title: Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks.
abstract: Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k=1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97-1.38). When less dispersed with k=2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.
authors.affiliation: School of Public Health, The University of Hong Kong, Level 6, Core F, Cyberport 3, 100 Cyberport Road, Pokfulam, Hong Kong; PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan. nishiura@hku.hk
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Nishiura
authors.forename: Ping
authors.initials: P
authors.lastname: Yan
authors.forename: Candace K
authors.initials: CK
authors.lastname: Sleeman
authors.forename: Charles J
authors.initials: CJ
authors.lastname: Mode
mesh_terms: D050936:Basic Reproduction Number; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D010930:Plague / Q000453:epidemiology / Q000635:transmission*
references.citation: Proc Biol Sci. 2007 Feb 22;274(1609):599-604
references.pmid: 17476782
references.citation: Bull Math Biol. 1991;53(1-2):3-32
references.pmid: 2059740
references.citation: Clin Infect Dis. 2005 Apr 15;40(8):1166-72
references.pmid: 15791518
references.citation: PLoS One. 2007 Feb 14;2(2):e180
references.pmid: 17299582
references.citation: PLoS One. 2009 Aug 31;4(8):e6852
references.pmid: 19718434
references.citation: Emerg Infect Dis. 2007 Apr;13(4):664-6
references.pmid: 17561574
references.citation: PLoS One. 2011;6(5):e17835
references.pmid: 21637342
references.citation: Med Hist. 1970 Jan;14(1):63-74
references.pmid: 4904731
references.citation: J Infect Dis. 1948 Jan-Feb;82(1):52-8
references.pmid: 18898004
references.citation: Emerg Infect Dis. 2006 Mar;12(3):460-7
references.pmid: 16704785
references.citation: Stat Methods Med Res. 1993;2(1):23-41
references.pmid: 8261248
references.citation: MMWR Morb Mortal Wkly Rep. 2009 Jul 24;58(28):778-81
references.pmid: 19629028
references.citation: Clin Infect Dis. 1995 Sep;21(3):650-2
references.pmid: 8527559
references.citation: BMC Infect Dis. 2011 May 03;11:111
references.pmid: 21539735
references.citation: Int J Epidemiol. 2007 Aug;36(4):881-9
references.pmid: 17517812
references.citation: Euro Surveill. 2010 Jul 22;15(29):
references.pmid: 20667300
references.citation: Nature. 2005 Nov 17;438(7066):355-9
references.pmid: 16292310
references.citation: Trans R Soc Trop Med Hyg. 2009 May;103(5):455-60
references.pmid: 19211117
references.citation: JAMA. 2000 May 3;283(17):2281-90
references.pmid: 10807389
references.citation: Theor Popul Biol. 2007 Mar;71(2):160-73
references.pmid: 17222879
references.citation: Comput Math Methods Med. 2011;2011:527610
references.pmid: 21860658
references.citation: Biostatistics. 2003 Apr;4(2):279-95
references.pmid: 12925522
references.citation: Am J Public Health (N Y). 1920 Jul;10(7):599-605
references.pmid: 18010342
references.citation: Lancet. 2000 Jan 8;355(9198):111-3
references.pmid: 10675169
references.citation: Bull Soc Pathol Exot Filiales. 1958 Jan-Feb;51(1):47-60
references.pmid: 13536775
references.citation: Yale J Biol Med. 1974 Mar;47(1):40-54
references.pmid: 4596466
references.citation: Int J Epidemiol. 2006 Aug;35(4):1059-65
references.pmid: 16684896
references.citation: Math Biosci Eng. 2007 Jul;4(3):457-70
references.pmid: 17658935
references.citation: Science. 2004 May 14;304(5673):968-9
references.pmid: 15143265
references.citation: Stat Med. 2011 Apr 30;30(9):984-94
references.pmid: 21284013
references.citation: J Theor Biol. 2011 Sep 7;284(1):52-60
references.pmid: 21704640
references.citation: PLoS One. 2011 Mar 24;6(3):e17908
references.pmid: 21455307
references.citation: J Theor Biol. 2008 Jul 21;253(2):228-37
references.pmid: 18423673
references.citation: Emerg Infect Dis. 2004 Apr;10(4):608-14
references.pmid: 15200849
references.citation: Math Biosci. 2009 Dec;222(2):109-16
references.pmid: 19837097
references.citation: Interdiscip Perspect Infect Dis. 2011;2011:194507
references.pmid: 21234337
references.citation: J Epidemiol Community Health. 2006 Jul;60(7):640-5
references.pmid: 16790838
references.citation: J R Soc Med. 2000 Oct;93(10):540-3
references.pmid: 11064697
references.citation: Theor Biol Med Model. 2010 Jan 07;7:1
references.pmid: 20056004
references.citation: J Theor Biol. 2011 Mar 7;272(1):123-30
references.pmid: 21168422
references.citation: Trans R Soc Trop Med Hyg. 2000 Jul-Aug;94(4):387-91
references.pmid: 11127240
references.citation: Math Biosci Eng. 2010 Oct;7(4):851-69
references.pmid: 21077712
references.citation: Lancet. 1948 Apr 24;1(6504):625-7
references.pmid: 18911234
references.citation: Theor Biol Med Model. 2010 Oct 25;7:39
references.pmid: 20973955