Are global epidemics predictable ?

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Are global epidemics predictable ?. V. Colizza School of Informatics, Indiana University, USA M. Barthélemy School of Informatics, Indiana University, USA A. Barrat Universite Paris-Sud, France A. Vespignani School of Informatics, Indiana University, USA. - PowerPoint PPT Presentation

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  • 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

    Entropy figures%Ninf%Ninf%Ninf%Ninf%Ninf%Ninf%Ninf%Ninf