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Multiscale Mobility Networks and the Spatial Spreading of Infectious Diseases

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Multiscale Mobility Networks and the Spatial Spreading of Infectious Diseases Multiscale mobility networks and the spatial spreading of infectious diseases Duygu Balcana,b, Vittoria Colizzac, Bruno Gonc¸alvesa,b, Hao Hud, Jose´ J. Ramascob, and Alessandro Vespignania,b,c,1 aCenter for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, IN 47408; bPervasive Technology Institute, Indiana University, Bloomington, IN 47404; cComputational Epidemiology Laboratory, Institute for Scientific Interchange Foundation, 10133 Torino, Italy; and dDepartment of Physics, Indiana University, Bloomington, IN 47406 Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved October 13, 2009 (received for review June 19, 2009) Among the realistic ingredients to be considered in the computational two questions stand out: (i) Is there a most relevant mobility scale modeling of infectious diseases, human mobility represents a crucial in the definition of the global epidemic pattern? and (ii) At which challenge both on the theoretical side and in view of the limited level of resolution of the epidemic behavior does a given mobility availability of empirical data. To study the interplay between short- scale become relevant, and to what extent? scale commuting flows and long-range airline traffic in shaping the To begin addressing these questions, we use high-resolution spatiotemporal pattern of a global epidemic we (i) analyze mobility worldwide population data that allow for the definition of sub- data from 29 countries around the world and find a gravity model populations according to a Voronoi decomposition of the world able to provide a global description of commuting patterns up to 300 surface centered on the locations of International Air Transport kms and (ii) integrate in a worldwide-structured metapopulation Association (IATA)-indexed airports (www.iata.org). We have then epidemic model a timescale-separation technique for evaluating the gathered data on the commuting patterns of 29 countries in five force of infection due to multiscale mobility processes in the disease continents, constructing short-range commuting networks for the dynamics. Commuting flows are found, on average, to be one order defined subpopulations. Extensive analysis of these networks allows of magnitude larger than airline flows. However, their introduction us to draw a general gravity law for commuting flows that repro- into the worldwide model shows that the large-scale pattern of the duces commuting patterns worldwide. This law, valid at the scale simulated epidemic exhibits only small variations with respect to the defined by the tessellation process, is statistically stable across the baseline case where only airline traffic is considered. The presence of world because of the globally homogeneous procedure applied to short-range mobility increases, however, the synchronization of sub- build the subpopulations around transportation hubs. The multi- populations in close proximity and affects the epidemic behavior at scale networks we obtain are integrated into the global epidemic the periphery of the airline transportation infrastructure. The present and mobility (GLEaM) model, a computational platform that uses approach outlines the possibility for the definition of layered a metapopulation stochastic model on a global scale to simulate the computational approaches where different modeling assumptions large-scale spreading of influenza-like illnesses (ILI). To fully and granularities can be used consistently in a unifying multiscale consider the effect of multiscale mobility processes in the disease framework. dynamics, we develop a timescale-separation technique for evalu- ating the force of infection due to different mobility couplings and complex networks ͉ computational epidemiology ͉ human mobility ͉ simulate global pandemics with tunable reproductive ratios. The multiscale phenomena results obtained from the full multiscale mobility network are compared with the simulations in which only the large-scale cou- pling of the airline transportation network is included. Our analysis omputational approaches to the realistic modeling of spatial shows that although commuting flows are, on average, one order of Cepidemic spread make use of a wide array of simulation magnitude larger than the long-range airline traffic, the global schemes (1) ranging from very detailed agent-based approaches spatiotemporal patterns of disease-spreading are mainly deter- (2–6) to structured metapopulation models based on data-driven mined by the airline network. Short-range commuting interactions mobility schemes at the interpopulation level (7–10). All these have, on the other hand, a role in defining a larger degree of approaches integrate a wealth of real-world data. However, it is not synchronization of nearby subpopulations and specific regions, yet clear how to discriminate the effects of the inclusion/lack of which can be considered weakly connected by the airline transpor- real-world features in specific models. This limitation is mainly tation system. In particular, it is possible to show that short-range related to our incomplete knowledge of human interactions and mobility has an impact in the definition of the subpopulation mobility processes, which are fundamental aspects to describe a infection hierarchy. The techniques developed here allow for an disease spread. Although recent efforts started to make available initial understanding of the level of data integration required to massive data on human mobility from different sources and at obtain reliable results in large-scale modeling of infectious diseases. different levels of description (11–20), the multiscale nature of human mobility is yet to be comprehensively explored. Human Results and Discussion mobility can be generally described by defining a network of Simulations of worldwide epidemic spread are generally based on interacting communities where the connections and the corre- structured metapopulation models that consider data-driven sponding intensity represent the flow of people among them (13, schemes for long-range mobility at the interpopulation level cou- 14). Global mobility flows therefore form very complex multiscale pled with coarse-grained techniques within each subpopulation networks (21) spanning several orders of magnitude in intensity and spatiotemporal scales ranging from the long-range intercontinental air traffic (13, 15) to the short range commuting flows (17–19). A Author contributions: D.B., V.C., B.G., H.H., J.J.R., and A.V. designed research, performed multitude of heuristic models for population structure and mobility research, analyzed data, and wrote the paper. patterns have been proposed, but they all depend on the specific The authors declare no conflict of interest. mobility process under consideration (22, 23). The limited under- This article is a PNAS Direct Submission. standing of the interrelations among the multiple scales entailed in Freely available online through the PNAS open access option. human mobility and their impact on the definition of epidemic 1To whom correspondence should be addressed. E-mail: [email protected]. patterns constitute a major road block in the development of This article contains supporting information online at www.pnas.org/cgi/content/full/ predictive large-scale data driven epidemic models. In this context, 0906910106/DCSupplemental. 21484–21489 ͉ PNAS ͉ December 22, 2009 ͉ vol. 106 ͉ no. 51 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0906910106 Downloaded by guest on September 25, 2021 2 C 10-2 D 10 γ j i α (M) 10-3 / (N N ) 0 / w 10 (D) -4 (D) w 10 w 105 -2 103 10-5 10 0 100 200 3000 100 200 101 A Distance (km) Distance (km) EF102 102 (M) (M) 0 0 / w 10 / w 10 (D) (D) w w 105 -2 -2 3 10 10 10 2 6 8 2 4 6 8 10 10 10 10 10 10 10 10 101 B Population of origin Population of destination Fig. 1. Multiscale mobility networks and gravity law fit. (A) Continental U.S. airline transportation network. (B) Continental U.S. commuting network. The width and color (from blue to red) of the edges represent on a logarithmic scale the intensity of the mobility flow. (C) Commuting flux obtained from data (w(D)) rescaled by the ␣ ␥ gravity law’s dependence on origin and destination populations (Ni Nj ), as a function of the distance between subpopulations. The number of people commuting between different urban areas decreases exponentially with distance up to 300 kms. (D–F) Ratio of commuting flux obtained from data (w(D)) to corresponding commuting flux predicted by the gravity model with fitted parameters (w(M)), as a function of distance, population of origin and population of destination, respectively. The three plots provide values spread Ϸ1, showing that the synthetic networks generated by the functional form (see Table 1) reproduce well the commuting fluxes obtained from data. Solid lines in all frames are guides to the eye. (7–10, 24–26). In this paper, we use the GLEaM computational 29 countries (a full list of countries and the database properties are scheme based on a georeferenced metapopulation approach. The reported in the SI Appendix) in five different continents. Each model consists of three data layers. The population and mobility dataset was mapped into the GLEaM Voronoi tessellation con- layers allows the partition of the world into geographical census structing the commuting networks at the subpopulation level. regions coupled by population movements. This partition defines In Fig. 1, we show the commuting network of the continental U.S. the subpopulation network where the
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