Neil Ferguson

MRC Centre for Outbreak Analysis and Modelling

Faculty of MedicineImperial College London

Outbreak Analysis

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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Hong Kong 2003

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

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.

Situational awareness:understanding the threat

• How bad is it?

• How far has it got?

• How fast is it spreading?

• What can we do?

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.

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.

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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.

Goals of mitigation measures

Buy time for seasonality to further reduce transmission, for vaccine production.

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How do we analyse outbreaks?

Key questions

• How bad is it?

• How far has it got?

• How fast is it spreading?

• What can we do?

Perspectives on epidemics:individuals

Another view: populations

H1N1, 1918-19 SARS, Hong Kong, 2003

H1N1, 2009

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Doubling time, attack rate

The bridge: contacts

Variola minor, England, 1966 SARS, Singapore, 2003

H1N1, UK, 2009

Secondary attack rate, offspring distribution, reproduction number, generation time

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.

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Wallinga & Teunis [AJE 2004] similar, but assumes cases only infectious after symptoms.

SARS – Singapore 2003

Data needs:detailed outbreak data

Mean of offspring distribution= reproduction number=R

Generation time

Can supplement inference with contact tracing data

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

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)(),()( ttt dtIttI

)()(),( tft ftt

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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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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

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.

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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.

Modelling susceptible populations

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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Equilibrium, or recurrent epidemicsy

e(R 0

-1)/T G

tRandom effects

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?

What data are needed?

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

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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Bootsma & Ferguson, 2007, PNAS

Cauchemez et al, Nature 2008

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

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.

Proportion of observations censored in the SARS outbreak

[Ghani et al, AJE, 2005]We do not know the outcome (death or recovery) yet.

Simple methods

• Method 1:

• Method 2:

CDCFR

D = Number of deaths

C = Total number of cases

)( RDDCFR

D = Number of deaths

R = Number recovered

Comparison of the estimates

(nb. death / nb. Cases)

nb. death/(nb. death+recovered)

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

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]

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

Proportion of first detected casesthat were infected by swine

Length of the chain of

transmission

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1/2=50%

1/3=33%

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• 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

R for H3N2v and for other strains

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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%.

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