Presentazione di PowerPoint

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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
Networks and Complex Systems talk series
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Epidemic spread 14th century
Black Death
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Epidemic spread nowadays
SARS
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Epidemic spread nowadays
SARS
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Modeling of global epidemics

• multi-level description
• intra-city
• epidemics
• inter-city travel

Ravchev, Longini. Mathematical Biosciences (1985)
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World-wide airport network

• complete 2002 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
gt99 of total traffic
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World-wide airport network
ltkgt 9.75 kmax 318 ltwgt 74584.4 wmin
4 wmax 6.167e06
Frankfurt
Sapporo - Tokyo
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World-wide airport network summary

• Broad distributions ? strong heterogeneities
• 3 different levels
• degree
• weight
• population

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Epidemics Stochastic Model
compartmental model air transportation data
Susceptible
N5
N2
N3
SIR model
w45
N0
Infected
w54
N1
N4
Recovered
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Stochastic Model Travel term
Travel probability from j to l
passengers in class X from j to l
multinomial distr.
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Stochastic Model Travel term
Transport operator
ingoing
outgoing

• other source of noise
• two-legs travel

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Stochastic Model Intra-city
S

• Homogeneous assumption
• b rate of transmission
• m-1 average infectious period

b
I
m
R
Independent Gaussian noises
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Epidemics Stochastic Model summary
compartmental model air transportation data
Intra-cities
Inter-cities
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Case study SARS
Susceptible
Infected
b
Hospitalized
Latent
e
Infected
dg
(1-d)g
HospitalizedD
HospitalizedR
gD
gR
Recovered
Dead
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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
• t0 ? Feb. 21st
• seed Hong Kong
• I01, L0 estimated, S0N

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Case study SARS ? results
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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

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Results Geographic spread
Epidemics starting in Hong Kong
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Results Geographic spread
Epidemics starting in Hong Kong
Gastner, Newman. PNAS (2004)
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Results Geographic spread
Epidemics starting in Hong Kong
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1st PART Heterogeneity

• maps ? heterogeneity epidemic spread
• appropriate measure
• role of specific structural
• properties
• topology, traffic, population
• comparison with null hypothesis

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Epidemic heterogeneity and Network structure
WAN
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Epidemic heterogeneity
prevalence in city j at time t
normalized prevalence
Entropy
H 0,1 H0 most het. H1 most hom.
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Results Epidemic heterogeneity

• global properties
• average over initial
• seed
• central zone Hgt0.9
• HETk WAN
• ? importance of P(k)

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Results Epidemic heterogeneity

• epidemics starting from
• a given city
• average entropy profile
• maximal dispersion
• noise small effect

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Results Epidemic heterogeneity

• epidemics starting
• from a given city
• percentage of
• infected cities

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2nd PART Predictability
One outbreak realization
time
Another outbreak realization ?

• epidemic forecast
• containment strategies

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Predictability
normalized probability
Similarity between 2 outbreak realizations
Hellinger affinity ? Overlap function
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Predictability
2 identical outbreaks 2 distinct outbreaks
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Results Predictability

• left seed airport hubs
• right seed poorly
• connected airports
• HOM HETw high overlap
• HETk low overlap
• WAN increased overlap !!

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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 !!!

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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