1. The impact of mobility networks on the worldwide spread of epidemics
Alessandro Vespignani
Complex Systems Group
Department of Informatics
Indiana University

2. Weather forecast Parameters
# u is the zonal velocity (velocity in the east/west direction tangent to the sphere).
# v is the meridional velocity (velocity in the north/south direction tangent to the sphere).
# ω is the vertical velocity
# T is the temperature
# φ is the geopotential
# f is the term corresponding to the Coriolis force, and is equal to 2Ωsin(φ), where Ω is the angular rotation rate of the Earth (2π / 24 radians/hour), and φ is the latitude.
# R is the gas constant
# p is the pressure
# cp is the specific heat
# J is the heat flow per unit time per unit mass
# π is the exner function
# θ is the potential temperature .
Numerical weather prediction uses mathematical models of the atmosphere to predict the weather. Manipulating the huge datasets with the most powerful supercomputers in the world.
The primitive equations can be simplified into the following equations:
# Temperature: ∂T/∂t = u (∂Tx/∂X) + v (∂Ty/∂Y) + w (∂Tz/∂Z)
# Wind in E-W direction: ∂u/∂t = ηv - ∂Φ/∂x – Cp θ (∂π/∂x) – z (∂u/∂σ) – [∂(u2 + y) / 2] / ∂x
# Wind in N-S direction: ∂v/∂t = -η(u/v) - ∂Φ/∂y – Cp θ (∂π/∂y) – z (∂v/∂σ) – [∂(u2 + y) / 2] / ∂y
# Precipitable water: ∂W/∂t = u (∂Wx/∂X) + v (∂Wy/∂Y) + z (∂Wz/∂Z)
# Pressure Thickness: ∂(∂p/∂σ)/∂t = u [(∂p/∂σ)x /∂X] + v [(∂p/∂σ)y /∂Y] + z [(∂p/∂σ)z /∂Z]

3. Super-computer simulations
Fracture in 1.6 millions atoms material
6.8 billion finite elements plasma
Ab initio simulations thousand of atoms
pico-second scale ……

4. Why not forecast on…
Emerging disease spreading evolution

5. Wide spectrum of complications and complex features to include…
Simple
Realistic
Ability to explain (caveats) trends at a population level
Model realism looses in transparency.
Validation is harder.

6. Collective human behavior….
Social phenomena involves
large numbers of heterogeneous individuals
over multiple time and size scales
huge richness of cognitive/social science
In other words
The complete temperature analysis of the sea surface, and satellite images of atmospheric turbulence are easier to get than the large scale knowledge of commuting patterns or the quantitative measure of the propensity of a certain social behavior.

7. Unprecedented amount of data…..
Transportation infrastructures
Behavioral Networks
Census data
Commuting/traveling patterns
Different scales:
International
Intra-nation (county/city/municipality)
Intra-city (workplace/daily commuters/individuals behavior)

8. Mobility networks

9. Airport network
Each edge is characterized by weight wij defined as the number of passengers in the year
MSP
DTW
DEN
ATL Atlanta
ORD Chicago
LAX Los Angeles
DFW Dallas
PHX Phoenix
DEN Denver
DTW Detroit
MSP Minneapolis
IAH Houston
SFO San Francisco
ORD
SFO
LAX
PHX
ATL
DFW
IAH

10. Statistical distribution…
Skewed
Heterogeneity and high variability
Very large fluctuations
(variance>>average)

11. Computational epidemiology in
complex realities

12. Mechanistic meta-population models
City i
City a
City j
Intra-population infection dynamics by stochastic compartmental modeling

13. Global spread of epidemics on the airport network
Urban areas +
Air traffic flows
Ravchev et al. (in russian) 1977
40-80 russian cities
Ravchev, Longini. Mathematical Biosciences (1985)
50 urban areas worldwide
R. Grais et al
150 urban areasin the US
T. Hufnagel et al. PNAS (2004)
500 top airports
Colizza, Barrat, Barthelemy, A.V. PNAS 103 (2006)
3100 urban areas+airports, 220 countries, 99% traffic

14. World-wide airport network
complete IATA database
V = 3100 airports
E = weighted edges
wij #seats / (different time scales)
Nj urban area population
(UN census, …)
>99% of total traffic
Barrat, Barthélemy, Pastor-Satorras,
Vespignani. PNAS (2004)

15. World-wide airport network complex properties…
Colizza, Barrat, Barthélemy, Vespignani. PNAS (2006)

16. b m S I R S
Homogenous mixing assumption
time

17. Intra-city infection dynamicsb m S I R I
St+Dt = St - Binom(St , bDt It/N)
It+Dt = It + Binom(St , bDt It/N) – Binom(It,mDt)
Rt+Dt = Rt + Binom(It , mDt)

18. Global spread of infective individuals
wjl j l
Probability that any individual in the class X travel from j→l
Proportional to the traffic flow
Inversely proportional to the population

19. Stochastic travel operator
Probability that x individuals travel from j→l given a population Xj
Net balance of individuals in the class X arriving and leaving the city j

20. Meta-population SIR model
Sj,t+Dt = Sj,t - Binomj(Sj,t , bDt Ij,t/N) + j (S)
Ij,t+Dt = Ij,t + Binomj(Sj,t , bDt Ij,t/N) – Binomj(Ij,t,mDt) + j (I)
Rj,t+Dt = Rj,t + Binomj(Ij,t , mDt) + j (R)
Stochastic
coupling terms =
Travel
3100 x 3 differential coupled stochastic equations

21. Directions….. Applications… Basic theoretical questions…
Historical data
Scenarios forecast
Basic theoretical questions…

22. Prediction and predictability
Q1: Do we have consistent scenario with respect to different stochastic realizations?
Q2: What are the network/disease features determining the predictability of epidemic outbreaks
Q3:Is it possible to have epidemic forecasts?
Colizza Barrat, Barthélemy,
Vespignani. PNAS 103, 2015 (2006);
Bulletin Math. Bio. (2006)

23. Historical data : The SARS case…

24. Statistical Predictions…

25. Quantitatively speaking

26. Correct predictions in 210 countries over 220 Quantitatively correct
How is that possible?
Stochastic noise + complex network

27. Taking advantage of complexity…
Two competing effects
Paths degeneracy (connectivity heterogeneity)
Traffic selection (heterogeneous accumulation of traffic on specific paths)
Definition of epidemic pathways as a backbone of dominant connections for spreading

28. 100% 10% Republic of Korea United Kingdom China Japan Germany India
Taiwan
Thailand
Switzerland
Vietnam
Philippines
France
Italy
Singapore
Malaysia
Spain
Indonesia
Australia

29. Avian H5N1 Pandemic ??? reassortment mutation H3N2 H5N1 165 cases
88 deaths
(Feb 6th, 2006)
mutation

30. Guessing exercise: similarities with influenza….
Recovered /
Removed
Infectious
Asympt.
Latent
Susceptible
Sympt. Not Tr.
Sympt. Tr.
rb b b
e pa
e (1-pa ) pt
e (1-pa ) (1-pt ) m
infectiousness
I Sympt.
I Asympt. S L R
time
(days)
1.9 3
Longini et al. Am. J. Epid. (2004)

31. A convenient quantity R0 Estimates for R0 = 1.1 - 30 !!
Basic reproductive number
The number of offspring cases generated by an infected individual in a susceptible population R0
Estimates for R0 = !!
(most likely [ ])

32. Pandemic forecast…
Feb 2007
May 2007
Jul 2007
Dec 2007
Feb 2008
Apr 2008
rmax
Pandemic with R0=1.6 starting from Hanoi (Vietnam) in October 2006
Baseline scenario

34. Country level
City level

35. Containment strategies….
Travel restrictions
Partial
Full (country quarantine???)
Antiviral
Amantadine and Rimantadine (inhibit matrix proteins)
Zanamivir and Oseltamivir (neuraminidase inhibitor)
Vaccination
Pre-vaccination to the present H5N1
Vaccine specific to the pandemic virus (6-9 months for preparation and large scale deployment)

36. Travel restrictions….

37. Antivirals….

38. Stockpiles management
Scenario 2
Stockpiles sufficient for 10% of the population in a limited number of countries + WHO emergency supply deployment in just two countries uncooperative strategy
Scenario 3
Global stockpiles management with the same amount of AV doses. Cooperative Strategy

39. Use of AV stockpiles in the
different scenarios

40. Cooperative versus uncooperative

41. Geographical regions…

42. Beneficial also for the donors
Uncooperative
Beneficial also for the donors
Cooperative

43. What we learn… Complex global world calls for a non-local perspective
Preparedness is not just a local issue
Real sharing of resources discussed by policy makers
…………

44. What’s for the future.. Refined census data Voronoi tassellation
2.5 arc/min resolution
Global Rural-Urban
Mapping Project (GRUMP)
Voronoi tassellation
Boundary mobility

45. Boundary mobility

46. World-wide scale

47. # cases

48. Same resolution worldwide…

49. Data integration + algorithms
Stochastic epidemic models
Network models
Data:
Census
3x105 grid population
IATA
Mobility (US, Europe (12), Australia, Asia)
Visualization packages

50. Collaborators http://cxnets.googlepages.com M. Barthelemy V. Colizza
A. Barrat
M. Barthelemy
R. Pastor Satorras
A.J. Valleron
PNAS, 103, (2006)
Plos Medicine, 4, e13 (2007)
Nature Physics, 3, (2007)
More Information/paper/data