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, 1 (3), 132-145

Modeling the Spatial Spread of Infectious Diseases: The GLobal Epidemic and Mobility Computational Model

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Modeling the Spatial Spread of Infectious Diseases: The GLobal Epidemic and Mobility Computational Model

Duygu Balcan et al. J Comput Sci.

Abstract

Here we present the Global Epidemic and Mobility (GLEaM) model that integrates sociodemographic and population mobility data in a spatially structured stochastic disease approach to simulate the spread of epidemics at the worldwide scale. We discuss the flexible structure of the model that is open to the inclusion of different disease structures and local intervention policies. This makes GLEaM suitable for the computational modeling and anticipation of the spatio-temporal patterns of global epidemic spreading, the understanding of historical epidemics, the assessment of the role of human mobility in shaping global epidemics, and the analysis of mitigation and containment scenarios.

Figures

Figure 1
Figure 1
GLEaM, GLobal Epidemic and Mobility model. The world surface is represented in a grid-like partition where each cell – corresponding to a population value – is assigned to the closest airport. Geographical census areas emerge that constitute the subpopulations of the metapopulation model. The demographic layer is coupled with two mobility layers, the short range commuting layer and the long range air travel layer.
Figure 2
Figure 2
Population database and Voronoi tessellation around main transportation hubs. The world surface is represented in a grid-like partition where each cell – corresponding to a population values – is assigned to the closest airport. Geographical census areas emerge that constitute the subpopulations of the metapopulation model.
Figure 3
Figure 3
Compartmental structure of the epidemic model within each subpopulation. A susceptible individual in contact with a symptomatic or asymptomatic infectious person contracts the infection at rate β or rββ, respectively, and enters the latent compartment where he is infected but not yet infectious. At the end of the latency period ε−1, each latent individual becomes infectious, entering the symptomatic compartments with probability 1 − pa or becoming asymptomatic with probability pa. The symptomatic cases are further divided between those who are allowed to travel (with probability pt) and those who would stop traveling when ill (with probability 1− pt). Infectious individuals recover permanently with rate μ. All transition processes are modeled through multinomial processes.
Figure 4
Figure 4
Schematic representation of the subdivision of the population in each geographical census area. The population in each geographical census area is divided into partial populations Nxy, where x represents the subpopulation of residence and y represents the subpopulation of the actual location at time t. Three subpopulations are shown −i, j, ℓ – to represent the various contributions to the force of infection (see Eq. (19))
Figure 5
Figure 5
Full illustration of the procedure used for the GLEaM simulation engine. The left column represents input databases and the right column the data structures that are generated. Program flow occurs along the center. The three steps in the center box are repeated for each simulated day.
Figure 6
Figure 6
Monte Carlo latin sampling. χ2 values as functions of effective reproduction ratio (Reff ) and seeding date (t0) of simulated epidemics obtained by 2, 000 stochastic runs for each pair of parameter values. Activity peak times of ILI consultations in the various French regions have been selected as probe and were compared with simulation results to obtain χ2. As seen in the figure, there are 4 local minimums. Parameter values chosen for the analysis in Fig. 7 are shown by the crosshairs.
Figure 7
Figure 7
Comparison of simulation results with the ILI consultations and number of confirmed cases of influenza A(H3N2). Simulations have been run by setting Reff = 1.5 and seeding date of July 11th, as marked in Fig. 6. In order to obtain epidemic activity timelines, empirical and each of simulated profiles have been normalized to 1. Then the time windows have been evaluated relative to the peak activities in each case. For instance, lightest yellow bars of empirical data (lightest gray of simulated data) correspond to the time window in which activity is between 60% and 70% of the peak activity. Simulation results correspond to 95% reference range of simulated epidemics. The overlap between the predicted and observed cases is striking. It should be noted that parameter values have been obtained only by fitting the surveillance data in France, which has enabled GLEaM to reproduce the global pattern of the influenza season successfully.

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