Multiplex mobility network and metapopulation epidemic simulations of Italy based on Open Data

TL;DR

This work tackles the lack of granular mobility data for epidemic forecasting by constructing a municipality-scale multiplex mobility network for Italy from open data and coupling it to a data-driven SIR metapopulation simulator. The network comprises four layers (intra-province, inter-province, train, and flight) with a moving fraction $p_M=0.1$ and parameters such as $R_0=2.5$ and $\mu=1/8$ governing disease dynamics, enabling scenario analyses under mobility restrictions. The authors show that open-data-based mobility flows reproduce smartphone-derived fluxes and provide insight into the relative importance of long-range travel modes for disease spread, using an effective distance metric to characterize outbreak potential. The framework offers a practical, adjustable tool for epidemic monitoring and policy assessment in contexts with limited proprietary mobility data, with future directions including incorporation of road networks and application to other regions.

Abstract

The patterns of human mobility play a key role in the spreading of infectious diseases and thus represent a key ingredient of epidemic modeling and forecasting. Unfortunately, as the Covid-19 pandemic has dramatically highlighted, for the vast majority of countries there is no availability of granular mobility data. This hinders the possibility of developing computational frameworks to monitor the evolution of the disease and to adopt timely and adequate prevention policies. Here we show how this problem can be addressed in the case study of Italy. We build a multiplex mobility network based solely on open data, and implement a SIR metapopulation model that allows scenario analysis through data-driven stochastic simulations. The mobility flows that we estimate are in agreement with real-time proprietary data from smartphones. Our modeling approach can thus be useful in contexts where high-resolution mobility data is not available.

Figures (3)

• Figure 1: Multiplex mobility network of Italy. A) The different layers of the mobility network of Italy, in order from left to right: intra-province, inter-province, trains and flights layer. B) Top-ranked municipalities according to weighted k-core decomposition, with circle size proportional to the k-core value. The largest metropolitan areas (Rome, Milan, Naples, Turin, Florence, Bologna, Venice, and so on) are at the top of the ranking. C) Comparison of the average population commuting among provinces between the Facebook data ( baseline value) and the model estimates for a time step of the dynamics. In the upper panel we show the scatter plot (in log-log scale) of these mobility proxies for each link, that is, each pair of provinces. Cyan dots are people moving between different provinces while pink crosses are those moving within each province. Dark green upper triangles are the links that are not present in the multiplex while the (more numerous) dark green lower triangles are those not present in the Facebook data. In the lower panel plot we show the difference of moving population between the Facebook data and the multiplex as a function of the distance between provinces. The multiplex slightly over-estimates the long distance travels, mainly due to the many lower triangles in the upper panel, and under-estimates the short distance movements.
• Figure 2: Epidemic spreading dynamics, scenarios for different geographic outbreaks and layer importance. A) Schematic representation of a single dynamical step of the model. The empty circles represents the municipalities of the network, while the edges colors are the different types (layers) of connections among them; lastly the color of the individuals represents the compartmental status: infected (red), susceptible (blue) and recovered (green). In each dynamical step we first model mobility, so that individuals move between the municipalities according to the transition probabilities, then we run disease contagion according to the SIR rules and lastly the moved individuals return to the municipality of departure. B) Snapshots of the disease evolution over the Italian mobility network for different starting points: from left to right, Milan, Rome, Naples. In all cases the fraction of infected individuals located in the respective municipality is the same and equal to $10^{-5}$. The nodes on the maps are colored according to the normalized logarithm of the total number of infected individuals in the corresponding municipalities after 45 time steps of the dynamics. C) Quantification of layers importance, according to the number of infected individuals for different starting points (from left to right: Milan, Rome and Naples). The dashed lines represent simulations on the full multiplex, whereas the various solid lines denote the difference with simulation outcomes performed by shutting down a given layer. In all cases we observe that in the early phase of the dynamics the trains layer leads to the largest difference in terms of number of infected, hence it has the largest impact. The flight layer can possibly become more important for later simulation stages.
• Figure 3: Epidemic scenarios for different seed sizes and travel restrictions , for an outbreak starting in Milan. A) Maximum distance travelled by the disease as a function of time for different mobility restriction scenarios , starting with a seed size of 25 at $t=0$ (the initially infected individuals). In a given scenario, at $t=10$ we remove all connections within a single or a pair of layers (as shown in the legend) and re-add them at $t = 40$. B) Maximum distance reached by the disease as a function of the time steps of the dynamics, for different initial seed sizes (shown in the legend). The distance is computed using the farthest municipality with a fraction of infected individuals at least equal to that of the initial seed location at $t=0$. For each seed size we show results of 100 simulations, with solid lines representing the bootstrapped means and the shaded areas the 95% C.I. C-D) Mean $\mu$ and variance $\sigma$ of effective distance of infected municipalities from potential outbreak locations at the simulation time $t=30$. The effective distance is computed considering only the mobility layers active at the given time. We consider as possible outbreak locations the top 1000 municipalities by number of populations; the red cross identifies the actual outbreak location (Milan), which is well separated from the other points.