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 “Networks and Complex Systems” talk series

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

Nov Mar Epidemic spread: nowadays SARS

SARS

Modeling of global epidemics Modeling of global epidemics Ravchev, 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 = weighted edges  w ij #seats / year  N j urban area population (UN census, …) V = 3100 airports E = weighted edges >99% of total traffic Barrat, Barthélemy, Pastor-Satorras, Vespignani. PNAS (2004)

World-wide airport network = 9.75 k max = 318 = w min = 4 w max = e +06 Frankfurt Sapporo - Tokyo

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

Epidemics: Stochastic Model compartmental model + air transportation data N1N1N1N1 N2N2N2N2 N0N0N0N0 N5N5N5N5 N4N4N4N4 N3N3N3N3 w 54 w 45 SIR model Susceptible Infected Recovered

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

Stochastic Model Travel term j lw jl Transport operator:  other source of noise:  two-legs travel: outgoing ingoing

Stochastic Model Intra-city S I R   Independent Gaussian noises  Homogeneous assumption   rate of transmission   -1 average infectious period

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

Case study: SARS Susceptible Latent Infected Hospitalized R Hospitalized D Recovered Dead   dd (1-d)  DD RR Infected Hospitalized

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. 21 st seed: Hong Kong I 0 =1, L 0 estimated, S 0 =N

Case study: SARS  results

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

Results: Geographic spread Epidemics starting in Hong Kong

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

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

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

Epidemic heterogeneity and Network structure HOM  HOM P(k) P(N) P(w) WANWAN P(w) P(k) k P(N) HETk  HETk P(k)P(w) w P(N) N HETw  HETw

Epidemic heterogeneity Entropy: 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

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

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

Predictability 2 identical outbreaks 2 distinct outbreaks time t

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

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