Are global epidemics predictable ?
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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
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