[1]

S. I. Aanonsen, G. Nævdal, D. S. Oliver, A. C. Reynolds and B. Vallès, Ensemble Kalman filter in reservoir engineering – A review, SPE Journal, 14 (2009), 393412.
doi: 10.2118/117274PA.

[2]

S. Abrams, The analysis of multivariate serological data, in Handbook of Infectious Disease Data Analysis, CRC Press, 2019.

[3]

J. L. Anderson and S. L. Anderson, A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts, Mon. Weather Rev., 127 (1999), 27412758.
doi: 10.1175/15200493(1999)127<2741:AMCIOT>2.0.CO;2.

[4]

E. Armstrong, M. Runge and J. Gerardin, Identifying the measurements required to estimate rates of COVID19 transmission, infection, and detection, using variational data assimilation, Infectious Disease Modelling, to appear.
doi: 10.1101/2020.05.27.20112987.

[5]

M. Asch, M. Bocquet and M. Nodet, Data Assimilation. Methods, Algorithms, and Applications, Fundamentals of Algorithms, 11, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2016.
doi: 10.1137/1.9781611974546.pt1.

[6]

L. M. A. Bettencourt, R. M. Ribeiro, G. Chowell, T. Lant and C. CastilloChavez, Towards real time epidemiology: Data assimilation, modeling and anomaly detection of health surveillance data streams, in Intelligence and Security Informatics: Biosurveillance, Lecture Notes in Computer Science, 4506, Springer, 2007, 79–90.
doi: 10.1007/9783540726081_8.

[7]

J. C. Blackwood and L. M. Childs, An introduction to compartmental modeling for the budding infectious disease modeler, Lett. Biomath., 5 (2018), 195221.
doi: 10.30707/LiB5.1Blackwood.

[8]

M. Bocquet and P. Sakov, An iterative ensemble Kalman smoother, Q. J. R. Meteorol. Soc., 140 (2014), 15211535.

[9]

M. Bocquet and P. Sakov, Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 20 (2013), 803818.
doi: 10.5194/npg208032013.

[10]

C. {B}rasil, Estimativa de Casos de COVID19, 2020. Available from: https://ciis.fmrp.usp.br/covid19subnotificacao/.

[11]

R. Buizza, M. Milleer and T. N. Palmer, Stochastic representation of model uncertainties in the ECMWF ensemble prediction system, Q. J. R. Meteorol. Soc., 125 (1999), 28872908.
doi: 10.1002/qj.49712556006.

[12]

G. Burgers, P. J. van Leeuwen and G. Evensen, Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126 (1998), 17191724.
doi: 10.1175/15200493(1998)126<1719:ASITEK>2.0.CO;2.

[13]

H. Cao and Y. Zhou, The discrete agestructured SEIT model with application to tuberculosis transmission in China, Math. Comput. Modelling, 55 (2012), 385395.
doi: 10.1016/j.mcm.2011.08.017.

[14]

A. Carrassi, M. Bocquet, L. Bertino and G. Evensen, Data assimilation in the Geosciences: An overview on methods, issues and perspectives, WIREs Climate Change, 9 (2018), 50pp.
doi: 10.1002/wcc.535.

[15]

CBS, Bevolkingspyramide, Statistics Netherlands (CBS), 2020. Available from: https://www.cbs.nl/nlnl/visualisaties/bevolkingspiramide.

[16]

CBS, Nearly 9 Thousand More Deaths in First 9 Weeks of COVID19, Statistics Netherlands (CBS), 2020. Available from: https://www.cbs.nl/engb/news/2020/20/nearly9thousandmoredeathsinfirst9weeksofcovid19.

[17]

N. K. Chada, M. A. Iglesias, L. Roininen and A. M. Stuart, Parameterizations for ensemble Kalman inversion, Inverse Problems, 34 (2018), 31pp.
doi: 10.1088/13616420/aab6d9.

[18]

Y. Chen and D. S. Oliver, Ensemble randomized maximum likelihood method as an iterative ensemble smoother, Math. Geosci., 44 (2012), 126.
doi: 10.1007/s110040119376z.

[19]

Y. Chen and D. S. Oliver, LevenbergMarquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification, Comput. Geosci., 17 (2013), 689703.
doi: 10.1007/s1059601393515.

[20]

COVID19 in Brazil: "So what?", The Lancet, 395 (2020).
doi: 10.1016/S01406736(20)310953.

[21]

A. A. Emerick and A. C. Reynolds, Ensemble smoother with multiple data assimilation, Comput. Geosci., 55 (2013), 315.
doi: 10.1016/j.cageo.2012.03.011.

[22]

R. Engbert, M. M. Rabe, R. Kliegl and S. Reich, Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID19 dynamics, Bull. Math. Biol., 83 (2021).
doi: 10.1007/s11538020008348.

[23]

G. Evensen, Accounting for model errors in iterative ensemble smoothers, Comput. Geosci., 23 (2019), 761775.
doi: 10.1007/s105960199819z.

[24]

G. Evensen, Analysis of iterative ensemble smoothers for solving inverse problems, Comput. Geosci., 22 (2018), 885908.
doi: 10.1007/s105960189731y.

[25]

G. Evensen, Data Assimilation. The Ensemble Kalman Filter, SpringerVerlag, Berlin, 2009.
doi: 10.1007/9783642037115.

[26]

G. Evensen, The ensemble Kalman filter for combined state and parameter estimation: Monte Carlo techniques for data assimilation in large systems, IEEE Control Syst. Mag., 29 (2009), 83104.
doi: 10.1109/MCS.2009.932223.

[27]

G. Evensen, Formulating the history matching problem with consistent error statistics, Comput. Geosci., to appear.

[28]

G. Evensen, Sampling strategies and square root analysis schemes for the EnKF, Ocean Dynamics, 54 (2004), 539560.
doi: 10.1007/s1023600400992.

[29]

G. Evensen, Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99 (1994).
doi: 10.1029/94JC00572.

[30]

G. Evensen, P. N. Raanes, A. S. Stordal and J. Hove, Efficient implementation of an iterative ensemble smoother for data assimilation and reservoir history matching, Front. Appl. Math. Stat., 5 (2019), 47pp.
doi: 10.3389/fams.2019.00047.

[31]

S. Flaxman, S. Mishra, A. Gandy, H. Unwin and H. Coupland, et al., Report 13: Estimating the number of infections and the impact of nonpharmaceutical interventions on COVID19 in 11 European countries, 2020. Available from: https://www.imperial.ac.uk/mrcglobalinfectiousdiseaseanalysis/covid19/report13europenpiimpact/.

[32]

Gouvernement de la République Française, COVID19: Carte et Données, 2020. Available from: https://www.gouvernement.fr/infocoronavirus/carteetdonnees.

[33]

H. Gupta, K. K. Verma and P. Sharma, Using data assimilation technique and epidemic model to predict TB epidemic, Internat. J. Comput. Appl., 128 (2015), 5pp.
doi: 10.5120/ijca2015906625.

[34]

P. L. Houtekamer and H. L. Mitchell, Data assimilation using an ensemble Kalman filter technique, Mon. Weather Rev., 126 (1998), 796811.
doi: 10.1175/15200493(1998)126<0796:DAUAEK>2.0.CO;2.

[35]

P. L. Houtekamer and F. Zhang, Review of the ensemble Kalman filter for atmospheric data assimilation, Mon. Weather Rev., 144 (2016), 44894532.
doi: 10.1175/MWRD150440.1.

[36]

M. A. Iglesias, K. J. Law and A. M. Stuart, Ensemble Kalman methods for inverse problems, Inverse Problems, 29 (2013), 20pp.
doi: 10.1088/02665611/29/4/045001.

[37]

Imperial College COVID19 Response Team, Shortterm forecasts of COVID19 deaths in multiple countries, 2020. Available from: https://mrcide.github.io/covid19shorttermforecasts/index.html.

[38]

A. J. Ing, C. Cocks and J. P. Green, COVID19: In the footsteps of Ernest Shackleton, Thorax, 75 (2020), 613613.
doi: 10.1136/thoraxjnl2020215091.

[39]

Institut de la Statistique Québec, 2020. Available from: https://www.stat.gouv.qc.ca/statistiques/populationdemographie/decesmortalite/nombrehebdomadairedeces.html.,

[40]

Institut de la Statistique Québec: Population Data, 2019. Available from: https://www.stat.gouv.qc.ca/statistiques/populationdemographie/structure/populationquebecagesexe.html#tri_pop=20.,

[41]

Institut National de Santé Publique Québec, 2020. Available from: https://www.inspq.qc.ca/covid19/donnees.,

[42]

C. Jarvis, K. Van Zandvoort and A. Gimma, et al., Quantifying the impact of physical distance measures on the transmission of COVID19 in the UK, BMC Med, 18 (2020), 14161430.
doi: 10.1186/s12916020015978.

[43]

M. A. Jorden, S. L. Rudman, E. Villarino, S. Hoferka and M. T. Patel, et al., Evidence for limited early spread of COVID19 within the United States, JanuaryFebruary 2020, Morbid. Mortal. Weekly Rep. (MMWR), 69 (2020), 680684,
doi: 10.15585/mmwr.mm6922e1.

[44]

A. A. King, E. L. Ionides, M. Pascual and M. J. Bouma, Inapparent infections and cholera dynamics, Nature, 454 (2008), 877880.
doi: 10.1038/nature07084.

[45]

R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang and J. Shaman, Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARSCoV2), Science, 368 (2020), 489493.
doi: 10.1126/science.abb3221.

[46]

T. A. Mellan, H. H. Hoeltgebaum, S. Mishra, C. Whittaker and R. Schnekenberg, et al., Report 21: Estimating COVID19 cases and reproduction number in Brazil, (2020).
doi: 10.25561/78872.

[47]

J. Mossong, N. Hens, M. Jit, P. Beutels and K. Auranen, et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med, 5.
doi: 10.1371/journal.pmed.0050074.

[48]

C. J. L. Murray, Forecasting the impact of the first wave of the COVID19 pandemic on hospital demand and deaths for the USA and European economic area countries, preprint.
doi: 10.1101/2020.04.21.20074732.

[49]

National Health Service, Covid19 Daily Deaths, 2020. Available from: https://www.england.nhs.uk/statistics/statisticalworkareas/covid19dailydeaths/.

[50]

R. M. Neal, Sampling from multimodal distributions using tempered transitions, Statist. Comput., 6 (1996), 353366.
doi: 10.1007/BF00143556.

[51]

NICE, COVID19 Infecties op de IC's, Nationale Intensive Care Evaluatie, 2020. Accessed from: https://www.stichtingnice.nl/.

[52]

NICE, COVID19 Infecties op de Verpleegadeling, Nationale Intensive Care Evaluatie, 2020. Available from: https://www.stichtingnice.nl/covid19opdezkh.jsp/

[53]

D. Pasetto, F. Finger, A. Rinaldo and E. Bertuzzo, Realtime projections of cholera outbreaks through data assimilation and rainfall forecasting, Adv. Water Res., 108 (2017), 345356.
doi: 10.1016/j.advwatres.2016.10.004.

[54]

Public Health, England, The health protection (coronavirus, business closure) (England) regulations 2020, 2020. Available from: https://web.archive.org/web/20200323004800/http://www.legislation.gov.uk/uksi/2020/327/pdfs/uksi_20200327_en.pdf.

[55]

P. N. Raanes, A. S. Stordal and G. Evensen, Revising the stochastic iterative ensemble smoother, Nonlin. Processes Geophys, 26 (2019), 325338.
doi: 10.5194/npg263252019.

[56]

Registro Civil, Portal da Transparencia  Especial COVID19, 2020. Available from: https://transparencia.registrocivil.org.br/especialcovid.

[57]

C. J. Rhodes and T. D. Hollingsworth, Variational data assimilation with epidemic models, J. Theoret. Biol., 258 (2009), 591602.
doi: 10.1016/j.jtbi.2009.02.017.

[58]

RIVM, Briefing Update Coronavirus Tweede Kamer 20 Mei 2020, National Institute for Public Health and the Environment, 2020. Available from: https://www.tweedekamer.nl/sites/default/files/atoms/files/presentatie_jaap_van_dissel__technische_briefing_20_mei_2020.pdf.

[59]

RIVM, Excess Mortality Caused by the Novel Coronavirus (COVID19), National Institute for Public Health and the Environment, 2020. Available from: https://www.rivm.nl/node/155011.

[60]

RIVM, Ontwikkeling COVID19 in Grafieken, National Institute for Public Health and the Environment, 2020. Available from: https://www.rivm.nl/coronaviruscovid19/grafieken.

[61]

H. Salje, C. Tran Kiem, N. Lefrancq, N. Courtejoie and P. Bosetti, et al., Estimating the burden of SARSCoV2 in France, Science, 369 (2020), 208211.
doi: 10.1126/science.abc3517.

[62]

J. L. Sesterhenn, Adjointbased data assimilation of an epidemiology model for the COVID19 pandemic in 2020, preprint, arXiv: 2003.13071.

[63]

J. Shaman, A. Karspeck, W. Yang, J. Tamerius and M. Lipsitch, Realtime influenza forecasts during the 2012–2013 season, Nature Commu., 4 (2013), 110.
doi: 10.1038/ncomms3837.

[64]

A. S. Stordal and A. H. Elsheikh, Iterative ensemble smoothers in the annealed importance sampling framework, Adv. Water Res., 86 (2015), 231239.
doi: 10.1016/j.advwatres.2015.09.030.

[65]

UK Government, Coronavirus (COVID19) in the UK, 2020. Available from: https://coronavirus.data.gov.uk.

[66]

UK Government, National COVID19 Surveillance Reports, 2020. Available from: https://www.gov.uk/government/publications/nationalcovid19surveillancereports/.

[67]

UK Government, Slides, Datasets and Transcripts to Accompany Coronavirus Press Conferences, 2020. Available from: https://www.gov.uk/government/collections/slidesanddatasetstoaccompanycoronaviruspressconferences/.

[68]

UK Office for National Statistics, Dataset: Deaths Registered Weekly in England and Wales, Provisional, 2020., Available from: https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/weeklyprovisionalfiguresondeathsregisteredinenglandandwales.

[69]

J. van Wees, S. Osinga, M. van der Kuip, M. Tanck and M. Hanegraaf, et al., Forecasting hospitalization and ICU rates of the COVID19 outbreak: An efficient SEIR model, Bull. World Health Org., (2020).
doi: 10.2471/BLT.20.256743.

[70]

J. S. Whitaker and T. M. Hamill, Evaluating methods to account for system errors in ensemble data assimilation, Mon. Weather. Rev., 140 (2012), 30783089.
doi: 10.1175/MWRD1100276.1.

[71]

WHO, Coronavirus Disease (COVID19): Similarities and Differences with Influenza, 2020. Available from: https://www.who.int/emergencies/diseases/novelcoronavirus2019/questionandanswershub/qadetail/qasimilaritiesanddifferencescovid19andinfluenza.

[72]

W. Yang, M. Lipsitch and J. Shaman, Inference of seasonal and pandemic influenza transmission dynamics, PNAS, 112 (2015), 27232728.
doi: 10.1073/pnas.1415012112.

[73]

W. Yang, W. Zhang, D. Kargbo, R. Yang and Y. Chen, et al., Transmission network of the 2014–2015 Ebola epidemic in Sierra Leone, J. Roy. Soc. Interface, 12 (2015).
doi: 10.1098/rsif.2015.0536.
