},
	url = {https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/datasets/coronaviruscovid19infectionsurveydata},
	note = {Citation Key: ons{\_}infections}
}

@misc{ons_antibody,
	title = {Coronavirus (COVID-19) antibody and vaccination data for the UK - Office for National Statistics},
	url = {https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/datasets/coronaviruscovid19antibodydatafortheuk},
	note = {Citation Key: ons{\_}antibody}
}

@misc{ons_pop,
	title = {Population estimates for the UK, England and Wales, Scotland and Northern Ireland - Office for National Statistics},
	url = {https://www.ons.gov.uk/peoplepopulationandcommunity/populationandmigration/populationestimates/bulletins/annualmidyearpopulationestimates/latest},
	note = {Citation Key: ons{\_}pop}
}


@misc{PHE,
author = {{Public Health England}},
month = {nov},
title = {{Official UK Coronavirus Dashboard}},
url = {https://coronavirus.data.gov.uk/details/cases},
year = {2020}
}
@manual{Boelle2015,
annote = {R package version 1.2-6},
author = {Boelle, Pierre-Yves and Obadia, Thomas},
title = {{R0: Estimation of R0 and Real-Time Reproduction Number from Epidemics}},
url = {https://cran.r-project.org/package=R0},
year = {2015}
}
@misc{cran,
title = {{The Comprehensive R Archive Network}}
}
@article{Doremalen_2020,
author = {van Doremalen, Neeltje and Bushmaker, Trenton and Morris, Dylan H. and Holbrook, Myndi G. and Gamble, Amandine and Williamson, Brandi N. and Tamin, Azaibi and Harcourt, Jennifer L. and Thornburg, Natalie J. and Gerber, Susan I. and Lloyd-Smith, James O. and de Wit, Emmie and Munster, Vincent J.},
doi = {10.1056/NEJMc2004973},
issn = {0028-4793},
journal = {New England Journal of Medicine},
month = {apr},
number = {16},
title = {{Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1}},
volume = {382},
year = {2020}
}
@article{Cowling2020,
abstract = {Background: A range of public health measures have been implemented to suppress local transmission of coronavirus disease 2019 (COVID-19) in Hong Kong. We examined the effect of these interventions and behavioural changes of the public on the incidence of COVID-19, as well as on influenza virus infections, which might share some aspects of transmission dynamics with COVID-19. Methods: We analysed data on laboratory-confirmed COVID-19 cases, influenza surveillance data in outpatients of all ages, and influenza hospitalisations in children. We estimated the daily effective reproduction number (Rt) for COVID-19 and influenza A H1N1 to estimate changes in transmissibility over time. Attitudes towards COVID-19 and changes in population behaviours were reviewed through three telephone surveys done on Jan 20–23, Feb 11–14, and March 10–13, 2020. Findings: COVID-19 transmissibility measured by Rt has remained at approximately 1 for 8 weeks in Hong Kong. Influenza transmission declined substantially after the implementation of social distancing measures and changes in population behaviours in late January, with a 44% (95% CI 34–53%) reduction in transmissibility in the community, from an estimated Rt of 1{\textperiodcentered}28 (95% CI 1{\textperiodcentered}26–1{\textperiodcentered}30) before the start of the school closures to 0{\textperiodcentered}72 (0{\textperiodcentered}70–0{\textperiodcentered}74) during the closure weeks. Similarly, a 33% (24–43%) reduction in transmissibility was seen based on paediatric hospitalisation rates, from an Rt of 1{\textperiodcentered}10 (1{\textperiodcentered}06–1{\textperiodcentered}12) before the start of the school closures to 0{\textperiodcentered}73 (0{\textperiodcentered}68–0{\textperiodcentered}77) after school closures. Among respondents to the surveys, 74{\textperiodcentered}5%, 97{\textperiodcentered}5%, and 98{\textperiodcentered}8% reported wearing masks when going out, and 61{\textperiodcentered}3%, 90{\textperiodcentered}2%, and 85{\textperiodcentered}1% reported avoiding crowded places in surveys 1 (n=1008), 2 (n=1000), and 3 (n=1005), respectively. Interpretation: Our study shows that non-pharmaceutical interventions (including border restrictions, quarantine and isolation, distancing, and changes in population behaviour) were associated with reduced transmission of COVID-19 in Hong Kong, and are also likely to have substantially reduced influenza transmission in early February, 2020. Funding: Health and Medical Research Fund, Hong Kong.},
author = {Cowling, Benjamin J. and Ali, Sheikh Taslim and Ng, Tiffany W.Y. and Tsang, Tim K. and Li, Julian C.M. and Fong, Min Whui and Liao, Qiuyan and Kwan, Mike YW and Lee, So Lun and Chiu, Susan S. and Wu, Joseph T. and Wu, Peng and Leung, Gabriel M.},
doi = {10.1016/S2468-2667(20)30090-6},
issn = {24682667},
journal = {The Lancet Public Health},
pmid = {32311320},
title = {{Impact assessment of non-pharmaceutical interventions against coronavirus disease 2019 and influenza in Hong Kong: an observational study}},
year = {2020}
}
@article{bellman_1952,
author = {Bellman, Richard and Harris, Theodore},
doi = {10.2307/1969779},
issn = {0003486X},
journal = {The Annals of Mathematics},
title = {{On Age-Dependent Binary Branching Processes}},
year = {1952}
}
@article{Faria_2021,
abstract = {<p>Cases of SARS-CoV-2 infection in Manaus, Brazil, resurged in late 2020, despite previously high levels of infection. Genome sequencing of viruses sampled in Manaus between November 2020 and January 2021 revealed the emergence and circulation of a novel SARS-CoV-2 variant of concern. Lineage P.1, acquired 17 mutations, including a trio in the spike protein (K417T, E484K and N501Y) associated with increased binding to the human ACE2 receptor. Molecular clock analysis shows that P.1 emergence occurred around mid-November 2020 and was preceded by a period of faster molecular evolution. Using a two-category dynamical model that integrates genomic and mortality data, we estimate that P.1 may be 1.7–2.4-fold more transmissible, and that previous (non-P.1) infection provides 54–79% of the protection against infection with P.1 that it provides against non-P.1 lineages. Enhanced global genomic surveillance of variants of concern, which may exhibit increased transmissibility and/or immune evasion, is critical to accelerate pandemic responsiveness.</p>},
author = {Faria, Nuno R. and Mellan, Thomas A. and Whittaker, Charles and Claro, Ingra M. and Candido, Darlan da S. and Mishra, Swapnil and Crispim, Myuki A. E. and Sales, Flavia C. S. and Hawryluk, Iwona and McCrone, John T. and Hulswit, Ruben J. G. and Franco, Lucas A. M. and Ramundo, Mariana S. and de Jesus, Jaqueline G. and Andrade, Pamela S. and Coletti, Thais M. and Ferreira, Giulia M. and Silva, Camila A. M. and Manuli, Erika R. and Pereira, Rafael H. M. and Peixoto, Pedro S. and Kraemer, Moritz U. G. and Gaburo, Nelson and Camilo, Cecilia da C. and Hoeltgebaum, Henrique and Souza, William M. and Rocha, Esmenia C. and de Souza, Leandro M. and de Pinho, Mariana C. and Araujo, Leonardo J. T and Malta, Frederico S. V. and de Lima, Aline B. and Silva, Joice do P. and Zauli, Danielle A. G. and Ferreira, Alessandro C. de S. and Schnekenberg, Ricardo P and Laydon, Daniel J. and Walker, Patrick G. T. and Schl{\"{u}}ter, Hannah M. and dos Santos, Ana L. P. and Vidal, Maria S. and {Del Caro}, Valentina S. and Filho, Rosinaldo M. F. and dos Santos, Helem M. and Aguiar, Renato S. and Proen{\c{c}}a-Modena, Jos{\'{e}} L. and Nelson, Bruce and Hay, James A. and Monod, M{\'{e}}lodie and Miscouridou, Xenia and Coupland, Helen and Sonabend, Raphael and Vollmer, Michaela and Gandy, Axel and Prete, Carlos A. and Nascimento, Vitor H. and Suchard, Marc A. and Bowden, Thomas A. and Pond, Sergei L. K. and Wu, Chieh-Hsi and Ratmann, Oliver and Ferguson, Neil M. and Dye, Christopher and Loman, Nick J. and Lemey, Philippe and Rambaut, Andrew and Fraiji, Nelson A. and Carvalho, Maria do P. S. S. and Pybus, Oliver G. and Flaxman, Seth and Bhatt, Samir and Sabino, Ester C.},
doi = {10.1126/science.abh2644},
issn = {0036-8075},
journal = {Science},
month = {apr},
title = {{Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil}},
year = {2021}
}
@article{kermack_1927,
abstract = {(1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.},
author = {{Kermack, William Ogilvy and McKendrick}, A. G.},
doi = {10.1098/rspa.1927.0118},
issn = {0950-1207},
journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
title = {{A contribution to the mathematical theory of epidemics}},
year = {1927}
}
@misc{FluSight,
title = {{FluSight: Flu Forecasting}},
url = {https://www.cdc.gov/flu/weekly/flusight/index.html},
urldate = {2021-05-13}
}
@article{fraser_2007,
abstract = {Reproduction numbers, defined as averages of the number of people infected by a typical case, play a central role in tracking infectious disease outbreaks. The aim of this paper is to develop methods for estimating reproduction numbers which are simple enough that they could be applied with limited data or in real time during an outbreak. I present a new estimator for the individual reproduction number, which describes the state of the epidemic at a point in time rather than tracking individuals over time, and discuss some potential benefits. Then, to capture more of the detail that micro-simulations have shown is important in outbreak dynamics, I analyse a model of transmission within and between households, and develop a method to estimate the household reproduction number, defined as the number of households infected by each infected household. This method is validated by numerical simulations of the spread of influenza and measles using historical data, and estimates are obtained for would-be emerging epidemics of these viruses. I argue that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation. {\textcopyright} 2007 Christophe Fraser.},
author = {Fraser, Christophe},
doi = {10.1371/journal.pone.0000758},
issn = {19326203},
journal = {PLoS ONE},
pmid = {17712406},
title = {{Estimating individual and household reproduction numbers in an emerging epidemic}},
year = {2007}
}
@article{stan_user_guide,
abstract = {RSTAN package Stan Development Team (2013). Stan: A C++ Library for Probability and Sampling, Version 2.2.0. URL http://mc-stan.org/. Stan Development Team (2013). Stan Modeling Language User's Guide and Reference Manual, Version 2.2.0. URL http://mc-stan.org/. Hoffman, Matthew D. and Andrew Gelman. In press. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research.},
author = {{Stan Development Team}},
journal = {Interaction Flow Modeling Language},
title = {{Stan Modeling Language User's Guide and Reference Manual, Version 2.19.2.}},
year = {2020}
}
@article{riley_2003,
abstract = {We present an analysis of the first 10 weeks of the severe acute respiratory syndrome (SARS) epidemic in Hong Kong. The epidemic to date has been characterized by two large clusters - initiated by two separate "super-spread" events (SSEs) - and by ongoing community transmission. By fitting a stochastic model to data on 1512 cases, including these clusters, we show that the etiological agent of SARS is moderately transmissible. Excluding SSES, we estimate that 2.7 secondary infections were generated per case on average at the start of the epidemic, with a substantial contribution from hospital transmission. Transmission rates fell during the epidemic, primarily as a result of reductions in population contact rates and improved hospital infection control, but also because of more rapid hospital attendance by symptomatic individuals. As a result, the epidemic is now in decline, although continued vigilance is necessary for this to be maintained. Restrictions on longer range population movement are shown to be a potentially useful additional control measure in some contexts. We estimate that most currently infected persons are now hospitalized, which highlights the importance of control of nosocomial transmission.},
author = {Riley, Steven and Fraser, Christophe and Donnelly, Christl A. and Ghani, Azra C. and Abu-Raddad, Laith J. and Hedley, Anthony J. and Leung, Gabriel M. and Ho, Lai Ming and Lam, Tai Hing and Thach, Thuan Q. and Chau, Patsy and Chan, King Pan and Lo, Su Vui and Leung, Pak Yin and Tsang, Thomas and Ho, William and Lee, Koon Hung and Lau, Edith M.C. and Ferguson, Neil M. and Anderson, Roy M.},
doi = {10.1126/science.1086478},
issn = {00368075},
journal = {Science},
pmid = {12766206},
title = {{Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions}},
year = {2003}
}
@article{bartoszynski_1967,
abstract = {1. Introduction In the present paper we shall discuss the extinction problem for certain branching processes. Our main purpose is to study those branching processes which can serve as models of epidemics; that is, spreads of an infectious disease. The phenomenon of epidemics is fairly complex, and all models necessarily have to be based on a certain compromise. This compromise consists of taking into account some of the (presumably important) factors governiing the spread of the disease at the cost of neglecting others. Our main idealization will consist of assuming such mechanisms of infection which yield a brailching process. Using informal language, it means that all infectives present in the population at a given time infect the susceptibles independently of each other. More precisely, if there are 7c infectives in the nth generation of the epidemics, then the distri-bution of the next (n + 1)st generation can be represented as the distribution of a sum of k independent, identically distributed random variables, with a specified distribution. These random variables represent the "progeny" of k infectives of nth generation. It is debatable whether the above assumption is justifiedlin the sense that},
author = {Bartoszynski, Robert},
journal = {Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability},
title = {{Branching Processes and the Theory of Epidemics}},
year = {1967}
}
@article{Meyer_2017,
author = {Meyer, Sebastian and Held, Leonhard and H{\"{o}}hle, Michael},
doi = {10.18637/jss.v077.i11},
issn = {1548-7660},
journal = {Journal of Statistical Software},
number = {11},
title = {{Spatio-Temporal Analysis of Epidemic Phenomena Using the <i>R</i> Package <b>surveillance</b>}},
volume = {77},
year = {2017}
}
@misc{Heesterbeek2015,
abstract = {Despite some notable successes in the control of infectious diseases, transmissible pathogens still pose an enormous threat to human and animal health. The ecological and evolutionary dynamics of infections play out on a wide range of interconnected temporal, organizational, and spatial scales, which span hours to months, cells to ecosystems, and local to global spread. Moreover, some pathogens are directly transmitted between individuals of a single species, whereas others circulate among multiple hosts, need arthropod vectors, or can survive in environmental reservoirs. Many factors, including increasing antimicrobial resistance, increased human connectivity and changeable human behavior, elevate prevention and control from matters of national policy to international challenge. In the face of this complexity, mathematical models offer valuable tools for synthesizing information to understand epidemiological patterns, and for developing quantitative evidence for decision-making in global health.},
author = {Heesterbeek, Hans and Anderson, Roy M. and Andreasen, Viggo and Bansal, Shweta and DeAngelis, Daniela and Dye, Chris and Eames, Ken T.D. and Edmunds, W. John and Frost, Simon D.W. and Funk, Sebastian and Hollingsworth, T. Deirdre and House, Thomas and Isham, Valerie and Klepac, Petra and Lessler, Justin and Lloyd-Smith, James O. and Metcalf, C. Jessica E. and Mollison, Denis and Pellis, Lorenzo and Pulliam, Juliet R.C. and Roberts, Mick G. and Viboud, Cecile and Arinaminpathy, Nimalan and Ball, Frank and Bogich, Tiffany and Gog, Julia and Grenfell, Bryan and Lloyd, Alun L. and Mclean, Angela and O'Neill, Philip and Pearson, Carl and Riley, Steven and Tomba, Gianpaolo Scalia and Trapman, Pieter and Wood, James},
booktitle = {Science},
doi = {10.1126/science.aaa4339},
file = {:Users/jamesscott/Documents/mendeley2/Heesterbeek et al. - 2015 - Modeling infectious disease dynamics in the complex landscape of global health.pdf:pdf},
issn = {10959203},
month = {mar},
number = {6227},
pmid = {25766240},
publisher = {American Association for the Advancement of Science},
title = {{Modeling infectious disease dynamics in the complex landscape of global health}},
url = {http://science.sciencemag.org/},
volume = {347},
year = {2015}
}
@article{Unwin_2020,
abstract = {As of 1st June 2020, the US Centres for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly model the US epidemic at the state-level, using publicly available death data within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We use changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on the rate of transmission of SARS-CoV-2. We estimate that Rt was only below one in 23 states on 1st June. We also estimate that 3.7% [3.4%–4.0%] of the total population of the US had been infected, with wide variation between states, and approximately 0.01% of the population was infectious. We demonstrate good 3 week model forecasts of deaths with low error and good coverage of our credible intervals.},
author = {Unwin, H. Juliette T. and Mishra, Swapnil and Bradley, Valerie C. and Gandy, Axel and Mellan, Thomas A. and Coupland, Helen and Ish-Horowicz, Jonathan and Vollmer, Michaela A.C. and Whittaker, Charles and Filippi, Sarah L. and Xi, Xiaoyue and Monod, M{\'{e}}lodie and Ratmann, Oliver and Hutchinson, Michael and Valka, Fabian and Zhu, Harrison and Hawryluk, Iwona and Milton, Philip and Ainslie, Kylie E.C. and Baguelin, Marc and Boonyasiri, Adhiratha and Brazeau, Nick F. and Cattarino, Lorenzo and Cucunuba, Zulma and Cuomo-Dannenburg, Gina and Dorigatti, Ilaria and Eales, Oliver D. and Eaton, Jeffrey W. and van Elsland, Sabine L. and FitzJohn, Richard G. and Gaythorpe, Katy A.M. and Green, William and Hinsley, Wes and Jeffrey, Benjamin and Knock, Edward and Laydon, Daniel J. and Lees, John and Nedjati-Gilani, Gemma and Nouvellet, Pierre and Okell, Lucy and Parag, Kris V. and Siveroni, Igor and Thompson, Hayley A. and Walker, Patrick and Walters, Caroline E. and Watson, Oliver J. and Whittles, Lilith K. and Ghani, Azra C. and Ferguson, Neil M. and Riley, Steven and Donnelly, Christl A. and Bhatt, Samir and Flaxman, Seth},
doi = {10.1038/s41467-020-19652-6},
issn = {20411723},
journal = {Nature Communications},
number = {1},
title = {{State-level tracking of COVID-19 in the United States}},
volume = {11},
year = {2020}
}
@techreport{who_2003,
author = {World Health Organization},
title = {{SARS: chronology of a serial killer.}},
year = {2003},
institution = {World Health Organization}
}
@misc{CDCForecastHub,
title = {{COVID 19 forecast hub}},
url = {https://covid19forecasthub.org/},
urldate = {2021-05-13}
}
@misc{goodrich_2020,
annote = {R package version 2.21.1},
author = {Goodrich, Ben and Gabry, Jonah and Ali, Imad and Brilleman, Sam},
title = {{rstanarm: {Bayesian} applied regression modeling via {Stan}.}},
url = {https://mc-stan.org/rstanarm/},
year = {2020}
}
@article{Bhatt2020,
author = {Bhatt, Samir and Ferguson, Neil and Flaxman, Seth and Gandy, Axel and Mishra, Swapnil and Scott, James A},
journal = {arXiv preprint arXiv:2012.00394},
title = {{Semi-Mechanistic Bayesian Modeling of COVID-19 with Renewal Processes}},
url = {https://arxiv.org/abs/2012.00394},
year = {2020}
}
@article{fraser_2009,
abstract = {A novel influenza A (H1N1) virus has spread rapidly across the globe. Judging its pandemic potential is difficult with limited data, but nevertheless essential to inform appropriate health responses. By analyzing the outbreak in Mexico, early data on international spread, and viral genetic diversity, we make an early assessment of transmissibility and severity. Our estimates suggest that 23,000 (range 6000 to 32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range: 0.3 to 1.8%) based on confirmed and suspected deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz, no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus, although substantial uncertainty remains, clinical severity appears less than that seen in the 1918 influenza pandemic but comparable with that seen in the 1957 pandemic. Clinical attack rates in children in La Gloria were twice that in adults (<15 years of age: 61%; =15 years: 29%). Three different epidemiological analyses gave basic reproduction number (R0) estimates in the range of 1.4 to 1.6, whereas a genetic analysis gave a central estimate of 1.2. This range of values is consistent with 14 to 73 generations of human-to-human transmission having occurred in Mexico to late April. Transmissibility is therefore substantially higher than that of seasonal flu, and comparable with lower estimates of R0 obtained from previous influenza pandemics.},
author = {Fraser, Christophe and Donnelly, Christl A. and Cauchemez, Simon and Hanage, William P. and {Van Kerkhove}, Maria D. and Hollingsworth, T. D{\'{e}}irdre and Griffin, Jamie and Baggaley, Rebecca F. and Jenkins, Helen E. and Lyons, Emily J. and Jombart, Thibaut and Hinsley, Wes R. and Grassly, Nicholas C. and Balloux, Francois and Ghani, Azra C. and Ferguson, Neil M. and Rambaut, Andrew and Pybus, Oliver G. and Lopez-Gatell, Hugo and Alpuche-Aranda, Celia M. and Chapela, Ietza Bojorquez and Zavala, Ethel Palacios and {Ma. Espejo Guevara}, Dulce and Checchi, Francesco and Garcia, Erika and Hugonnet, Stephane and Roth, Cathy},
doi = {10.1126/science.1176062},
issn = {00368075},
journal = {Science},
pmid = {19433588},
title = {{Pandemic potential of a strain of influenza A (H1N1): Early findings}},
year = {2009}
}
@article{Volz_2021,
abstract = {The SARS-CoV-2 lineage B.1.1.7, designated a Variant of Concern 202012/01 (VOC) by Public Health England1, originated in the UK in late Summer to early Autumn 20202. Whole genome SARS-CoV-2 sequence data collected from community-based diagnostic testing shows an unprecedentedly rapid expansion of the B.1.1.7 lineage during Autumn 2020, suggesting a selective advantage. We find 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 the VOC has higher transmissibility than non-VOC lineages, even if the VOC has a different latent period or generation time. The SGTF data indicate a transient shift in the age composition of reported cases, with a larger share of under 20 year olds among reported VOC than non-VOC cases. Time-varying reproduction numbers for the VOC and cocirculating lineages were estimated using SGTF and genomic data. The best supported models did not indicate a substantial difference in VOC transmissibility among different age groups. There is a consensus among all analyses that the VOC has a substantial transmission advantage with a 50% to 100% higher reproduction number.},
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, Roberto 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.},
doi = {10.1038/s41586-021-03470-x},
issn = {14764687},
journal = {Nature},
title = {{Assessing transmissibility of SARS-CoV-2 lineage B.1.1.7 in England}},
year = {2021}
}
@article{Gelman_2013,
author = {Gelman, Andrew and Shalizi, Cosma Rohilla},
doi = {10.1111/j.2044-8317.2011.02037.x},
issn = {00071102},
journal = {British Journal of Mathematical and Statistical Psychology},
month = {feb},
number = {1},
title = {{Philosophy and the practice of Bayesian statistics}},
volume = {66},
year = {2013}
}
@misc{stan_2020,
annote = {Version 2.18.0},
author = {{Stan Development Team}},
title = {{The {Stan} Core Library}},
url = {http://mc-stan.org/},
year = {2018}
}
@inproceedings{Kucukelbir_2015,
abstract = {Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI); we implement it in Stan (code available), a probabilistic programming system. In ADVI the user provides a Bayesian model and a dataset, nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.},
author = {Kucukelbir, Alp and Ranganath, Rajesh and Gelman, Andrew and Blei, David M.},
booktitle = {Advances in Neural Information Processing Systems},
issn = {10495258},
title = {{Automatic variational inference in Stan}},
volume = {2015-January},
year = {2015}
}
@article{Hawryluk_2020,
abstract = {<p> Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalized with COVID-19 using a large dataset ( <italic>N</italic> = 21 000 − 157 000) from the Brazilian Sistema de Informa{\c{c}}{\~{a}}o de Vigil{\^{a}}ncia Epidemiol{\'{o}}gica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and shows significant variation in the mean of the symptom-onset-to-death time, with ranges between 11.2 and 17.8 days across the different states, and a mean of 15.2 days for Brazil. We find strong evidence in favour of specific probability density function choices: for example, the gamma distribution gives the best fit for onset-to-death and the generalized lognormal for onset-to-hospital-admission. Our results show that epidemiological distributions have considerable geographical variation, and provide the first estimates of these distributions in a low and middle-income setting. At the subnational level, variation in COVID-19 outcome timings are found to be correlated with poverty, deprivation and segregation levels, and weaker correlation is observed for mean age, wealth and urbanicity. </p>},
author = {Hawryluk, Iwona and Mellan, Thomas A. and Hoeltgebaum, Henrique and Mishra, Swapnil and Schnekenberg, Ricardo P. and Whittaker, Charles and Zhu, Harrison and Gandy, Axel and Donnelly, Christl A. and Flaxman, Seth and Bhatt, Samir},
doi = {10.1098/rsif.2020.0596},
issn = {1742-5689},
journal = {Journal of The Royal Society Interface},
month = {nov},
number = {172},
title = {{Inference of COVID-19 epidemiological distributions from Brazilian hospital data}},
volume = {17},
year = {2020}
}
@article{champredon_2018,
abstract = {Most compartmental epidemic models can be represented using the renewal equation. The value of the renewal equation is not widely appreciated in the epidemiological modelling community, perhaps because its equivalence to standard models has not been presented rigorously in nontrivial cases. Here, we provide analytical expressions for the intrinsic generation-interval distribution that must be used in the renewal equation in order to yield epidemic dynamics that are identical to those of the susceptible-exposed-infectious-recovered (SEIR) compartmental model with Erlang-distributed latent and infectious periods. This class of models includes the standard (exponentially distributed) SIR and SEIR models as special cases.},
author = {Champredon, David and Dushoff, Jonathan and Earn, David J.D.},
doi = {10.1137/18M1186411},
issn = {00361399},
journal = {SIAM Journal on Applied Mathematics},
keywords = {Differential equations,Epidemic models,Erlang distribution,Generation-interval distribution,Renewal equation,SEIR},
title = {{Equivalence of the Erlang-distributed SEIR epidemic model and the renewal equation}},
year = {2018}
}
@article{Gibbons_2014,
author = {Gibbons, Cheryl L and Mangen, Marie-Jos{\'{e}}e J and Plass, Dietrich and Havelaar, Arie H and Brooke, Russell John and Kramarz, Piotr and Peterson, Karen L and Stuurman, Anke L and Cassini, Alessandro and F{\`{e}}vre, Eric M and Kretzschmar, Mirjam EE},
doi = {10.1186/1471-2458-14-147},
issn = {1471-2458},
journal = {BMC Public Health},
month = {dec},
number = {1},
title = {{Measuring underreporting and under-ascertainment in infectious disease datasets: a comparison of methods}},
volume = {14},
year = {2014}
}
@article{dym_1980,
author = {Dym, Clive L. and Ivey, Elizabeth S. and Stewart, Maurice Bruce},
doi = {10.1119/1.12359},
issn = {0002-9505},
journal = {American Journal of Physics},
month = {nov},
number = {11},
title = {{Principles of Mathematical Modeling}},
volume = {48},
year = {1980}
}
@misc{Vollmer_2020,
abstract = {Italy was the first European country to experience sustained local transmission of COVID-19. As of 1st May 2020, the Italian health authorities reported 28,238 deaths nationally. To control the epidemic, the Italian government implemented a suite of non-pharmaceutical interventions (NPIs), including school and university closures, social distancing and full lockdown involving banning of public gatherings and non essential movement. In this report, we model the effect of NPIs on transmission using data on average mobility. We estimate that the average reproduction number (a measure of transmission intensity) is currently below one for all Italian regions, and significantly so for the majority of the regions. Despite the large number of deaths, the proportion of population that has been infected by SARS-CoV-2 (the attack rate) is far from the herd immunity threshold in all Italian regions, with the highest attack rate observed in Lombardy (13.18% [10.66%-16.70%]). Italy is set to relax the currently implemented NPIs from 4th May 2020. Given the control achieved by NPIs, we consider three scenarios for the next 8 weeks: a scenario in which mobility remains the same as during the lockdown, a scenario in which mobility returns to pre-lockdown levels by 20%, and a scenario in which mobility returns to pre-lockdown levels by 40%. The scenarios explored assume that mobility is scaled evenly across all dimensions, that behaviour stays the same as before NPIs were implemented, that no pharmaceutical interventions are introduced, and it does not include transmission reduction from contact tracing, testing and the isolation of confirmed or suspected cases. New interventions, such as enhanced testing and contact tracing are going to be introduced and will likely contribute to reductions in transmission; therefore our estimates should be viewed as pessimistic projections. We find that, in the absence of additional interventions, even a 20% return to pre-lockdown mobility could lead to a resurgence in the number of deaths far greater than experienced in the current wave in several regions. Future increases in the number of deaths will lag behind the increase in transmission intensity and so a second wave will not be immediately apparent from just monitoring of the daily number of deaths. Our results suggest that SARS-CoV-2 transmission as well as mobility should be closely monitored in the next weeks and months. To compensate for the increase in mobility that will occur due to the relaxation of the currently implemented NPIs, adherence to the recommended social distancing measures alongside enhanced community surveillance including swab testing, contact tracing and the early isolation of infections are of paramount importance to reduce the risk of resurgence in transmission.},
author = {Vollmer, Michaela A.C. and Mishra, Swapnil and {T Unwin}, H. Juliette and Gandy, Axel and Mellan, Thomas A. and Bradley, Valerie and Zhu, Harrison and Coupland, Helen and Hawryluk, Iwona and Hutchinson, Michael and Ratmann, Oliver and Monod, Melodie and Walker, Patrick and Whittaker, Charlie and Cattarino, Lorenzo and Ciavarella, Constance and Cilloni, Lucia and Ainslie, Kylie and Baguelin, Marc and Bhatia, Sangeeta and Boonyasiri, Adhiratha and Brazeau, Nicholas and Charles, Giovanni and Cooper, Laura V. and Cucunuba, Zulma and Cuomo-Dannenburg, Gina and Dighe, Amy and Djaafara, Bimandra and Eaton, Jeff and van Elsland, Sabine L. and FitzJohn, Richard and Fraser, Keith and Gaythorpe, Katy and Green, Will and Hayes, Sarah and Imai, Natsuko and Jeffrey, Ben and Knock, Edward and Laydon, Daniel and Lees, John and Mangal, Tara and Mousa, Andria and Nedjati-Gilani, Gemma and Nouvellet, Pierre and Olivera, Daniela and Parag, Kris V. and Pickles, Michael and Thompson, Hayley A. and Verity, Robert and Walters, Caroline and Wang, Haowei and Wang, Yuanrong and Watson, Oliver J. and Whittles, Lilith and Xi, Xiaoyue and Ghani, Azra and Riley, Steven M. and Okell, Lucy and Donnelly, Christl A. and Ferguson, Neil M. and Dorigatti, Ilaria and Flaxman, Seth and Bhatt, Samir},
booktitle = {medRxiv},
doi = {10.1101/2020.05.05.20089359},
title = {{Report 20: Using mobility to estimate the transmission intensity of COVID-19 in Italy: A subnational analysis with future scenarios}},
year = {2020}
}
@article{Li_2020,
abstract = {Estimation of the prevalence and contagiousness of undocumented novel coronavirus [severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2)] infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here, we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model, and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV-2, including the fraction of undocumented infections and their contagiousness. We estimate that 86% of all infections were undocumented [95% credible interval (CI): 82–90%] before the 23 January 2020 travel restrictions. The transmission rate of undocumented infections per person was 55% the transmission rate of documented infections (95% CI: 46–62%), yet, because of their greater numbers, undocumented infections were the source of 79% of the documented cases. These findings explain the rapid geographic spread of SARS-CoV-2 and indicate that containment of this virus will be particularly challenging.},
author = {Li, Ruiyun and Pei, Sen and Chen, Bin and Song, Yimeng and Zhang, Tao and Yang, Wan and Shaman, Jeffrey},
doi = {10.1126/science.abb3221},
issn = {10959203},
journal = {Science},
pmid = {32179701},
title = {{Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2)}},
year = {2020}
}
@manual{Vasileios_2015,
annote = {R package version 2.1},
author = {Vasileios, Siakoulis},
title = {{acp: Autoregressive Conditional Poisson}},
url = {https://cran.r-project.org/package=acp},
year = {2015}
}
@incollection{getz_2006,
abstract = {The evolution of disease requires a firm understanding of hetero-geneity among pathogen strains and hosts with regard to the processes of transmission, movement, recovery, and pathobiology. In this and a companion chapter (Getz et al. this volume), we focus on the question of how to model the invasion and spread of diseases in heterogeneous environments, without making an explicit link to natural selection-the topic of other chapters in this volume. We begin in this chapter by providing an overview of current methods used to model epidemics in homogeneous populations, covering continuous and discrete time formulations in both deterministic and stochastic frameworks. In particular, we introduce Kermack and McKendricks SIR (susceptible, infected, removed) formulation for the case where the removed (R) disease class is partitioned into immune (V class) and dead (D class) individuals. We also focus on transmission, contrasting mass-action and frequency-dependent formulations and results. This is followed by a presentation of various extensions including the consideration of the latent period of infection, the staging of disease classes, and the addition of vital and demographic processes. We then discuss the relative merits of continuous versus discrete time formulations to model real systems, particularly in the context of stochastic analyses. The overview is completed with a presentation of basic branching process theory as a sto-chastic generation-based model for the invasion of disease into populations of infinite size, with numerical extensions generalizing results to populations of finite size. In framework of branching process theory, we explore the question of minor versus major stochastic epidemics and illuminate the relationship between minor epidemics and a deterministic theory of disease invasion, as well as major epidemics and the deterministic theory of disease establishment. We conclude this chapter with a demonstration of how the basic ideas can be used to model containment policies associated with the outbreak of SARS in Asia in the early part of 2003.},
author = {Getz, Wayne and Lloyd-Smith, James},
doi = {10.1090/dimacs/071/05},
title = {{Basic methods for modeling the invasion and spread of contagious diseases}},
booktitle = {Disease Evolution: Models, Concepts, and Data Analyses},
publisher = {DIMACS Series in Discrete Mathematics and Theoretical Computer Science},
year = {2006}
}
@manual{Cori2020,
annote = {R package version 2.2-3},
author = {Cori, Anne},
title = {{EpiEstim: Estimate Time Varying Reproduction Numbers from Epidemic Curves}},
url = {https://cran.r-project.org/package=EpiEstim},
year = {2020}
}
@article{Gelman_2008,
author = {Gelman, Andrew and Jakulin, Aleks and Pittau, Maria Grazia and Su, Yu-Sung},
doi = {10.1214/08-AOAS191},
issn = {1932-6157},
journal = {The Annals of Applied Statistics},
month = {dec},
number = {4},
title = {{A weakly informative default prior distribution for logistic and other regression models}},
volume = {2},
year = {2008}
}
@article{tokuda2011,
author = {Tokuda, Tomoki and Goodrich, Ben and {Van Mechelen}, I and Gelman, Andrew and Tuerlinckx, F},
journal = {Columbia Univ., New York, USA, Tech. Rep},
pages = {18},
publisher = {Citeseer},
title = {{Visualizing distributions of covariance matrices}},
year = {2011}
}
@article{anderson_1982,
abstract = {Mathematical models for the dynamics of directly transmitted viral and bacterial infections are guides to the understanding of observed patterns in the age-specific incidence of some common childhood diseases of humans, before and after the advent of vaccination programs. For those infections that show recurrent epidemic behavior, the interepidemic period can be related to parameters characterizing the infection (such as latent and infectious periods and the average age of first infection); this relation agrees with the data for a variety of childhood diseases. Criteria for the eradication of a disease are given, in terms of the proportion of the population to be vaccinated and the age-specific vaccination schedule. These criteria are compared with a detailed analysis of the vaccination programs against measles and whooping cough in Britain, and estimates are made of the levels of protection that would be needed to eradicate these diseases.},
author = {Anderson, Roy M. and May, Robert M.},
doi = {10.1126/science.7063839},
issn = {00368075},
journal = {Science},
pmid = {7063839},
title = {{Directly transmitted infectious diseases: Control by vaccination}},
year = {1982}
}
@article{Paul_2011,
author = {Paul, M. and Held, L.},
doi = {10.1002/sim.4177},
issn = {02776715},
journal = {Statistics in Medicine},
month = {may},
number = {10},
title = {{Predictive assessment of a non-linear random effects model for multivariate time series of infectious disease counts}},
volume = {30},
year = {2011}
}
@misc{Mellan_2020,
abstract = {Brazil is currently reporting the second highest number of COVID-19 deaths in the world. Here we characterise the initial dynamics of COVID-19 across the country and assess the impact of non-pharmaceutical interventions (NPIs) that were implemented using a semi-mechanistic Bayesian hierarchical modelling approach. Our results highlight the significant impact these NPIs had across states, reducing an average Rt > 3 to an average of 1.5 by 9-May-2020, but that these interventions failed to reduce Rt < 1, congruent with the worsening epidemic Brazil has experienced since. We identify extensive heterogeneity in the epidemic trajectory across Brazil, with the estimated number of days to reach 0.1% of the state population infected since the first nationally recorded case ranging from 20 days in S{\~{a}}o Paulo compared to 60 days in Goi{\'{a}}s, underscoring the importance of sub-national analyses in understanding asynchronous state-level epidemics underlying the national spread and burden of COVID-19.},
author = {Mellan, Thomas A. and Hoeltgebaum, Henrique H. and Mishra, Swapnil and Whittaker, Charlie and Schnekenberg, Ricardo P. and Gandy, Axel and Unwin, H. Juliette T. and Vollmer, Michaela A.C. and Coupland, Helen and Hawryluk, Iwona and Faria, Nuno Rodrigues and Vesga, Juan and Zhu, Harrison and Hutchinson, Michael and Ratmann, Oliver and Monod, M{\'{e}}lodie and Ainslie, Kylie E.C. and Baguelin, Marc and Bhatia, Sangeeta and Boonyasiri, Adhiratha and Brazeau, Nicholas and Charles, Giovanni and Cucunuba, Zulma and Cuomo-Dannenburg, Gina and Dighe, Amy and Eaton, Jeff and van Elsland, Sabine L. and Gaythorpe, Katy A.M. and Green, Will and Knock, Edward and Laydon, Daniel and Lees, John A. and Mousa, Andria and Nedjati-Gilani, Gemma and Nouvellet, Pierre and Parag, Kris V. and Thompson, Hayley A. and Verity, Robert and Walters, Caroline E. and Wang, Haowei and Wang, Yuanrong and Watson, Oliver J. and Whittles, Lilith and Xi, Xiaoyue and Dorigatti, Ilaria and Walker, Patrick and Ghani, Azra C. and Riley, Steven and Ferguson, Neil M. and Donnelly, Christl A. and Flaxman, Seth and Bhatt, Samir},
booktitle = {medRxiv},
doi = {10.1101/2020.05.09.20096701},
title = {{Subnational analysis of the COVID-19 epidemic in Brazil}},
year = {2020}
}
@article{May1976,
abstract = {First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them. {\textcopyright} 1976 Nature Publishing Group.},
author = {May, Robert M.},
doi = {10.1038/261459a0},
issn = {00280836},
journal = {Nature},
pmid = {934280},
title = {{Simple mathematical models with very complicated dynamics}},
year = {1976}
}
@misc{ECDCForecastHub,
title = {{European Covid-19 Forecast Hub}},
url = {https://covid19forecasthub.eu/},
urldate = {2021-05-25}
}

@Manual{rcore_2011,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2020},
    url = {https://www.R-project.org/},
  }

@article{Box_1962,
abstract = {It is often necessary to adjust some variable X, such as the concentration of consecutive batches of a product, to keep X close to a specified target value. A second more complicated problem occurs when the independent variables X in a response function ?(X) are to be adjusted so that the derivatives ??/? X are kept close to a target value zero, thus maximizing or minimizing the response. These are shown to be problems of prediction, essentially, and the paper is devoted mainly to the estimation from past data of the "best" adjustments to be applied in the first problem.},
author = {Box, G. E. P. and Jenkins, G. M.},
doi = {10.1111/j.2517-6161.1962.tb00460.x},
journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
month = {jul},
number = {2},
pages = {297--331},
publisher = {Wiley},
title = {{Some Statistical Aspects of Adaptive Optimization and Control}},
url = {https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.2517-6161.1962.tb00460.x https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1962.tb00460.x https://rss.onlinelibrary.wiley.com/doi/10.1111/j.2517-6161.1962.tb00460.x},
volume = {24},
year = {1962}
}
@article{Liboschik_2017,
author = {Liboschik, Tobias and Fokianos, Konstantinos and Fried, Roland},
doi = {10.18637/jss.v082.i05},
journal = {Journal of Statistical Software},
number = {5},
pages = {1--51},
title = {{{tscount}: An {R} Package for Analysis of Count Time Series Following Generalized Linear Models}},
volume = {82},
year = {2017}
}
@article{Olney_2021,
abstract = {<p>Since its global emergence in 2020, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused multiple epidemics in the United States. Because medical treatments for the virus are still emerging and a vaccine is not yet available, state and local governments have sought to limit its spread by enacting various social distancing interventions such as school closures and lockdown, but the effectiveness of these interventions is unknown. We applied an established, semi-mechanistic Bayesian hierarchical model of these interventions on SARS-CoV-2 spread in Europe to the United States, using case fatalities from February 29, 2020 up to April 25, 2020, when some states began reversing their interventions. We estimated the effect of interventions across all states, contrasted the estimated reproduction number, Rt, for each state before and after lockdown, and contrasted predicted future fatalities with actual fatalities as a check on the model's validity. Overall, school closures and lockdown are the only interventions modeled that have a reliable impact on Rt, and lockdown appears to have played a key role in reducing Rt below 1.0. We conclude that reversal of lockdown, without implementation of additional, equally effective interventions, will enable continued, sustained transmission of SARS-CoV-2 in the United States.</p>},
author = {Olney, Andrew M and Smith, Jesse and Sen, Saunak and Thomas, Fridtjof and Unwin, H Juliette T},
doi = {10.1093/aje/kwaa293},
issn = {0002-9262},
journal = {American Journal of Epidemiology},
month = {jan},
title = {{Estimating the Effect of Social Distancing Interventions on COVID-19 in the United States}},
year = {2021}
}
@book{gelman_2006,
abstract = {Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout. Author resource page: http://www.stat.columbia.edu/$\sim$gelman/arm/},
author = {Gelman, Andrew and Hill, Jennifer},
booktitle = {Data Analysis Using Regression and Multilevel/Hierarchical Models},
doi = {10.1017/cbo9780511790942},
title = {{Data Analysis Using Regression and Multilevel/Hierarchical Models}},
publisher = {Cambridge University Press},
year = {2006}
}
@article{nouvellet_2018,
abstract = {Outbreaks of novel pathogens such as SARS, pandemic influenza and Ebola require substantial investments in reactive interventions, with consequent implementation plans sometimes revised on a weekly basis. Therefore, short-term forecasts of incidence are often of high priority. In light of the recent Ebola epidemic in West Africa, a forecasting exercise was convened by a network of infectious disease modellers. The challenge was to forecast unseen “future” simulated data for four different scenarios at five different time points. In a similar method to that used during the recent Ebola epidemic, we estimated current levels of transmissibility, over variable time-windows chosen in an ad hoc way. Current estimated transmissibility was then used to forecast near-future incidence. We performed well within the challenge and often produced accurate forecasts. A retrospective analysis showed that our subjective method for deciding on the window of time with which to estimate transmissibility often resulted in the optimal choice. However, when near-future trends deviated substantially from exponential patterns, the accuracy of our forecasts was reduced. This exercise highlights the urgent need for infectious disease modellers to develop more robust descriptions of processes – other than the widespread depletion of susceptible individuals – that produce non-exponential patterns of incidence.},
author = {Nouvellet, Pierre and Cori, Anne and Garske, Tini and Blake, Isobel M. and Dorigatti, Ilaria and Hinsley, Wes and Jombart, Thibaut and Mills, Harriet L. and Nedjati-Gilani, Gemma and {Van Kerkhove}, Maria D. and Fraser, Christophe and Donnelly, Christl A. and Ferguson, Neil M. and Riley, Steven},
doi = {10.1016/j.epidem.2017.02.012},
issn = {18780067},
journal = {Epidemics},
keywords = {Branching process,Forecasting,MCMC,Rapid response,Renewal equation},
pmid = {28351674},
title = {{A simple approach to measure transmissibility and forecast incidence}},
year = {2018}
}
@article{merl_2010,
author = {Merl, Daniel and Johnson, Leah R. and Gramacy, Robert B. and Mangel, Marc},
doi = {10.18637/jss.v036.i06},
issn = {1548-7660},
journal = {Journal of Statistical Software},
number = {6},
title = {{<b>amei</b> : An <i>R</i> Package for the Adaptive Management of Epidemiological Interventions}},
volume = {36},
year = {2010}
}
@article{Held_2012,
author = {Held, Leonhard and Paul, Michaela},
doi = {10.1002/bimj.201200037},
issn = {03233847},
journal = {Biometrical Journal},
month = {nov},
number = {6},
title = {{Modeling seasonality in space-time infectious disease surveillance data}},
volume = {54},
year = {2012}
}
@techreport{hksar_2003,
address = {Hong Kong},
author = {SARS Expert Committee of HKSAR Government},
title = {{Chronology of the SARS epidemic in Hong Kong.}},
institution = {SARS Expert Committee of HKSAR Government},
year = {2003}
}
@article{mishra2020,
author = {Mishra, Swapnil and Berah, Tresnia and Mellan, Thomas A and Unwin, H Juliette T and Vollmer, Michaela A and Parag, Kris V and Gandy, Axel and Flaxman, Seth and Bhatt, Samir},
journal = {arXiv preprint arXiv:2006.16487},
title = {{On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective}},
year = {2020}
}
@article{Zhang_2019,
abstract = {East Asia is as a principal hotspot for emerging zoonotic infections. Understanding the likely pathways for their emergence and spread requires knowledge on human-human and human-animal contacts, but such studies are rare. We used self-completed and interviewer-completed contact diaries to quantify patterns of these contacts for 965 individuals in 2017/2018 in a high-income densely-populated area of China, Shanghai City. Interviewer-completed diaries recorded more social contacts (19.3 vs. 18.0) and longer social contact duration (35.0 vs. 29.1 hours) than self-reporting. Strong age-assortativity was observed in all age groups especially among young participants (aged 7–20) and middle aged participants (25–55 years). 17.7% of participants reported touching animals (15.3% (pets), 0.0% (poultry) and 0.1% (livestock)). Human-human contact was very frequent but contact with animals (especially poultry) was rare although associated with frequent human-human contact. Hence, this densely populated area is more likely to act as an accelerator for human-human spread but less likely to be at the source of a zoonosis outbreak. We also propose that telephone interview at the end of reporting day is a potential improvement of the design of future contact surveys.},
author = {Zhang, Juanjuan and Klepac, Petra and Read, Jonathan M. and Rosello, Alicia and Wang, Xiling and Lai, Shengjie and Li, Meng and Song, Yujian and Wei, Qingzhen and Jiang, Hao and Yang, Juan and Lynn, Henry and Flasche, Stefan and Jit, Mark and Yu, Hongjie},
doi = {10.1038/s41598-019-51609-8},
issn = {20452322},
journal = {Scientific Reports},
pmid = {31641189},
title = {{Patterns of human social contact and contact with animals in Shanghai, China}},
year = {2019}
}
@article{Paul_2008,
author = {Paul, M. and Held, L. and Toschke, A. M.},
doi = {10.1002/sim.3440},
issn = {02776715},
journal = {Statistics in Medicine},
month = {dec},
number = {29},
title = {{Multivariate modelling of infectious disease surveillance data}},
volume = {27},
year = {2008}
}
@article{Roosa_2019,
author = {Roosa, Kimberlyn and Chowell, Gerardo},
doi = {10.1186/s12976-018-0097-6},
issn = {1742-4682},
journal = {Theoretical Biology and Medical Modelling},
month = {dec},
number = {1},
title = {{Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models}},
volume = {16},
year = {2019}
}
@book{kreft_2011,
abstract = {This is a user-oriented guide to the practicalities of multilevel modeling in social research. The authors introduce the researcher to the practical issues and problems of doing multilevel analyses. On the basis of genuine data sets, they illustrate the technique through worked examples, using the leading computer package for multilevel modeling, MLn. This book will be useful for students and researchers who need to know how to apply multilevel models appropriately and effectively. (PsycINFO Database Record (c) 2003 APA, all rights reserved)},
author = {Kreft, Ita and de Leeuw, Jan},
booktitle = {Introducing Multilevel Modeling},
doi = {10.4135/9781849209366},
title = {{Introducing Multilevel Modeling}},
publisher = {SAGE Publications Ltd},
year = {2011}
}
@article{wallinga_2004,
abstract = {Severe acute respiratory syndrome (SARS) has been the first severe contagious disease to emerge in the 21st century. The available epidemic curves for SARS show marked differences between the affected regions with respect to the total number of cases and epidemic duration, even for those regions in which outbreaks started almost simultaneously and similar control measures were implemented at the same time. The authors developed a likelihood-based estimation procedure that infers the temporal pattern of effective reproduction numbers from an observed epidemic curve. Precise estimates for the effective reproduction numbers were obtained by applying this estimation procedure to available data for SARS outbreaks that occurred in Hong Kong, Vietnam, Singapore, and Canada in 2003. The effective reproduction numbers revealed that epidemics in the various affected regions were characterized by markedly similar disease transmission potentials and similar levels of effectiveness of control measures. In controlling SARS outbreaks, timely alerts have been essential: Delaying the institution of control measures by 1 week would have nearly tripled the epidemic size and would have increased the expected epidemic duration by 4 weeks.},
author = {Wallinga, Jacco and Teunis, Peter},
doi = {10.1093/aje/kwh255},
issn = {00029262},
journal = {American Journal of Epidemiology},
keywords = {Disease outbreaks,Estimation,Infection,Models,SARS virus,Severe acute respiratory syndrome,Statistics,statistical},
pmid = {15353409},
title = {{Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures}},
year = {2004}
}
@article{cauchemez_2008,
abstract = {The threat posed by the highly pathogenic H5N1 influenza virus requires public health authorities to prepare for a human pandemic. Although pre-pandemic vaccines and antiviral drugs might significantly reduce illness rates, their stockpiling is too expensive to be practical for many countries. Consequently, alternative control strategies, based on non-pharmaceutical interventions, are a potentially attractive policy option. School closure is the measure most often considered. The high social and economic costs of closing schools for months make it an expensive and therefore controversial policy, and the current absence of quantitative data on the role of schools during influenza epidemics means there is little consensus on the probable effectiveness of school closure in reducing the impact of a pandemic. Here, from the joint analysis of surveillance data and holiday timing in France, we quantify the role of schools in influenza epidemics and predict the effect of school closure during a pandemic. We show that holidays lead to a 20-29% reduction in the rate at which influenza is transmitted to children, but that they have no detectable effect on the contact patterns of adults. Holidays prevent 16-18% of seasonal influenza cases (18-21% in children). By extrapolation, we find that prolonged school closure during a pandemic might reduce the cumulative number of cases by 13-17% (18-23% in children) and peak attack rates by up to 39-45% (47-52% in children). The impact of school closure would be reduced if it proved difficult to maintain low contact rates among children for a prolonged period. {\textcopyright}2008 Nature Publishing Group.},
author = {Cauchemez, Simon and Valleron, Alain Jacques and Bo{\"{e}}lle, Pierre Yves and Flahault, Antoine and Ferguson, Neil M.},
doi = {10.1038/nature06732},
issn = {14764687},
journal = {Nature},
pmid = {18401408},
title = {{Estimating the impact of school closure on influenza transmission from Sentinel data}},
year = {2008}
}
@article{Thompson1985,
abstract = {Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. * Realistic applications from a variety of disciplines integrated throughout the text* Plentiful, updated and more rigorous problems, including computer "challenges"* Revised end-of-chapter exercises sets-in all, 250 exercises with answers* New chapter on Brownian motion and related processes* Additional sections on Matingales and Poisson process* Solutions manual available to adopting instructors},
author = {Thompson, W. A. and Taylor, Howard M. and Karlin, Samuel},
doi = {10.2307/2287941},
issn = {01621459},
journal = {Journal of the American Statistical Association},
title = {{An Introduction to Stochastic Modeling.}},
year = {1985}
}
@article{ferguson_2006,
abstract = {Development of strategies for mitigating the severity of a new influenza pandemic is now a top global public health priority. Influenza prevention and containment strategies can be considered under the broad categories of antiviral, vaccine and non-pharmaceutical (case isolation, household quarantine, school or workplace closure, restrictions on travel) measures. Mathematical models are powerful tools for exploring this complex landscape of intervention strategies and quantifying the potential costs and benefits of different options. Here we use a large-scale epidemic simulation to examine intervention options should initial containment of a novel influenza outbreak fail, using Great Britain and the United States as examples. We find that border restrictions and/or internal travel restrictions are unlikely to delay spread by more than 2-3 weeks unless more than 99% effective. School closure during the peak of a pandemic can reduce peak attack rates by up to 40%, but has little impact on overall attack rates, whereas case isolation or household quarantine could have a significant impact, if feasible. Treatment of clinical cases can reduce transmission, but only if antivirals are given within a day of symptoms starting. Given enough drugs for 50% of the population, household-based prophylaxis coupled with reactive school closure could reduce clinical attack rates by 40-50%. More widespread prophylaxis would be even more logistically challenging but might reduce attack rates by over 75%. Vaccine stockpiled in advance of a pandemic could significantly reduce attack rates even if of low efficacy. Estimates of policy effectiveness will change if the characteristics of a future pandemic strain differ substantially from those seen in past pandemics. {\textcopyright} 2006 Nature Publishing Group.},
author = {Ferguson, Neil M. and Cummings, Derek A.T. and Fraser, Christophe and Cajka, James C. and Cooley, Philip C. and Burke, Donald S.},
doi = {10.1038/nature04795},
issn = {14764687},
journal = {Nature},
pmid = {16642006},
title = {{Strategies for mitigating an influenza pandemic}},
year = {2006}
}
@article{hohle_2007,
author = {H{\"{o}}hle, Michael and Feldmann, Ulrike},
doi = {10.1016/j.csda.2006.11.016},
issn = {01679473},
journal = {Computational Statistics \& Data Analysis},
month = {oct},
number = {2},
title = {{RLadyBug—An R package for stochastic epidemic models}},
volume = {52},
year = {2007}
}
@article{badr_2020,
abstract = {Background: Within 4 months of COVID-19 first being reported in the USA, it spread to every state and to more than 90% of all counties. During this period, the US COVID-19 response was highly decentralised, with stay-at-home directives issued by state and local officials, subject to varying levels of enforcement. The absence of a centralised policy and timeline combined with the complex dynamics of human mobility and the variable intensity of local outbreaks makes assessing the effect of large-scale social distancing on COVID-19 transmission in the USA a challenge. Methods: We used daily mobility data derived from aggregated and anonymised cell (mobile) phone data, provided by Teralytics (Z{\"{u}}rich, Switzerland) from Jan 1 to April 20, 2020, to capture real-time trends in movement patterns for each US county, and used these data to generate a social distancing metric. We used epidemiological data to compute the COVID-19 growth rate ratio for a given county on a given day. Using these metrics, we evaluated how social distancing, measured by the relative change in mobility, affected the rate of new infections in the 25 counties in the USA with the highest number of confirmed cases on April 16, 2020, by fitting a statistical model for each county. Findings: Our analysis revealed that mobility patterns are strongly correlated with decreased COVID-19 case growth rates for the most affected counties in the USA, with Pearson correlation coefficients above 0{\textperiodcentered}7 for 20 of the 25 counties evaluated. Additionally, the effect of changes in mobility patterns, which dropped by 35–63% relative to the normal conditions, on COVID-19 transmission are not likely to be perceptible for 9–12 days, and potentially up to 3 weeks, which is consistent with the incubation time of severe acute respiratory syndrome coronavirus 2 plus additional time for reporting. We also show evidence that behavioural changes were already underway in many US counties days to weeks before state-level or local-level stay-at-home policies were implemented, implying that individuals anticipated public health directives where social distancing was adopted, despite a mixed political message. Interpretation: This study strongly supports a role of social distancing as an effective way to mitigate COVID-19 transmission in the USA. Until a COVID-19 vaccine is widely available, social distancing will remain one of the primary measures to combat disease spread, and these findings should serve to support more timely policy making around social distancing in the USA in the future. Funding: None.},
author = {Badr, Hamada S. and Du, Hongru and Marshall, Maximilian and Dong, Ensheng and Squire, Marietta M. and Gardner, Lauren M.},
doi = {10.1016/S1473-3099(20)30553-3},
issn = {14744457},
journal = {The Lancet Infectious Diseases},
pmid = {32621869},
title = {{Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study}},
year = {2020}
}
@article{fraser_2004,
abstract = {The aim of this study is to identify general properties of emerging infectious agents that determine the likely success of two simple public health measures in controlling outbreaks, namely (i) isolating symptomatic individuals and (ii) tracing and quarantining their contacts. Because these measures depend on the recognition of specific disease symptoms, we investigate the relative timing of infectiousness and the appearance of symptoms by using a mathematical model. We show that the success of these control measures is determined as much by the proportion of transmission occurring prior to the onset of overt clinical symptoms (or via asymptomatic infection) as the inherent transmissibility of the etiological agent (measured by the reproductive number R0). From published studies, we estimate these quantities for two moderately transmissible viruses, severe acute respiratory syndrome coronavirus and HIV, and for two highly transmissible viruses, smallpox and pandemic influenza. We conclude that severe acute respiratory syndrome and smallpox are easier to control using these simple public health measures. Direct estimation of the proportion of asymptomatic and presymptomatic infections is achievable by contact tracing and should be a priority during an outbreak of a novel infectious agent.},
author = {Fraser, Christophe and Riley, Steven and Anderson, Roy M. and Ferguson, Neil M.},
doi = {10.1073/pnas.0307506101},
issn = {00278424},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
keywords = {Epidemiology,HIV,Influenza,Severe acute respiratory syndrome,Smallpox},
pmid = {15071187},
title = {{Factors that make an infectious disease outbreak controllable}},
year = {2004}
}
@article{Chatzilena_2019,
author = {Chatzilena, Anastasia and van Leeuwen, Edwin and Ratmann, Oliver and Baguelin, Marc and Demiris, Nikolaos},
doi = {10.1016/j.epidem.2019.100367},
issn = {17554365},
journal = {Epidemics},
month = {dec},
title = {{Contemporary statistical inference for infectious disease models using Stan}},
volume = {29},
year = {2019}
}
@article{Zhao_2020,
abstract = {BACKGROUND: The novel coronavirus SARS-CoV-2 is a newly emerging virus. The antibody response in infected patient remains largely unknown, and the clinical values of antibody testing have not been fully demonstrated. METHODS: A total of 173 patients with SARS-CoV-2 infection were enrolled. Their serial plasma samples (n=535) collected during the hospitalization were tested for total antibodies (Ab), IgM and IgG against SARS-CoV-2. The dynamics of antibodies with the disease progress was analyzed. RESULTS: Among 173 patients, the seroconversion rate for Ab, IgM and IgG was 93.1%, 82.7% and 64.7%, respectively. The reason for the negative antibody findings in 12 patients might due to the lack of blood samples at the later stage of illness. The median seroconversion time for Ab, IgM and then IgG were day-11, day-12 and day-14, separately. The presence of antibodies was <40% among patients within 1-week since onset, and rapidly increased to 100.0% (Ab), 94.3% (IgM) and 79.8% (IgG) since day-15 after onset. In contrast, RNA detectability decreased from 66.7% (58/87) in samples collected before day-7 to 45.5% (25/55) during day 15-39. Combining RNA and antibody detections significantly improved the sensitivity of pathogenic diagnosis for COVID-19 (p<0.001), even in early phase of 1-week since onset (p=0.007). Moreover, a higher titer of Ab was independently associated with a worse clinical classification (p=0.006). CONCLUSIONS: The antibody detection offers vital clinical information during the course of SARS-CoV-2 infection. The findings provide strong empirical support for the routine application of serological testing in the diagnosis and management of COVID-19 patients.},
author = {Zhao, Juanjuan and Yuan, Quan and Wang, Haiyan and Liu, Wei and Liao, Xuejiao and Su, Yingying and Wang, Xin and Yuan, Jing and Li, Tingdong and Li, Jinxiu and Qian, Shen and Hong, Congming and Wang, Fuxiang and Liu, Yingxia and Wang, Zhaoqin and He, Qing and Li, Zhiyong and He, Bin and Zhang, Tianying and Fu, Yang and Ge, Shengxiang and Liu, Lei and Zhang, Jun and Xia, Ningshao and Zhang, Zheng},
doi = {10.1093/cid/ciaa344},
issn = {15376591},
journal = {Clinical infectious diseases : an official publication of the Infectious Diseases Society of America},
keywords = {COVID-19,SARS-CoV-2,antibody},
pmid = {32221519},
title = {{Antibody responses to SARS-CoV-2 in patients of novel coronavirus disease 2019}},
year = {2020}
}
@book{Anderson_2000,
address = {New York, NY},
author = {Andersson, H{\aa}kan and Britton, Tom},
doi = {10.1007/978-1-4612-1158-7},
isbn = {978-0-387-95050-1},
publisher = {Springer New York},
title = {{Stochastic Epidemic Models and Their Statistical Analysis}},
volume = {151},
year = {2000}
}
@article{bettencourt_2008,
abstract = {Background: Fast changes in human demographics worldwide, coupled with increased mobility, and modified land uses make the threat of emerging infectious diseases increasingly important. Currently there is worldwide alert for H5N1 avian influenza becoming as transmissible in humans as seasonal influenza, and potentially causing a pandemic of unprecedented proportions. Here we show how epidemiological surveillance data for emerging infectious diseases can be interpreted in real time to assess changes in transmissibility with quantified uncertainty, and to perform running time predictions of new cases and guide logistics allocations. Methodology/Principal Findings: We develop an extension of standard epidemiological models, appropriate for emerging infectious diseases, that describes the probabilistic progression of case numbers due to the concurrent effects of (incipient) human transmission and multiple introductions from a reservoir. The model is cast in terms of surveillance observables and immediately suggests a simple graphical estimation procedure for the effective reproductive number R (mean number of cases generated by an infectious individual) of standard epidemics. For emerging infectious diseases, which typically show large relative case number fluctuations over time, we develop a Bayesian scheme for real time estimation of the probability distribution of the effective reproduction number and show how to use such inferences to formulate significance tests on future epidemiological observations. Conclusions/Significance: Violations of these significance tests define statistical anomalies that may signal changes in the epidemiology of emerging diseases and should trigger further field investigation. We apply the methodology to case data from World Health Organization reports to place bounds on the current transmissibility of H5N1 influenza in humans and establish a statistical basis for monitoring its evolution in real time. {\textcopyright} 2008 Bettencourt, Ribeiro.},
author = {Bettencourt, Lu{\'{i}}s M.A. and Ribeiro, Ruy M.},
doi = {10.1371/journal.pone.0002185},
issn = {19326203},
journal = {PLoS ONE},
pmid = {18478118},
title = {{Real time bayesian estimation of the epidemic potential of emerging infectious diseases}},
year = {2008}
}
@article{Cori2013,
abstract = {The quantification of transmissibility during epidemics is essential to designing and adjusting public health responses. Transmissibility can be measured by the reproduction number R, the average number of secondary cases caused by an infected individual. Several methods have been proposed to estimate R over the course of an epidemic; however, they are usually difficult to implement for people without a strong background in statistical modeling. Here, we present a ready-to-use tool for estimating R from incidence time series, which is implemented in popular software including Microsoft Excel (Microsoft Corporation, Redmond, Washington). This tool produces novel, statistically robust analytical estimates of R and incorporates uncertainty in the distribution of the serial interval (the time between the onset of symptoms in a primary case and the onset of symptoms in secondary cases). We applied the method to 5 historical outbreaks; the resulting estimates of R are consistent with those presented in the literature. This tool should help epidemiologists quantify temporal changes in the transmission intensity of future epidemics by using surveillance data. {\textcopyright} The Author 2013.},
author = {Cori, Anne and Ferguson, Neil M. and Fraser, Christophe and Cauchemez, Simon},
doi = {10.1093/aje/kwt133},
issn = {00029262},
journal = {American Journal of Epidemiology},
keywords = {Incidence,Influenza,Measles,Reproduction number,SARS,Smallpox,Software,cori_2013},
mendeley-tags = {cori_2013},
pmid = {24043437},
title = {{A new framework and software to estimate time-varying reproduction numbers during epidemics}},
year = {2013}
}
@article{Groendyke_2018,
author = {Groendyke, Chris and Welch, David},
doi = {10.18637/jss.v083.i11},
issn = {1548-7660},
journal = {Journal of Statistical Software},
number = {11},
title = {{<b>epinet</b> : An <i>R</i> Package to Analyze Epidemics Spread across Contact Networks}},
volume = {83},
year = {2018}
}
@article{Jombart_2020,
abstract = {We estimate the number of COVID-19 cases from newly reported deaths in a population without previous reports. Our results suggest that by the time a single death occurs, hundreds to thousands of cases are likely to be present in that population. This suggests containment via contact tracing will be challenging at this point, and other response strategies should be considered. Our approach is implemented in a publicly available, user-friendly, online tool.},
author = {Jombart, Thibaut and van Zandvoort, Kevin and Russell, Timothy W. and Jarvis, Christopher I. and Gimma, Amy and Abbott, Sam and Clifford, Sam and Funk, Sebastian and Gibbs, Hamish and Liu, Yang and Pearson, Carl A.B. and Bosse, Nikos I. and Eggo, Rosalind M. and Kucharski, Adam J. and Edmunds, W. John},
doi = {10.12688/wellcomeopenres.15786.1},
issn = {2398502X},
journal = {Wellcome Open Research},
keywords = {Covid-19,Epidemics,Estimation,Modelling,Outbreak,SARS-CoV-2,Statistics},
pmid = {32511459},
title = {{Inferring the number of COVID-19 cases from recently reported deaths}},
year = {2020}
}
@misc{Unkel2012,
abstract = {Unusual clusters of disease must be detected rapidly for effective public health interventions to be introduced. Over the past decade there has been a surge in interest in statistical methods for the early detection of infectious disease outbreaks. This growth in interest has given rise to much new methodological work, ranging across the spectrum of statistical methods. The paper presents a comprehensive review of the statistical approaches that have been proposed. Applications to both laboratory and syndromic surveillance data are provided to illustrate the various methods. {\textcopyright} 2011 Royal Statistical Society.},
author = {Unkel, Steffen and Farrington, C. Paddy and Garthwaite, Paul H. and Robertson, Chris and Andrews, Nick},
booktitle = {Journal of the Royal Statistical Society. Series A: Statistics in Society},
doi = {10.1111/j.1467-985X.2011.00714.x},
issn = {09641998},
keywords = {Biosurveillance,Clusters,Control chart,Epidemics,Infectious diseases,Outbreak,Prospective detection,Surveillance},
month = {jan},
number = {1},
pages = {49--82},
publisher = {John Wiley & Sons, Ltd},
title = {{Statistical methods for the prospective detection of infectious disease outbreaks: A review}},
url = {https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1467-985X.2011.00714.x https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-985X.2011.00714.x https://rss.onlinelibrary.wiley.com/doi/10.1111/j.1467-985X.2011.00714.x},
volume = {175},
year = {2012}
}
@article{kermack_1932,
abstract = {In a previous communication an attempt was made to investigate mathe­matically the course of an epidemic in a closed population of susceptible individuals. In order to simplify the problem certain definite assumptions were made, namely, that all individuals were equally susceptible, and that death resulted, or complete immunity was conferred, as the result of an attack. The infectivity of the individual and his chances of death or recovery were represented by arbitrary functions, and the chance of a new infection occurring was assumed to be proportional to the product of the infected and susceptible members of the population. In spite of the introduction of the arbitrary functions, it was shown that in general a critical density of population existed, such that if the actual density was less than this, no epidemic could occur, but if it exceeded this by n an epidemic would appear on the introduction of a focus of infection, and further that if n was small relative to the population density, the size of the epidemic would be 2 n per unit area. It was shown that these conclusions could be readily extended to the case of a metaxenous disease, that is, one in which transmission takes place through an intermediate host. It is the purpose of the present paper to consider the effect of the continuous introduction of fresh susceptible individuals into the population. It appeared desirable to investigate this point, since it might make it possible to interpret certain aspects of the incidence of disease not only in human communities where there is usually an influx of fresh susceptible individuals either by immigration or by birth, but also in the animal experiments carried out by Topley and others—where fresh animals were introduced at a constant rate into the cages in which cases of disease were already present—from which certain definite results were obtained.},
author = {{Kermack, William Ogilvy and McKendrick}, A. G.},
doi = {10.1098/rspa.1932.0171},
issn = {0950-1207},
journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
month = {oct},
number = {834},
title = {{Contributions to the mathematical theory of epidemics. II. —The problem of endemicity}},
volume = {138},
year = {1932}
}
@book{hox_2010,
author = {Hox, Joop J and Moerbeek, Mirjam and de Schoot, Rens},
publisher = {Routledge},
title = {{Multilevel analysis: Techniques and applications}},
year = {2010}
}
@article{Flaxman2020,
abstract = {Following the emergence of a novel coronavirus1 (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions such as closure of schools and national lockdowns. We study the impact of major interventions across 11 European countries for the period from the start of COVID-19 until the 4th of May 2020 when lockdowns started to be lifted. Our model calculates backwards from observed deaths to estimate transmission that occurred several weeks prior, allowing for the time lag between infection and death. We use partial pooling of information between countries with both individual and shared effects on the reproduction number. Pooling allows more information to be used, helps overcome data idiosyncrasies, and enables more timely estimates. Our model relies on fixed estimates of some epidemiological parameters such as the infection fatality rate, does not include importation or subnational variation and assumes that changes in the reproduction number are an immediate response to interventions rather than gradual changes in behavior. Amidst the ongoing pandemic, we rely on death data that is incomplete, with systematic biases in reporting, and subject to future consolidation. We estimate that, for all the countries we consider, current interventions have been sufficient to drive the reproduction number $${R}_{t}$$Rt below 1 (probability $${R}_{t}\,$$Rt< 1.0 is 99.9%) and achieve epidemic control. We estimate that, across all 11 countries, between 12 and 15 million individuals have been infected with SARS-CoV-2 up to 4th May, representing between 3.2% and 4.0% of the population. Our results show that major non-pharmaceutical interventions and lockdown in particular have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.},
author = {Flaxman, Seth and Mishra, Swapnil and Gandy, Axel and Unwin, H Juliette T and Mellan, Thomas A and Coupland, Helen and Whittaker, Charles and Zhu, Harrison and Berah, Tresnia and Eaton, Jeffrey W and Monod, M{\'{e}}lodie and Perez-Guzman, Pablo N and Schmit, Nora and Cilloni, Lucia and Ainslie, Kylie E C and Baguelin, Marc and Boonyasiri, Adhiratha and Boyd, Olivia and Cattarino, Lorenzo and Cooper, Laura V and Cucunub{\'{a}}, Zulma and Cuomo-Dannenburg, Gina and Dighe, Amy and Djaafara, Bimandra and Dorigatti, Ilaria and van Elsland, Sabine L and FitzJohn, Richard G and Gaythorpe, Katy A M and Geidelberg, Lily and Grassly, Nicholas C and Green, William D and Hallett, Timothy and Hamlet, Arran and Hinsley, Wes and Jeffrey, Ben and Knock, Edward and Laydon, Daniel J and Nedjati-Gilani, Gemma and Nouvellet, Pierre and Parag, Kris V and Siveroni, Igor and Thompson, Hayley A and Verity, Robert and Volz, Erik and Walters, Caroline E and Wang, Haowei and Wang, Yuanrong and Watson, Oliver J and Winskill, Peter and Xi, Xiaoyue and Walker, Patrick G T and Ghani, Azra C and Donnelly, Christl A and Riley, Steven M and Vollmer, Michaela A C and Ferguson, Neil M and Okell, Lucy C and Bhatt, Samir and Team, Imperial College COVID-19 Response},
doi = {10.1038/s41586-020-2405-7},
issn = {1476-4687},
journal = {Nature},
title = {{Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe}},
url = {https://doi.org/10.1038/s41586-020-2405-7},
year = {2020}
}
@article{Kucukelbir_2017,
abstract = {Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (advi). Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. advi automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. advi supports a broad class of models-no conjugacy assumptions are required. We study advi across ten modern probabilistic models and apply it to a dataset with millions of observations. We deploy advi as part of Stan, a probabilistic programming system.},
author = {Kucukelbir, Alp and Blei, David M. and Gelman, Andrew and Ranganath, Rajesh and Tran, Dustin},
issn = {15337928},
journal = {Journal of Machine Learning Research},
title = {{Automatic Differentiation Variational Inference}},
volume = {18},
year = {2017}
}
@book{anderson_1992,
author = {{Anderson, Roy M and Anderson, B and May}, Robert M},
publisher = {Oxford university press},
title = {{Infectious diseases of humans: dynamics and control}},
year = {1992}
}
@article{Hauser_2020,
author = {Hauser, Anthony and Counotte, Michel J. and Margossian, Charles C. and Konstantinoudis, Garyfallos and Low, Nicola and Althaus, Christian L. and Riou, Julien},
doi = {10.1371/journal.pmed.1003189},
issn = {1549-1676},
journal = {PLOS Medicine},
month = {jul},
number = {7},
title = {{Estimation of SARS-CoV-2 mortality during the early stages of an epidemic: A modeling study in Hubei, China, and six regions in Europe}},
volume = {17},
year = {2020}
}
@article{obadia_2012,
author = {Obadia, Thomas and Haneef, Romana and Bo{\"{e}}lle, Pierre-Yves},
doi = {10.1186/1472-6947-12-147},
issn = {1472-6947},
journal = {BMC Medical Informatics and Decision Making},
month = {dec},
number = {1},
title = {{The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks}},
volume = {12},
year = {2012}
}
@article{bellman_1948,
author = {Bellman, R. and Harris, T. E.},
doi = {10.1073/pnas.34.12.601},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
pmid = {16588841},
title = {{On the Theory of Age-Dependent Stochastic Branching Processes}},
year = {1948}
}
@misc{scott_2020,
annote = {R package version 0.6.0},
author = {Scott, James A and Gandy, Axel and Mishra, Swapnil and Unwin, Juliette and Flaxman, Seth and Bhatt, Samir},
title = {{epidemia: Modeling of Epidemics using Hierarchical Bayesian Models}},
url = {https://imperialcollegelondon.github.io/epidemia/},
year = {2020}
}
@article{Jenness_2018,
author = {Jenness, Samuel M. and Goodreau, Steven M. and Morris, Martina},
doi = {10.18637/jss.v084.i08},
issn = {1548-7660},
journal = {Journal of Statistical Software},
number = {8},
title = {{<b>EpiModel</b> : An <i>R</i> Package for Mathematical Modeling of Infectious Disease over Networks}},
volume = {84},
year = {2018}
}

@Misc{stan_modeling_language,
title = {{RStan}: the {R} interface to {Stan}},
author = {{Stan Development Team}},
note = {R package version 2.21.2},
year = {2020},
url = {http://mc-stan.org/},
}

@article{miller_2020,
author = {Miller, Andrew C and Foti, Nicholas J and Lewnard, Joseph A and Jewell, Nicholas P and Guestrin, Carlos and Fox, Emily B},
doi = {10.1101/2020.05.07.20094441},
journal = {medRxiv},
publisher = {Cold Spring Harbor Laboratory Press},
title = {{Mobility trends provide a leading indicator of changes in SARS-CoV-2 transmission}},
url = {https://www.medrxiv.org/content/early/2020/05/11/2020.05.07.20094441},
year = {2020}
}
@article{Wong_2020,
abstract = {<p>Superspreaders, infected individuals who result in an outsized number of secondary cases, are believed to underlie a significant fraction of total SARS-CoV-2 transmission. Here, we combine empirical observations of SARS-CoV and SARS-CoV-2 transmission and extreme value statistics to show that the distribution of secondary cases is consistent with being fat-tailed, implying that large superspreading events are extremal, yet probable, occurrences. We integrate these results with interaction-based network models of disease transmission and show that superspreading, when it is fat-tailed, leads to pronounced transmission by increasing dispersion. Our findings indicate that large superspreading events should be the targets of interventions that minimize tail exposure.</p>},
author = {Wong, Felix and Collins, James J.},
doi = {10.1073/pnas.2018490117},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences},
month = {nov},
number = {47},
title = {{Evidence that coronavirus superspreading is fat-tailed}},
volume = {117},
year = {2020}
}
@article{Myers2000,
abstract = {Emerging infectious diseases pose a growing threat to human populations. Many of the world's epidemic diseases (particularly those transmitted by intermediate hosts) are known to be highly sensitive to long-term changes in climate and short-term fluctuations in the weather. The application of environmental data to the study of disease offers the capability to demonstrate vector-environment relationships and potentially forecast the risk of disease outbreaks or epidemics. Accurate disease forecasting models would markedly improve epidemic prevention and control capabilities. This chapter examines the potential for epidemic forecasting and discusses the issues associated with the development of global networks for surveillance and prediction. Existing global systems for epidemic preparedness focus on disease surveillance using either expert knowledge or statistical modelling of disease activity and thresholds to identify times and areas of risk. Predictive health information systems would use monitored environmental variables, linked to a disease system, to be observed and provide prior information of outbreaks. The components and varieties of forecasting systems are discussed with selected examples, along with issues relating to further development.},
author = {Myers, M. F. and Rogers, D. J. and Cox, J. and Flahault, A. and Hay, S. I.},
doi = {10.1016/s0065-308x(00)47013-2},
file = {:Users/jamesscott/Documents/mendeley2/Myers et al. - 2000 - Forecasting disease risk for increased epidemic preparedness in public health.pdf:pdf},
issn = {0065308X},
journal = {Advances in Parasitology},
pages = {309--330},
pmid = {10997211},
publisher = {Academic Press},
title = {{Forecasting disease risk for increased epidemic preparedness in public health}},
url = {/pmc/articles/PMC3196833/ /pmc/articles/PMC3196833/?report=abstract https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3196833/},
volume = {47},
year = {2000}
}
@article{Flaxman2020MA,
author = {Flaxman, Seth and Mishra, Swapnil and Scott, James and Ferguson, Neil and Gandy, Axel and Bhatt, Samir},
doi = {10.1038/s41586-020-3026-x},
isbn = {1476-4687},
journal = {Nature},
number = {7839},
pages = {E29----E32},
title = {{Reply to: The effect of interventions on COVID-19}},
url = {https://doi.org/10.1038/s41586-020-3026-x},
volume = {588},
year = {2020}
}
@article{bates_2015,
author = {Bates, Douglas and M{\"{a}}chler, Martin and Bolker, Ben and Walker, Steve},
doi = {10.18637/jss.v067.i01},
journal = {Journal of Statistical Software},
number = {1},
pages = {1--48},
title = {{Fitting Linear Mixed-Effects Models Using {lme4}}},
volume = {67},
year = {2015}
}
@misc{recon,
title = {{The R Epidemics Consortium}},
url = {https://www.repidemicsconsortium.org/}
}
@misc{rstan_2020,
annote = {R package version 2.21.2},
author = {{Stan Development Team}},
title = {{{RStan}: the {R} interface to {Stan}}},
url = {https://mc-stan.org/},
year = {2020}
}
@misc{Grinsztajn_2021,
archivePrefix = {arXiv},
arxivId = {stat.CO/2006.02985},
author = {Grinsztajn, L{\'{e}}o and Semenova, Elizaveta and Margossian, Charles C and Riou, Julien},
eprint = {2006.02985},
primaryClass = {stat.CO},
title = {{Bayesian workflow for disease transmission modeling in Stan}},
year = {2021}
}
@article{ferguson_2001,
abstract = {The foot and mouth disease (FMD) epidemic in British livestock remains an ongoing cause for concern, with new cases still arising in previously unaffected areas. Epidemiological analyses have been vital in delivering scientific advice to government on effective control measures. Using disease, culling and census data on all livestock farms in Great Britain, we analysed the risk factors determining the spatiotemporal evolution of the epidemic and of the impact of control policies on FMD incidence. Here we show that the species mix, animal numbers and the number of distinct land parcels in a farm are central to explaining regional variation in transmission intensity. We use the parameter estimates thus obtained in a dynamical model of disease spread to show that extended culling programmes were essential for controlling the epidemic to the extent achieved, but demonstrate that the epidemic could have been substantially reduced in scale had the most efficient control measures been rigorously applied earlier.},
author = {Ferguson, N. M. and Donnelly, C. A. and Anderson, R. M.},
doi = {10.1038/35097116},
issn = {00280836},
journal = {Nature},
pmid = {11586365},
title = {{Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain}},
year = {2001}
}
@article{Reich_2019,
author = {Reich, Nicholas G. and McGowan, Craig J. and Yamana, Teresa K. and Tushar, Abhinav and Ray, Evan L. and Osthus, Dave and Kandula, Sasikiran and Brooks, Logan C. and Crawford-Crudell, Willow and Gibson, Graham Casey and Moore, Evan and Silva, Rebecca and Biggerstaff, Matthew and Johansson, Michael A. and Rosenfeld, Roni and Shaman, Jeffrey},
doi = {10.1371/journal.pcbi.1007486},
issn = {1553-7358},
journal = {PLOS Computational Biology},
month = {nov},
number = {11},
title = {{Accuracy of real-time multi-model ensemble forecasts for seasonal influenza in the U.S.}},
volume = {15},
year = {2019}
}
@article{kermack_1933,
abstract = {In a previous paper (Part II of this series) an attempt was made to treat from a general point of view the problem of a single disease in a population which consisted of three categories of people—namely, never infected, sick and recovered—and in which the infectivity of the disease was a function of the period of illness, whilst the susceptibility of a recovered person was a function of the period which had elapsed since the time of his recovery. New individuals entering the population either by birth or by immigration naturally entered the category of the never infected which for convenience we called “virgins.” It was pointed out that the results obtained were subject to two important limitations: (1) that the disease under consideration was the only cause of death, and (2) that the age of the individuals did not affect their infectivity, susceptibility or reproductiveness. It is the purpose of the present paper to remove the first of these limitations by the introduction of constant non-specific death rates, which for the sake of generality are assumed to be different for virgins, sick, and recovered. It may be stated at once that the introduction of this additional factor produces surprisingly little change in the general nature of the results previously obtained, and that the conclusions of the previous paper hold with very little modifica­tion.},
author = {{Kermack, William Ogilvy and McKendrick}, A. G.},
doi = {10.1098/rspa.1933.0106},
issn = {0950-1207},
journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
month = {jul},
number = {843},
title = {{Contributions to the mathematical theory of epidemics. III.—Further studies of the problem of endemicity}},
volume = {141},
year = {1933}
}
@article{hoffman_2014,
abstract = {Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than simpler methods such as random walk Metropolis or Gibbs sampling. However, HMC's performance is highly sensitive to two user-specified parameters: a step size e and a desired number of steps L. In particular, if L is too small then the algorithm exhibits undesirable random walk behavior, while if L is too large the algorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace its steps. Empirically, NUTS performs at least as efficiently as (and sometimes more efficiently than) a well tuned standard HMC method, without requiring user intervention or costly tuning runs. We also derive a method for adapting the step size parameter e on the fly based on primal-dual averaging. NUTS can thus be used with no hand-tuning at all, making it suitable for applications such as BUGS-style automatic inference engines that require efficient "turnkey" samplers. {\textcopyright} 2014 Matthew D. Hoffman and Andrew Gelman.},
author = {Hoffman, Matthew D. and Gelman, Andrew},
issn = {15337928},
journal = {Journal of Machine Learning Research},
title = {{The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo}},
volume = {15},
year = {2014}
}
@misc{Chretien2014,
abstract = {Forecasts of influenza activity in human populations could help guide key preparedness tasks. We conducted a scoping review to characterize these methodological approaches and identify research gaps. Adapting the PRISMA methodology for systematic reviews, we searched PubMed, CINAHL, Project Euclid, and Cochrane Database of Systematic Reviews for publications in English since January 1, 2000 using the terms "influenza AND (forecast*OR predict*)", excluding studies that did not validate forecasts against independent data or incorporate influenza-related surveillance data from the season or pandemic for which the forecasts were applied. We included 35 publications describing population-based (N = 27), medical facility-based (N = 4), and regional or global pandemic spread (N = 4) forecasts. They included areas of North America (N = 15), Europe (N = 14), and/or Asia-Pacific region (N = 4), or had global scope (N = 3). Forecasting models were statistical (N = 18) or epidemiological (N = 17). Five studies used data assimilation methods to update forecasts with new surveillance data. Models used virological (N = 14), syndromic (N = 13), meteorological (N = 6), internet search query (N = 4), and/or other surveillance data as inputs. Forecasting outcomes and validation metrics varied widely. Two studies compared distinct modeling approaches using common data, 2 assessed model calibration, and 1 systematically incorporated expert input. Of the 17 studies using epidemiological models, 8 included sensitivity analysis. This review suggests need for use of good practices in influenza forecasting (e.g., sensitivity analysis); direct comparisons of diverse approaches; assessment of model calibration; integration of subjective expert input; operational research in pilot, real-world applications; and improved mutual understanding among modelers and public health officials. {\textcopyright} 2014 Chretien et al.},
author = {Chretien, Jean Paul and George, Dylan and Shaman, Jeffrey and Chitale, Rohit A. and McKenzie, F. Ellis},
booktitle = {PLoS ONE},
doi = {10.1371/journal.pone.0094130},
file = {:Users/jamesscott/Documents/mendeley2/Chretien et al. - 2014 - Influenza forecasting in human populations A scoping review.pdf:pdf},
issn = {19326203},
keywords = {Database searching,Epidemiology,Forecasting,Infectious disease surveillance,Influenza,Pandemics,Public and occupational health,Systematic reviews},
month = {apr},
number = {4},
pages = {94130},
pmid = {24714027},
publisher = {Public Library of Science},
title = {{Influenza forecasting in human populations: A scoping review}},
url = {www.plosone.org},
volume = {9},
year = {2014}
}
@article{Held_2005,
abstract = {<p>A framework for the statistical analysis of counts from infectious disease surveillance databases is proposed. In its simplest form, the model can be seen as a Poisson branching process model with immigration. Extensions to include seasonal effects, time trends and overdispersion are outlined. The model is shown to provide an adequate fit and reliable one-step-ahead prediction intervals for a typical infectious disease time series. In addition, a multivariate formulation is proposed, which is well suited to capture space-time dependence caused by the spatial spread of a disease over time. An analysis of two multivariate time series is described. All analyses have been done using general optimization routines, where ML estimates and corresponding standard errors are readily available.</p>},
author = {Held, Leonhard and H{\"{o}}hle, Michael and Hofmann, Mathias},
doi = {10.1191/1471082X05st098oa},
issn = {1471-082X},
journal = {Statistical Modelling},
month = {oct},
number = {3},
title = {{A statistical framework for the analysis of multivariate infectious disease surveillance counts}},
volume = {5},
year = {2005}
}
@article{kelly_2010,
abstract = {Background: In mid-June 2009 the State of Victoria in Australia appeared to have the highest notification rate of pandemic (H1N1) 2009 influenza in the world. We hypothesise that this was because community transmission of pandemic influenza was already well established in Victoria at the time testing for the novel virus commenced. In contrast, this was not true for the pandemic in other parts of Australia, including Western Australia (WA). Methods: We used data from detailed case follow-up of patients with confirmed infection in Victoria and WA to demonstrate the difference in the pandemic curve in two Australian states on opposite sides of the continent. We modelled the pandemic in both states, using a susceptible-infected-removed model with Bayesian inference accounting for imported cases. Results: Epidemic transmission occurred earlier in Victoria and later in WA. Only 5% of the first 100 Victorian cases were not locally acquired and three of these were brothers in one family. By contrast, 53% of the first 102 cases in WA were associated with importation from Victoria. Using plausible model input data, estimation of the effective reproductive number for the Victorian epidemic required us to invoke an earlier date for commencement of transmission to explain the observed data. This was not required in modelling the epidemic in WA. Conclusion: Strong circumstantial evidence, supported by modelling, suggests community transmission of pandemic influenza was well established in Victoria, but not in WA, at the time testing for the novel virus commenced in Australia. The virus is likely to have entered Victoria and already become established around the time it was first identified in the US and Mexico. {\textcopyright} 2010 Kelly et al.},
author = {Kelly, Heath A. and Mercer, Geoff N. and Fielding, James E. and Dowse, Gary K. and Glass, Kathryn and Carcione, Dale and Grant, Kristina A. and Effler, Paul V. and Lester, Rosemary A.},
doi = {10.1371/journal.pone.0011341},
issn = {19326203},
journal = {PLoS ONE},
pmid = {20596536},
title = {{Pandemic (H1N1) 2009 influenza community transmission was established in one Australian state when the virus was first identified in North America}},
year = {2010}
}
