The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks

Thomas Obadia1, Romana Haneef2, Pierre‐Yves Boëlle3
1Inserm U707, Paris, France
2EHESP, Paris, France
3APHP, Saint-Antoine Hospital, Paris, France

Tóm tắt

Abstract Background Several generic methods have been proposed to estimate transmission parameters during an outbreak, especially the reproduction number. However, as of today, no dedicated software exists that implements these methods and allow comparisons. Results A review of generic methods used to estimate transmissibility parameters during outbreaks was carried out. Most methods used the epidemic curve and the generation time distribution. Two categories of methods were available: those estimating the initial reproduction number, and those estimating a time dependent reproduction number. We implemented five methods as an R library, developed sensitivity analysis tools for each method and provided numerical illustrations of their use. A comparison of the performance of the different methods on simulated datasets is reported. Conclusions This software package allows a standardized and extensible approach to the estimation of the reproduction number and generation interval distribution from epidemic curves.

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Tài liệu tham khảo

Khan K, Arino J, Hu W, Raposo P, Sears J, Calderon F, Heidebrecht C, Macdonald M, Liauw J, Chan A, Gardam M: Spread of a Novel Influenza A (H1N1) Virus via Global Airline Transportation. N Engl J Med. 2009, 361: 212-214. 10.1056/NEJMc0904559.

World Health Organization: Global Surveillance during an Influenza Pandemic. 2009,http://www.who.int/csr/disease/swineflu/global_pandemic_influenza_surveilance_apr09.pdf,

Boëlle P-Y, Ansart S, Cori A, Valleron A-J: Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review. Influenza and Other Respiratory Viruses. 2011, 5: 306-316. 10.1111/j.1750-2659.2011.00234.x.

Wallinga J, Lipsitch M: How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences. 2007, 274: 599-10.1098/rspb.2006.3754.

Chowell G, Viboud C, Simonsen L, Miller MA, Acuna-Soto R, Díaz J, Martínez-Martín AF: The 1918–19 Influenza Pandemic in Boyacá. Colombia. Emerging infectious diseases. 2012, 18: 48-

Boëlle PY, Bernillon P, Desenclos JC: A preliminary estimation of the reproduction ratio for new influenza A(H1N1) from the outbreak in Mexico, March-April 2009. Euro Surveill. 2009, 14 (19): pii=19205

Nishiura H, Wilson N, Baker M: Estimating the reproduction number of the novel influenza A virus (H1N1) in a Southern Hemisphere setting: preliminary estimate in New Zealand. N. Z. Med. J. 2009, 122: 73-77.

Svensson Å: A note on generation times in epidemic models. Math Biosci. 2007, 208: 300-311. 10.1016/j.mbs.2006.10.010.

Dietz K: The estimation of the basic reproduction number for infectious diseases. Statistical Methods in Medical Research. 1993, 2: 23-41. 10.1177/096228029300200103.

Hens N, Van Ranst M, Aerts M, Robesyn E, Van Damme P, Beutels P: Estimating the effective reproduction number for pandemic influenza from notification data made publicly available in real time: a multi-country analysis for influenza A/H1N1v 2009. Vaccine. 2011, 29: 896-904. 10.1016/j.vaccine.2010.05.010.

Forsberg White L, Pagano M: A likelihood-based method for real-time estimation of the serial interval and reproductive number of an epidemic. Statist. Med. 2008, 27: 2999-3016. 10.1002/sim.3136.

Bettencourt LMA, Ribeiro RM: Real time bayesian estimation of the epidemic potential of emerging infectious diseases. PLoS One. 2008, 3: e2185-10.1371/journal.pone.0002185.

Wallinga J, Teunis P: Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol. 2004, 160: 509-10.1093/aje/kwh255.

Cauchemez S, Boëlle P-Y, Donnelly CA, Ferguson NM, Thomas G, Leung GM, Hedley AJ, Anderson RM, Valleron A-J: Real-time estimates in early detection of SARS. Emerg Infect Dis. 2006, 12: 110-113.

Tomas JA: epitools: epidemiology Tools. R package version 0.5-7. 2012,http://CRAN.R-project.org/package=epitools,

Nishiura H: Time variations in the transmissibility of pandemic influenza in Prussia, Germany, from 1918–19. Theor Biol Med Model. 2007, 4: 20-10.1186/1742-4682-4-20.

Carrat F, Vergu E, Ferguson NM, Lemaitre M, Cauchemez S, Leach S, Valleron A-J: Time lines of infection and disease in human influenza: a review of volunteer challenge studies. Am J Epidemiol. 2008, 167: 775-785. 10.1093/aje/kwm375.

Nishiura H, Castillo-Chavez C, Safan M, Chowell G: Transmission potential of the new influenza A (H1N1) virus and its age-specificity in Japan. Euro Surveill. 2009, 14: 19227-

Cori A, Valleron AJ, Carrat F, Scalia Tomba G, Thomas G, Boëlle PY: Estimating influenza latency and infectious period durations using viral excretion data. Epidemics. 2012, 4: 132-138. 10.1016/j.epidem.2012.06.001.

Brookmeyer R, Gail MH: Minimum size of the acquired immunodeficiency syndrome (AIDS) epidemic in the United States. Lancet. 1986, 328: 1320-1322. 10.1016/S0140-6736(86)91444-3.

Nishiura H, Chowell G, Heesterbeek H, Wallinga J: The ideal reporting interval for an epidemic to objectively interpret the epidemiological time course. J. R. Soc. Interface. 2010, 7: 297-307. 10.1098/rsif.2009.0153.

Lessler J, Cummings DAT, Fishman S, Vora A, Burke DS: Transmissibility of swine flu at Fort Dix, 1976. J. R. Soc. Interface. 2007, 4: 755-762. 10.1098/rsif.2007.0228.

Cauchemez S, Bhattarai A, Marchbanks TL, Fagan RP, Ostroff S, Ferguson NM, Swerdlow D, Sodha SV, Moll ME, Angulo FJ, Palekar R, Archer WR, Finelli L: Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza. PNAS. 2011, 108: 2825-2830. 10.1073/pnas.1008895108.

Lessler J, Reich NG, Cummings DAT: Outbreak of 2009 pandemic influenza A (H1N1) at a New York City school. N Engl J Med. 2009, 361: 2628-2636. 10.1056/NEJMoa0906089.

McBryde ES, Bergeri I, van Gemert C, Rotty J, Headley EJ, Simpson K, Lester RA, Hellard M, Fielding JE: Early transmission characteristics of influenza A(H1N1)v in Australia: Victorian state. Euro Surveill. 16 May - 3 June 2009, 14 (42): pii=19363

White LF, Wallinga J, Finelli L, Reed C, Riley S, Lipsitch M, Pagano M: Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA. Influenza and Other Respiratory Viruses. 2009, 3: 267-276. 10.1111/j.1750-2659.2009.00106.x.

Glass K, Becker N, Clements M: Predicting case numbers during infectious disease outbreaks when some cases are undiagnosed. Statistics in Medicine. 2007, 26: 171-183. 10.1002/sim.2523.