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Are global epidemics predictable ?

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.

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Are global epidemics predictable ?

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  1. Are global epidemics predictable ? V. ColizzaSchool of Informatics, Indiana University, USA M. BarthélemySchool of Informatics, Indiana University, USA A. BarratUniversite Paris-Sud, France A. VespignaniSchool of Informatics, Indiana University, USA “Networks and Complex Systems” talk series

  2. Dec. 1350 June 1350 Dec. 1349 June 1349 Dec. 1347 Dec. 1348 June 1348 Dec. 1347 Dec. 1347 Dec. 1350 Epidemic spread: 14th century Black Death

  3. Nov. 2002 Mar. 2003 Epidemic spread: nowadays SARS

  4. Epidemic spread: nowadays SARS

  5. Modeling of global epidemics • multi-level description : • intra-city epidemics • inter-city travel Ravchev, Longini. Mathematical Biosciences (1985)

  6. World-wide airport network • complete2002 IATA database • V = 3880 airports • E = 18810 weighted edges • wij #seats / year • Nj urban area population (UN census, …) Barrat, Barthélemy, Pastor-Satorras, Vespignani. PNAS (2004) V = 3100 airports E = 17182 weighted edges >99% of total traffic

  7. World-wide airport network <k> = 9.75 kmax = 318 <w> = 74584.4 wmin = 4 wmax = 6.167e+06 Frankfurt Sapporo - Tokyo

  8. World-wide airport network summary Broad distributions  strong heterogeneities 3 different levels: • degree • weight • population

  9. Epidemics: Stochastic Model compartmental model+air transportation data Susceptible N5 N2 N3 SIR model w45 N0 Infected w54 N1 N4 Recovered

  10. wjl l j Stochastic Model Travel term Travel probability from j to l # passengers in class X from j to l multinomial distr.

  11. wjl l j Stochastic Model Travel term Transport operator: ingoing outgoing • other source of noise: • two-legs travel:

  12. Stochastic Model Intra-city S • Homogeneous assumption • brate of transmission • m-1average infectious period b I m R Independent Gaussian noises

  13. SIR model Does it work ? Epidemics: Stochastic Model summary compartmental model+air transportation data Intra-cities Inter-cities

  14. Case study: SARS Susceptible Infected b Hospitalized Latent e Infected dg (1-d)g HospitalizedD HospitalizedR gD gR Dead Recovered

  15. 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

  16. Case study: SARS  results

  17. SIR model statistical properties epidemic pattern ? • strong heterogeneity in no. infected cases: 0-103 • large fluctuations • Full scale computational • study of global epidemics: • statistical properties epidemic pattern • effect of complexity of transportation network • forecast reliability

  18. Results: Geographic spread Epidemics starting in Hong Kong

  19. Results: Geographic spread Epidemics starting in Hong Kong Gastner, Newman. PNAS (2004)

  20. t=160 days t=66 days t=56 days t=48 days t=24 days Results: Geographic spread Epidemics starting in Hong Kong

  21. 1st PART: Heterogeneity • maps  heterogeneity epidemic spread • appropriate measure • role of specific structural properties: topology, traffic, population • comparison with null hypothesis

  22. HOM P(k) P(k) P(N) P(N) <k> P(w) P(w) P(w) P(N) P(k) <N> <N> • HETw <w> <w> w <k> k N • HETk Epidemic heterogeneity and Network structure WAN

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

  24. Results: Epidemic heterogeneity • global properties • average over initial seed • central zone: H>0.9 • HETk WAN •  importance of P(k)

  25. Results: Epidemic heterogeneity • epidemics starting from • a given city • average entropy profile • + maximal dispersion • noise: small effect

  26. Results: Epidemic heterogeneity • epidemics starting • from a given city • percentage of • infected cities

  27. t=160 days t=24 days t=66 days t=56 days t=48 days ? ? ? ? ? t=160 days t=48 days t=66 days t=56 days t=24 days 2nd PART: Predictability One outbreak realization: time Another outbreak realization ? • epidemic forecast • containment strategies

  28. Predictability normalized probability Similarity between 2 outbreak realizations: Hellinger affinity  Overlap function

  29. time t time t time t time t Predictability 2 identical outbreaks 2 distinct outbreaks

  30. Results: Predictability • left:seed = airport hubs • right:seed =poorly connected airports • HOM & HETw high overlap • HETk low overlap • WAN increased overlap !!

  31. wjl l j + weight heterog. Results: Predictability HOM:  few channels  high overlap + degree heterog. HETk: broad P(k) lots of channels!  low overlap wjl l j WAN: broad P(k),P(w) lots of channels!  emergence of preferred channels  increased overlap !!!

  32. 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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