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The impact of mobility networks on the worldwide spread of epidemics

Complex Systems Group Department of Informatics Indiana University. The impact of mobility networks on the worldwide spread of epidemics. Alessandro Vespignani. Weather forecast. Parameters. # u is the zonal velocity (velocity in the east/west direction tangent to the sphere).

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The impact of mobility networks on the worldwide spread of epidemics

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

  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. ATL Atlanta ORD Chicago LAX Los Angeles DFW Dallas PHX Phoenix DEN Denver DTW Detroit MSP Minneapolis IAH Houston SFO San Francisco Airport network • Each edge is characterized by weight wij defined as the number of passengers in the year MSP DTW DEN ORD SFO ATL PHX LAX 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 • completeIATA database • V = 3100 airports • E = 17182 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 dynamics b m S I R I St+Dt = St - Binom(St , bDt It/N) It+Dt = It + Binom(St , bDtIt/N) – Binom(It,mDt) Rt+Dt = Rt + Binom(It , mDt)

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

  19. Stochastic travel operator • Probability that x individuals travel from j→l given a population Xj • Net balance of individuals in the class Xarriving 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 , bDtIj,t/N) – Binomj(Ij,t,mDt) + j (I) Rj,t+Dt = Rj,t + Binomj(Ij,t , mDt) + j (R) • 3100 x 3 differential coupled stochastic equations Stochastic coupling terms = Travel

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

  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 China United Kingdom Japan India Germany Taiwan Thailand Vietnam Switzerland Philippines France Malaysia Italy Singapore Spain Indonesia Australia

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

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

  31. A convenient quantity • Basic reproductive number • The number of offspring cases generated by an infected individual in a susceptible population R0 Estimates for R0 = 1.1 - 30 !! (most likely [1.5 - 3.0])

  32. rmax Feb 2007 May 2007 Jul 2007 Dec 2007 Apr 2008 Feb 2008 0 Pandemic forecast… Pandemic with R0=1.6 starting from Hanoi (Vietnam) in October 2006 Baseline scenario

  33. Country level City level

  34. 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)

  35. Travel restrictions….

  36. Antivirals….

  37. 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

  38. Use of AV stockpiles in the different scenarios

  39. Cooperative versus uncooperative

  40. Geographical regions…

  41. Beneficial also for the donors Uncooperative Cooperative

  42. 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 • …………

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

  44. Boundary mobility

  45. World-wide scale

  46. # cases

  47. Same resolution worldwide…

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

  49. V. Colizza A. Barrat M. Barthelemy R. Pastor Satorras Collaborators • A.J. Valleron • PNAS, 103, 2015-2020 (2006) • Plos Medicine, 4, e13 (2007) • Nature Physics, 3, 276-282(2007) More Information/paper/data http://cxnets.googlepages.com

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