neil ferguson
DESCRIPTION
Outbreak Analysis. Neil Ferguson MRC Centre for Outbreak Analysis and Modelling Faculty of Medicine Imperial College London . Focus of this lecture: outbreaks. Particular challenging for applied (i.e. policy-relevant) modelling. Two aspects: Modelling for preparedness Real-time analysis - PowerPoint PPT PresentationTRANSCRIPT
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Neil Ferguson
MRC Centre for Outbreak Analysis and Modelling
Faculty of MedicineImperial College London
Outbreak Analysis
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Focus of this lecture: outbreaks
• Particular challenging for applied (i.e. policy-relevant) modelling.
• Two aspects: Modelling for preparedness Real-time analysis
• Not fundamentally different from applied modelling for endemic disease control (e.g. malaria).
• Parallels with elimination (e.g. polio).• Cost-benefit – critical, not discussed
here.
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Daily
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Hong Kong 2003
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The process of emergence
• Constant exposure to animal pathogens.
• Only a few break through to cause human epidemics.
• Want to predict and detect emergence.
• Both hard, but detection easier.
Viral ‘chatter’
Antia et al. Nature 2003
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Modelling and decision-making
• Rarely asked: ‘tell us what to do?’
• Key – improve ‘situational awareness’• Decisions are typically organisational output:
Science only one input/consideration Modelling only one part of the science
• Quantitative analyses have clear advantages over qualitative analysis/opinion.
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Situational awareness:understanding the threat
• How bad is it?
• How far has it got?
• How fast is it spreading?
• What can we do?
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Early detection key
• Severe infections likely to be picked up earlier (e.g. H5N1 vs H1N1).
• Want to detect clusters of severe disease.
• Field-based surveillance still key- enhanced with modern technology.
• Alternatives use digital media.
• Global Public Health Intelligence Network (GPHIN) detected SARS in 2002-3, and H5N1 in ducks in China in 2004.
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Initial goal: containment
• Feasibility depends on the pathogen.
• Probably only possible for severe disease with clear case definition.
• e.g. SARS, human H5N1.
• Impossible for mild/ asymptomatic disease (e.g. H1N1 in 2009) – detect outbreak too late.
• Even for H5N1 flu, need to move very fast with intensive measures.
50%
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1.1 1.3 1.5 1.7 1.9R 0
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Mitigation
• Know what to do for flu:Vaccine productionAntiviralsSocial distancing
• Problems - speed of spread, need for targeting.
• For other pathogens, limited to non-pharmaceutical interventions.
• Key issue is scaling response to level of threat.
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Goals of mitigation measures
Buy time for seasonality to further reduce transmission, for vaccine production.
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How do we analyse outbreaks?
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Key questions
• How bad is it?
• How far has it got?
• How fast is it spreading?
• What can we do?
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Perspectives on epidemics:individuals
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Another view: populations
H1N1, 1918-19 SARS, Hong Kong, 2003
H1N1, 2009
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Doubling time, attack rate
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The bridge: contacts
Variola minor, England, 1966 SARS, Singapore, 2003
H1N1, UK, 2009
Secondary attack rate, offspring distribution, reproduction number, generation time
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Epidemic asbranchingprocess
Key: how many other people one person infects, on average. = the Reproduction Number of an epidemic – R. = R0 at the start of an epidemic, when no-one is immune.
Need R0 >1 for a large outbreak.
Modelling the transmission chain
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Real-time assessment ofoutbreaks
• Just examine the branching process (no need to include susceptibles).
• FMD, SARS showed the potential.
• Initial goal – ‘now-casting’ – correcting for censorship/delays in reporting
• Second, to estimate key parameters (R, mortality, TG), predict future trends, evaluate sufficiency of control measures.
• Key – inferring infection trees – FMD 2001 (Woolhouse, Haydon, Ferguson et al), SARS 2003 (Wallinga & Teunis)
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Basic approach:individual case data
• Set of cases {1,..,M}, with disease onset times {t1,…,tM}.• Incubation period distribution g(t).• Infectiousness profile (generation time dist) f(t).• Transmission risk covariates {x1,…,xM}.
• Transmission risk function h(xi,xj).• Define
• Conditional probability i infected j: - indep of fj
• Secondary cases caused by i:
• Approximate – independence of tj incorrect.
ijjij
tt
jjiiijij ddhgttfgQiij
ttttttft
0 0
),()()()( xx
jkkj
ijij Q
QR
ij
iji RR
Wallinga & Teunis [AJE 2004] similar, but assumes cases only infectious after symptoms.
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SARS – Singapore 2003
Data needs:detailed outbreak data
Mean of offspring distribution= reproduction number=R
Generation time
Can supplement inference with contact tracing data
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Aggregate data
• Now assume we know incidence of infection through time, I(t).• Renewal equation:
• Instantaneous reproduction number:
• Factorise:• If f() is normalised,
• So
• Or Fraser, PloS One, 2007
0
)(),()( ttt dtIttI
)()(),( tft ftt
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),()( tt dttR
)()( ttR f
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)()(
)()(ttt dtIf
tItR
n
j jji
ii
fIItR0
)(
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Relation to growth rates
• If epidemic is growing exponentially then:
• So
• [Laplace transform of f()].
• For SIR model with exponential f():
• Most errors in estimating R from epidemic growth rates are due to carelessness about the generation time distribution (e.g. assuming exponential distributions).
Wallinga and Lipstich, PRSB 2007
rteItI )0()(
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( ) r
Rf e dtt t
grTR
11
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Data: natural history(Generation time distribution)
• Latent period, symptoms, serial interval distribution, shedding.
• Models no longer just SIR – include real-world complexity.
• Natural history key to control: Long incubation period
allowed smallpox to be eliminated.
Clear symptoms and no non-symptomatic transmission key to SARS control.
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Examples
UK FMD 2001UK BSE 1999
HK SARS 2003
H1N1 2009
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Epidemic establishment:offspring distributions
• Offspring distribution describes number of secondary cases per primary case (mean=R)
• Geometric offspring distribution (simple SIR model) gives highest extinction rate:
• Poisson offspring distribution (fixed generation time) gives the lowest:
• Negative binomial offspring distributions interpolate between these extremes (Lloyd-Smith, Nature 2005).
• Need to beware of selection bias in analysing outbreaks of novel diseases (H5N1, SARS) – we only see the larger ones.
0small
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Pluses and minuses
• Robust analytical approaches, with relatively few assumptions.
• Results hold even when heterogeneity in susceptibility, infectiousness and mixing large.
• Assumption of fixed generation time distribution sometimes wrong.
• Understanding the branching process gives little prior insight into the likely impact of interventions – need mechanistic understanding of R.
• Unless depletion of susceptibles is estimated, difficult to make predictions of future course of epidemic.
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Modelling susceptible populations
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Why?
• Need to examine those not infected to:
Predict epidemic trajectory
Understand risk factors for transmission
• But need to make many more assumptions about the nature of the transmission process.
• Increasing model complexity driven by desire to more closely mimic true complexity.
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What we want to captureR
ate
of n
ew in
fect
ions
establish-ment
Time
exhaustion of
susceptibles
endemicity
Equilibrium, or recurrent epidemicsy
e(R 0
-1)/T G
tRandom effects
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Going beyond homogenous mixing: deconstructing R0
• R0 determines effort required for control – 50% for R0=2, 75% for R0=4.
• But R0 not a fundamental constant.
• Determined by: Pathogen biology. Host factors. Host population structure.
• Want mechanistic understanding of R0 to predict impact of controls.
• Need DATA.
e.g.
• How much transmission occurs in the household, school or workplace?
• How much can be prevented by case-finding/contact tracing?
• How long are people infectious for?
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What data are needed?
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Data: epidemiological surveillance
Exposed
Clinical specimen
Disease
Pos. specimen
Infected
Seek medical attention
Report
Surveillance:
“you see what you look at”
Laboratory-based surveillance
Clinically-based surveillance
Serological survey
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Data needs: transmission
• Almost never observed.
• Little quantitative data on mechanisms.
• Some estimates of transmission rates for households etc.
• But mostly estimate from surveillance data
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On demography, contacts, movements…
Data: populations
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Data needs: interventions
• Trial data useful for drugs/vaccines.• But very limited data for non-
pharmaceutical measures.
• Need to rely on (complex)analysis of observational data.
• Also gives insight into basic transmission parameters.
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St Louis
Philadelphia
Bootsma & Ferguson, 2007, PNAS
Cauchemez et al, Nature 2008
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Some examples
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• Was controlled when hospital infection procedures intensified.• Lucky – only sick people transmitted, and universally severe.• Modelling gave epidemiological insight:
basic parameters (incubation period, mortality) rate of spread [R=2.7] and impact of controls. general insight.
SARS 2003
Cases in Hong Kong
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Case fatality ratio
• Proportion of cases who eventually die from the disease;• Often estimated by using aggregated numbers of cases and deaths at a
single time point: e.g.: case fatality ratios compiled daily by WHO during the SARS outbreak=
number of deaths to date / total number of cases to date can be misleading if, at the time of the analysis, the outcome (death or
recovery) is unknown for an important proportion of patients.
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Proportion of observations censored in the SARS outbreak
[Ghani et al, AJE, 2005]We do not know the outcome (death or recovery) yet.
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Simple methods
• Method 1:
• Method 2:
CDCFR
D = Number of deaths
C = Total number of cases
)( RDDCFR
D = Number of deaths
R = Number recovered
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Comparison of the estimates
(nb. death / nb. Cases)
nb. death/(nb. death+recovered)
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Assessing pre-emergence transmissibility
• How much does a virus need to change phenotypically?
• H3N2v – new swine variant causing human cases (2011-), associated with animal fairs etc.
• Key questions: Is H3N2v more transmissible in
humans than other swine strains?
Can H3N2v generate sustained epidemics in humans?
Cauchemez S. et al., 2013, PLoS Medicine, 10:e1001399
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What is the epidemic potential of H3N2v?
• H3N2v – new swine variant of influenza A/H3N2 causing cases in people (2011-), associated with animal fairs etc.
• Key questions: Is H3N2v more transmissible in humans than other swine strains?
Can H3N2v generate sustained epidemics in humans?
[Cauchemez S, Epperson S, Biggerstaff M., et al., 2013, PLoS Medicine, 10:e1001399-e1001399]
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Challenge
Data we would like to havecomplete & representative chains of transmission
Data we havelow detection rate
selection biasincomplete outbreak investigations
In general, we know the source of infection of detected cases
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Proportion of first detected casesthat were infected by swine
Length of the chain of
transmission
1
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3
1/1=100%
1/2=50%
1/3=33%
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Size of lineage
P(fi
rst r
epor
ted
case
was
infe
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by
pig)
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Pro
porti
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y pi
g
• From proportion, can estimate length of transmission chain;• From length of chain, can estimate the reproduction number.
Proportion of first detected cases infected by swine
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R for H3N2v and for other strains
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Case detection rate
Pro
porti
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y sw
ine
Reproduction number R
H3N2v: 50% (3/6) infected by swineR=0.5 (95%CI: 0.2,0.8)
0.50.2
Other strains: 81% (17/21) infected by swineR=0.2 (95%CI: 0.1,0.4)
• Significantly <1 if detection rate=0.4%; but not if detection rate=1%.
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Conclusions
• More mobile, more populous world – diseases spread faster than ever before.
• Planning and response need to keep up.
• Fortunately new methods and more data now available.
• Analysis and modelling can help in: Contingency planning Characterising new threats Informing surveillance design Assessing control policy options