Are global epidemicspredictable ?V. Colizza School of Informatics, Indiana University, USA M. Barthlemy School of Informatics, Indiana University, USA A. Barrat Universite Paris-Sud, FranceA. Vespignani School of Informatics, Indiana University, USA Networks and Complex Systems talk series

Epidemic spread: 14th centuryBlack Death

Epidemic spread: nowadaysSARS

Epidemic spread: nowadaysSARS

Modeling of global epidemicsRavchev, Longini. Mathematical Biosciences (1985)multi-level description :

intra-city epidemics

inter-city travel

World-wide airport network complete 2002 IATA database

V = 3880 airports E = 18810 weighted edges wij #seats / year

Nj urban area population (UN census, )

V = 3100 airportsE = 17182 weighted edges>99% of total trafficBarrat, Barthlemy, Pastor-Satorras, Vespignani. PNAS (2004)

World-wide airport network = 9.75 kmax = 318

= 74584.4 wmin = 4wmax = 6.167e+06 FrankfurtSapporo - Tokyo

Broad distributions strong heterogeneities3 different levels:

degree

weight

populationWorld-wide airport networksummary

Epidemics: Stochastic Modelcompartmental model + air transportation data N1N2N0N5N4N3w54w45SIR modelSusceptibleInfectedRecovered

Stochastic ModelTravel termTravel probabilityfrom j to l # passengers in class X from j to l multinomial distr.

Stochastic ModelTravel termTransport operator: other source of noise:

two-legs travel:outgoingingoing

Stochastic ModelIntra-city

SIRbmIndependent Gaussian noises Homogeneous assumption

b rate of transmission m-1 average infectious period

compartmental model + air transportation data Intra-citiesInter-citiesEpidemics: Stochastic Modelsummary

Case study: SARSSusceptibleLatentInfectedHospitalizedRHospitalizedDRecoveredDeadbedg(1-d)ggDgRInfectedHospitalized

Case study: SARS

data: WHO reported cases final report: 28 infected countries 8095 infected cases 774 deaths refined compartmentalization parameter estimation: literature best fit initial condition: t=0 Feb. 21st seed: Hong Kong I0=1, L0 estimated, S0=N

Case study: SARS results

statistical propertiesepidemic pattern ? strong heterogeneity in no. infected cases: 0-103 large fluctuationsFull scale computational study of global epidemics:

statistical properties epidemic pattern effect of complexity of transportation network forecast reliability

Results: Geographic spreadEpidemics starting in Hong Kong

Results: Geographic spreadEpidemics starting in Hong KongGastner, Newman. PNAS (2004)

Results: Geographic spreadEpidemics starting in Hong Kong

maps heterogeneity epidemic spread

appropriate measure

role of specific structural properties: topology, traffic, population

comparison with null hypothesis

1st PART: Heterogeneity

Epidemic heterogeneityand Network structureWAN

Epidemic heterogeneityEntropy:prevalence in city j at time t normalized prevalence H [0,1]H=0 most het.H=1 most hom.

Results: Epidemic heterogeneity global properties

average over initial seed

central zone: H>0.9

HETk WAN importance of P(k)

Results: Epidemic heterogeneity epidemics starting from a given city

average entropy profile + maximal dispersion

noise: small effect

Results: Epidemic heterogeneity epidemics starting from a given city

percentage of infected cities

2nd PART: PredictabilitytimeOne outbreak realization:Another outbreak realization ?

epidemic forecast containment strategies

Predictabilitynormalized probability Similarity between 2 outbreak realizations:Hellinger affinity Overlap function

Predictability2 identical outbreaks

2 distinct outbreaks

Results: Predictability left: seed = airport hubs right: seed = poorly connected airports

HOM & HETw high overlap

HETk low overlap

WAN increased overlap !!

Results: Predictabilityj l wjl HOM: few channels high overlapHETk: broad P(k) lots of channels! low overlapWAN: broad P(k),P(w) lots of channels! emergence of preferred channels increased overlap !!!+ degree heterog.

Conclusions

air transportation network properties

global pattern of emerging disease spatio-temporal heterogeneity of epidemic pattern

quantitative measurement of the predictability of epidemic pattern

epidemic forecast, risk analysis of containment strategies

Ref.: http://arxiv.org/ qbio/0507029

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