Comment modeliser la propagation d

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Comment modeliser la propagation depidemies a
lechelle mondiale ?

• Marc Barthelemy
• CEA, France

Forum Theorie 02/2008
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Outline

• Motivations
• Global scale metapopulation model
• Theoretical results
• Predictability
• Epidemic threshold, arrival times
• Applications
• SARS
• Pandemic flu Control strategy and Antivirals

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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,

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Epidemiology an interdisciplinary field
Transportation systems
Social networks
Urbanism
Biology, virology
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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

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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
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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, )

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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
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Modeling in Epidemiology


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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)
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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,
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Metapopulation model

• Theoretical studies
• Predictability ?
• Epidemic threshold ?
• Arrival times distribution ?

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

degree heterogeneity

weight heterogeneity
Colizza, Barrat, Barthelemy Vespignani, PNAS
(2006)
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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

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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)
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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)
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Applications

• 1. SARS test of the model
• 2. Control strategy testing antivirals

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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

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SARS predictions
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SARS predictions (2)

Colizza, Barrat, Barthelemy Vespignani, bmc
med (2007)
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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)

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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

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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)

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Predictions pandemic flu
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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

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Effect of antivirals Strategy comparison
Best strategy Cooperative !
Colizza, Barrat, Barthelemy, Valleron,
Vespignani, PLoS Med (2007)
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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

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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
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The End
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Geographic spread
Epidemics starting in Hong Kong
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Geographic spread
Epidemics starting in Hong Kong
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Geographic spread
Epidemics starting in Hong Kong
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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
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Theoretical result average arrival time

• Test on the world-wide air travel network

Gautreau, Barrat, Barthelemy, JSTAT (2007)
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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)
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Effect of antivirals

• Flu type disease Compartments

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Discussion scale vs. complexity
World
Modeling ?
City
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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

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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, )

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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)

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Epidemic spread Detecting robust patterns
?

• Detecting epidemic pathways from epidemic data

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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 ?

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Epidemic spread Detecting robust patterns
New cases per 100,000 inhabitants and per Unit
time
week

• Correlation between A and B Pearson coeff

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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)
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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

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Detecting robust patterns

• Existence pairs with large P (USA)
• Correlations with states
• California
• Illinois
• New York

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Detecting robust patterns

• Existence of pairs with large P (France)

Bretagne IdF Rhone-Alpes
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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 !

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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 !
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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