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Multiscale mobility networks and the large scale spreading of infectious diseases
Duygu Balcan, Vittoria Colizza, Bruno Goncalves, Hao Hu, Jose J. Ramasco, Alessandro Vespignani
TL;DR
Human mobility is central to realistic epidemic modeling, but commuting data are limited and its interaction with airline traffic is difficult to quantify. The paper fits a global commuting gravity law from data in 29 countries and integrates it into a worldwide metapopulation model. Commuting is much larger than airline traffic, yet changes global epidemic patterns only slightly while increasing local synchronization and altering peripheral transmission behavior.
Problem
Human mobility is difficult to model realistically because commuting data are limited and the effects of adding mobility features are not yet clearly distinguishable.
Method
The study fits a commuting gravity law from 29 countries and incorporates synthetic short-range commuting into the GLEaM worldwide metapopulation model using time-scale separation.
Results
Commuting flows are one order of magnitude larger than airline flows, but adding them leaves overall epidemic timing, size, and global outbreak probability largely unchanged.
Takeaways & Limitations
Short-range mobility mainly affects synchronization among nearby subpopulations, peripheral airline-connected regions, and the hierarchy and timing of epidemic invasion.
Abstract
from arXiv · showhide
Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms; ii) integrate in a worldwide structured metapopulation epidemic model a time-scale separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short range mobility increases however the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multi-scale framework.
I. INTRODUCTION
The paper addresses how small-scale commuting and long-range airline mobility jointly shape global epidemic spread despite incomplete mobility data. It combines worldwide commuting analysis with a multiscale epidemic model to compare their effects.
- Human mobility is difficult to incorporate realistically because empirical data are limited and models integrate heterogeneous real-world features.
- Data from 29 countries support a gravity model describing worldwide commuting patterns at short range.
- Commuting flows are one order of magnitude larger than airline flows, yet global epidemic patterns remain mainly determined by the airline network.
- Short-range commuting synchronizes nearby subpopulations and affects epidemic behavior in regions weakly connected to the airline network.
II. MODEL DESCRIPTION
The model uses a structured metapopulation framework in which geographically defined subpopulations are coupled by population movements. Its gravity-law parameters provide the basis for constructing synthetic commuting connections.
- GLEaM is a georeferenced structured metapopulation model coupling geographical census regions through population movements.
- Gravity-law exponents estimated from global commuting data are used to construct the synthetic worldwide commuting network.
A. Multiscale mobility networks
The study constructs multiscale mobility networks by mapping commuting data onto airport-centered geographic subpopulations and fitting a gravity law. The resulting short-range network complements long-range airline traffic while remaining dependent on the chosen spatial granularity.
- A. Multiscale mobility networks: High-resolution population data define airport-centered Voronoi-like subpopulations for representing short-range commuting flows.
- A. Multiscale mobility networks: Commuting flows form a neighboring, grid-like network, whereas airline traffic is dominated by long-range connections.
- A. Multiscale mobility networks: Commuting flows are one order of magnitude larger on average than airline traffic and have a characteristic round-trip time of about 1/3 days.
- A. Multiscale mobility networks: The gravity model represents flow using origin and destination populations together with a distance-dependent function.
- A. Multiscale mobility networks: More than 10^4 worldwide flows show that an exponential distance function provides the best fit for commuting decay.
- A. Multiscale mobility networks: The fitted gravity law reproduces country-level commuting flows, but its validity cannot be extrapolated to different spatial granularities.
B. Epidemic simulations
GLEaM simulations compare worldwide influenza spread with airline mobility alone versus multiscale mobility including commuting. Commuting has limited global impact but increases local synchronization and changes invasion timing near weakly airline-connected areas.
- Simulation framework: The simulations model an ILI beginning in Hanoi on April 1, using GLEaM's stochastic compartmental and airline-transport framework.Commuting is added through a time-scale separation approximation for short visits between neighboring subpopulations.
- Global and regional effects: Both the probability of global outbreak and the first-year global epidemic size remain nearly unchanged when commuting flows are included.The comparison uses pandemic influenza with R0 = 1.9 and profiles averaged over 103 realizations.
- Global and regional effects: Commuting mainly affects epidemic tails by enhancing synchronization among local epidemic profiles.Without commuting, differing outbreak times across subpopulations broaden aggregated profiles.
- Local effects: In neighboring cities around Boston, commuting reduces the interval between prevalence peaks by over one month and removes multiple peaks.The hub profile changes little, while nearby locations with limited airline connections are strongly affected.
- Invasion hierarchy: Adding commuting reduces airline hubs' dominance and makes epidemic invasion paths more geographically local.Without commuting, nearby locations lacking frequent direct flights may be infected later through convoluted flight sequences.
III. VORONOI TESSELLATION AROUND MAIN TRANSPORTATION HUBS
The model constructs airport-centered geographical census areas from high-resolution global population data using a Voronoi-like assignment constrained by country and distance.
- Airport-centered tessellation: Population cells are assigned to the nearest IATA airport within the same country when the airport is within 200 km.This defines the geographical census areas used for the subpopulation network.
- Population data: The underlying population database covers the planet on a 15 × 15 minute-of-arc lattice.The tessellation is therefore based on high-resolution gridded population estimates.
IV. DISEASE STRUCTURE, SEASONALITY AND R0
The disease model uses a compartmental ILI structure with symptomatic and asymptomatic infectious states, travel restrictions, and specified latency and infectious periods.
- Disease compartments: Susceptible individuals enter a latent compartment after infection, then become symptomatic or asymptomatic according to probability pa.Symptomatic infections are divided by whether individuals can travel.
- Disease parameters: The model assumes a 1.9-day latent period and a 3-day infectious period.Asymptomatic infection probability is pa = 0.33, asymptomatic relative infectiousness is rβ = 0.5, and symptomatic travel probability is pt = 0.5.
V. COMMUTING SHORT RANGE COUPLINGS
The model represents commuting by separating home residents from visitors in neighboring subpopulations and using equilibrium visitor populations to calculate infection transmission across local commuting links.
- Commuting visitors are represented separately from residents at home, with traveling compartments indexed by origin and destination subpopulations.
- Individuals in traveling compartments visit neighboring subpopulations at rate σij for an average duration of τ^-1.
- When τ ≫ σi, relaxation is dominated by return home, allowing equilibrium population values to approximate commuting populations during infection calculations.
- New infections arise locally and during visits, including interactions between residents and infectious visitors in neighboring subpopulations.
- The force of infection combines transmission involving local infectious individuals, infectious visitors, visiting susceptibles, and infectious individuals encountered in neighboring subpopulations.
VI. CONCLUSIONS
The study uses mobility data from 29 countries across 5 continents to fit a gravity law for modeling short-range commuting in a worldwide epidemic model. It then adds this commuting network to an airline-based model to distinguish the contributions of short- and long-range mobility flows.
- Data from 29 countries across 5 continents were used to fit a gravity law for commuting behavior.
- The gravity law models commuting between Voronoi geographical census areas centered on airports indexed by IATA.
- The worldwide epidemic model includes airline traffic among 3362 airport locations and an added short-range commuting network.
- Adding short-range commuting allows the model to distinguish the contributions of long- and short-range mobility flows.