Estimating individual and household reproduction numbers in an emerging epidemic.
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.
Fraser
Christophe
C
Medical Research Council Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College London, London, United Kingdom. c.fraser@imperial.ac.uk
D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission; D003198:Computer Simulation; D004196:Disease Outbreaks; D005191:Family Characteristics; D006801:Humans; D007251:Influenza, Human / Q000453:epidemiology / Q000635:transmission; D008433:Mathematics; D008457:Measles / Q000453:epidemiology / Q000635:transmission; D008962:Models, Theoretical; D013997:Time Factors
Nature. 2001 Oct 4;413(6855):542-8
11586365
Math Biosci. 2007 Jul;208(1):300-11
17174352
Math Biosci. 2002 Nov-Dec;180:73-102
12387917
Science. 2003 Jun 20;300(5627):1961-6
12766206
Science. 2003 Jun 20;300(5627):1966-70
12766207
Science. 2003 Aug 8;301(5634):804
12907792
Proc Natl Acad Sci U S A. 2004 Apr 20;101(16):6146-51
15071187
Am J Epidemiol. 2004 Sep 15;160(6):509-16
15353409
Am J Epidemiol. 1982 May;115(5):736-51
7081204
Biometrics. 1982 Mar;38(1):115-26
7082755
Math Biosci. 1995 Jun;127(2):207-19
7795319
Epidemiol Infect. 1996 Dec;117(3):443-55
8972668
Stat Med. 2004 Nov 30;23(22):3469-87
15505892
Lancet. 1952 Sep 20;2(6734):549-54
12981903
Nature. 2004 Dec 16;432(7019):904-6
15602562
Epidemiol Infect. 2004 Dec;132(6):1139-49
15635973
J Infect Dis. 2005 May 1;191(9):1403-9
15809897
Science. 2005 Aug 12;309(5737):1083-7
16079251
Nature. 2005 Sep 8;437(7056):209-14
16079797
Nature. 2005 Nov 17;438(7066):355-9
16292310
Proc Natl Acad Sci U S A. 2006 Apr 11;103(15):5935-40
16585506
Nature. 2006 Jul 27;442(7101):448-52
16642006
PLoS Med. 2006 Sep;3(9):e361
16881729
Proc Natl Acad Sci U S A. 2006 Aug 15;103(33):12637-42
16894173
Am J Epidemiol. 2006 Sep 15;164(6):591-7
16887892
AIDS. 2006 Sep 11;20(14):1898-901
16954735
Stat Methods Med Res. 2006 Oct;15(5):481-97
17089950
Science. 2006 Nov 17;314(5802):1150-3
17110580
PLoS One. 2006;1:e12
17183638
Proc Biol Sci. 2007 Feb 22;274(1609):599-604
17476782
Science. 2007 Jun 1;316(5829):1298-301
17540894
Parasitology. 2002 Mar;124(Pt 3):247-63
11922427