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Title: Comment modeliser la propagation d


1
Comment modeliser la propagation depidemies a
lechelle mondiale ?
  • Marc Barthelemy
  • CEA, France

Forum Theorie 02/2008
2
Outline
  • Motivations
  • Global scale metapopulation model
  • Theoretical results
  • Predictability
  • Epidemic threshold, arrival times
  • Applications
  • SARS
  • Pandemic flu Control strategy and Antivirals

3
Theoretical physics and interdisciplinarity
  • Theoretical physics in other fields
  • Biology, ecology, epidemiology, economy, social
    sciences,
  • Tools, concepts and methods
  • Data analysis scaling laws, data collapse
  • Modeling minimal model, relevant parameters,

4
Epidemiology an interdisciplinary field
Transportation systems
Social networks
Urbanism
Biology, virology
5
Epidemiology vs. Etiology Two levels
  • Microscopic level (bacteria, viruses)
    compartments
  • Understanding and killing off new viruses
  • Quest for new vaccines and medicines
  • Macroscopic level (communities, species)
  • Integrating biology, movements and interactions
  • Vaccination campaigns and immunization strategies

6
Epidemiology past and current
  • Human movements and disease spread
  • Complex movement patterns different means,
    different scales (SARS) Importance of networks

Black death Spatial diffusion Model
7
21st century Networks and epidemics
Epidemics spread on a contact network
Different scales, different networks
  • Individual Social networks (STDs on sexual
    contact network) NB Sometimes no network !
  • Intra-urban Location network (office, home,
    shops, )
  • Inter-urban Railways, highways
  • Global Airlines (SARS, Flu, )

8
Airline network and epidemic spread
Complete IATA database - 3100 airports
worldwide - 220 countries - 20,000
connections - wij passengers on connection
i-j - gt99 total traffic
9
Modeling in Epidemiology


10
Metapopulation model
j
l
Baroyan et al, 1969 40 russian cities Rvachev
Longini, 1985 50 airports worldwide Grais
et al, 1988 150 airports in the US Hufnagel
et al, 2004 500 top airports worldwide
Colizza, Barrat, Barthelemy Vespignani, PNAS
(2006)
11
Metapopulation model
Reaction-diffusion models FKPP equation
  • Rvachev Longini (1985)

Inner city term
Travel term
  • Transport operator

Flahault Valleron (1985) Hufnagel et al, PNAS
2004, Colizza, Barrat, Barthelemy, Vespignani
PNAS 2006, BMB, 2006. Theory Colizza
Vespignani, Gautreau al,
12
Metapopulation model
  • Theoretical studies
  • Predictability ?
  • Epidemic threshold ?
  • Arrival times distribution ?

13
Predictability
One outbreak realization
Another outbreak realization ? Effect of noise ?
?
?
?
?
?
?
14
Overlap measure
Similarity between 2 outbreak realizations
Overlap function
time t
time t
time t
time t
15
Predictability
no degree fluctuations no weight fluctuations

degree heterogeneity

weight heterogeneity
Colizza, Barrat, Barthelemy Vespignani, PNAS
(2006)
16
Predictability
  • Effect of heterogeneity
  • degree heterogeneity
  • decreases predictability

l
wjl
j
  • Weight heterogeneity
  • increases predictability !
  • Good news Existence of preferred channels !
  • Epidemic forecast, risk analysis of containment
    strategies

17
Theoretical result Threshold
  • Reproductive number for a population
  • moments of the degree distribution
  • travel probability

Travel restrictions not efficient !!!
  • Effective for reproductive number for a network
    of populations

Colizza Vespignani, PRL (2007)
18
Theoretical result average arrival time
  • Ansatz for the arrival time at site t (starting
    from s)
  • Population of city k
  • Traffic between k and l
  • Transmissibility
  • Set of paths between s and t

Gautreau, Barrat, Barthelemy, JSTAT (2007)
19
Applications
  • 1. SARS test of the model
  • 2. Control strategy testing antivirals

20
Application SARS
pop i
pop j
  • refined compartmentalization
  • parameter estimation clinical data local
    fit
  • geotemporal initial conditions available
    empirical data
  • modeling intervention measures standard
    effective modeling

21
SARS predictions
22
SARS predictions (2)

Colizza, Barrat, Barthelemy Vespignani, bmc
med (2007)
23
More from SARS - Epidemic pathways
  • For every infected country
  • where is the epidemic coming from ?
  • - Redo the simulation for many disorder
    realizations
  • (same initial conditions)
  • - Monitor the occurrence of the paths
  • (source-infected country)

24
(No Transcript)
25
SARS- what did we learn ?
  • Metapopulation model, no tunable parameter
  • good agreement with WHO data !
  • Existence of pathways
  • confirms the possibility of epidemic forecasting
    !
  • Useful information for control strategies

26
Application of the metapopulation model effect
of antivirals
  • Threat Avian Flu
  • Question use of antivirals
  • Best strategy for the countries ?
  • Model
  • Etiology of the disease (compartments)
  • MetapopulationTransportation mode (air travel)

27
Predictions pandemic flu
28
Effect of antivirals
  • Comparison of strategies (travel restrictions not
    efficient)
  • Baseline reference point (no antivirals)
  • Uncooperative each country stockpiles AV
  • Cooperative each country gives 10 (20) of
    its own stock

29
Effect of antivirals Strategy comparison
Best strategy Cooperative !
Colizza, Barrat, Barthelemy, Valleron,
Vespignani, PLoS Med (2007)
30
Conclusions and perspectives
  • Global scale (metapopulation model)
  • Pandemic forecasting
  • Theoretical problems (reaction-diffusion on
    networks)
  • Smaller scales-country, city (?)
  • Global level simplicity due to the dominance
    of air travel
  • Urban area ? Model ? What can we say about the
    spread of a disease ? Always more data available

31
Collaborators and links
  • Collaborators
  • - A. Barrat (LPT, Orsay)
  • - V. Colizza (ISI, Turin)
  • - A.-J. Valleron (Inserm, Paris)
  • - A. Vespignani (IU, Bloomington)
  • Collaboratory
  • PhD students
  • - P. Crepey (Inserm, Paris)
  • - A. Gautreau (LPT, Orsay)

http//cxnets.googlepages.com
marc.barthelemy_at_cea.fr
32
The End
33
Geographic spread
Epidemics starting in Hong Kong
34
Geographic spread
Epidemics starting in Hong Kong
35
Geographic spread
Epidemics starting in Hong Kong
36
Collaborators and links
  • Collaborators
  • - A. Barrat (LPT)
  • - V. Colizza (IU ISI)
  • - A.-J. Valleron (Inserm)
  • - A. Vespignani (IU)
  • Collaboratory
  • PhD students
  • - P. Crepey (Inserm)
  • - A. Gautreau (LPT)

http//cxnets.googlepages.com
marc.barthelemy_at_gmail.com
37
Theoretical result average arrival time
  • Test on the world-wide air travel network

Gautreau, Barrat, Barthelemy, JSTAT (2007)
38
SARS predictions (3) - False positives
Country Median 90 CI
Japan 30 9-114
Netherlands 2 1-10
United Arab Emir. 2 1-11
Bangladesh 2 1-14
Bahrain 1 1-20
Cambodia 1 1-8
Nepal 1 1-20
Brunei 1 1-8
Israel 1 1-13
Mauritius 1 1-32
Saudi Arabia 1 1-11
Colizza, Barrat, Barthelemy Vespignani, bmc
med (2007)
39
Effect of antivirals
  • Flu type disease Compartments

40
Discussion scale vs. complexity
World
Modeling ?
City
41
Predictability
  • Predictability Reliability of epidemic forecast
  • Robustness of epidemic scenario versus noise
  • Measure of statistical similarity of the
    history of epidemic outbreak with
  • - same initial conditions
  • - different noise realization

42
Global spread Summary
  • Metapopulation model
  • Importance of heterogeneity-high predictability
  • Possibility of forecasting existence of epidemic
    pathways
  • Why does it work ?
  • Existence of a dominant network air travel !!!
  • Other scales ? (country, urban area, )

43
Epidemic spread at the country level Detecting
robust patterns
  • Detecting epidemic pathways from epidemic data
  • Case-studies flu in the USA (1972-2002) and
    France (1984-2004)

44
Epidemic spread Detecting robust patterns
?
  • Detecting epidemic pathways from epidemic data

45
Epidemic spread Detecting robust patterns
New cases per 100,000 inhabitants and per Unit
time
week
  • Correlation between A and B ?
  • Effect of transportations modes ? Existence of a
    dominant mode ?

46
Epidemic spread Detecting robust patterns
New cases per 100,000 inhabitants and per Unit
time
week
  • Correlation between A and B Pearson coeff

47
Detecting robust patterns
  • Value of the pearson-comparison value ?
    Correlations due to constraints

Null model Reshuffling
Maximal correlation Synchronized peaks
Crepey and Barthelemy, Amer. J. Epidemiology
(2007)
48
Detecting robust patterns
  • Average X for the correlation between CA and the
    other states
  • Existence of a robust channel large ltXgt and
    small dispersion
  • Encoded in

49
Detecting robust patterns
  • Existence pairs with large P (USA)
  • Correlations with states
  • California
  • Illinois
  • New York

50
Detecting robust patterns
  • Existence of pairs with large P (France)

Bretagne IdF Rhone-Alpes
51
Detecting robust patterns - relation with
transport modes
  • Relation between P and transportation modes
    (Multivariate analysis air travel, distance,
    temperature)
  • Existence of a dominant mode for inter state
    spread
  • in the US !



52
Detecting robust patterns (France)
  • Relation between P and transportation modes
    (Multivariate analysis air travel, car, train)

Parameter Coefficient
Distance -9.220e-02
Car traffic 2.645e-01
Train traffic 2.043e-01
No dominant transportation mode !
53
Summary
  • Two factors
  • Heterogeneity of flows (epidemic pathways) at
    all scales
  • Existence of a dominant transportation mode
    depends on the scale
  • Global scale air travel
  • USA air travel (interstate case)
  • France car, train, equivalent
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