Comparing large-scale computational approaches to epidemic modeling: agent-based versus structured metapopulation models

Abstract

Background: In recent years large-scale computational models for the realistic simulation of epidemic outbreaks have been used with increased frequency. Methodologies adapt to the scale of interest and range from very detailed agent-based models to spatially-structured metapopulation models. One major issue thus concerns to what extent the geotemporal spreading pattern found by different modeling approaches may differ and depend on the different approximations and assumptions used.

Methods: We provide for the first time a side-by-side comparison of the results obtained with a stochastic agent-based model and a structured metapopulation stochastic model for the progression of a baseline pandemic event in Italy, a large and geographically heterogeneous European country. The agent-based model is based on the explicit representation of the Italian population through highly detailed data on the socio-demographic structure. The metapopulation simulations use the GLobal Epidemic and Mobility (GLEaM) model, based on high-resolution census data worldwide, and integrating airline travel flow data with short-range human mobility patterns at the global scale. The model also considers age structure data for Italy. GLEaM and the agent-based models are synchronized in their initial conditions by using the same disease parameterization, and by defining the same importation of infected cases from international travels.

Results: The results obtained show that both models provide epidemic patterns that are in very good agreement at the granularity levels accessible by both approaches, with differences in peak timing on the order of a few days. The relative difference of the epidemic size depends on the basic reproductive ratio, R0, and on the fact that the metapopulation model consistently yields a larger incidence than the agent-based model, as expected due to the differences in the structure in the intra-population contact pattern of the approaches. The age breakdown analysis shows that similar attack rates are obtained for the younger age classes.

Conclusions: The good agreement between the two modeling approaches is very important for defining the tradeoff between data availability and the information provided by the models. The results we present define the possibility of hybrid models combining the agent-based and the metapopulation approaches according to the available data and computational resources.

Figure 1

Agent-based model and GLEaM. Top: The agent-based model is a stochastic and spatially-explicit simulation model where the agents represent individuals. The basic spatial structures considered in the model are the municipalities. The force of infection in the general population is assumed to decrease with the geographic distance among municipalities. The dependence on the distance is modeled by a gravity model as derived by the analysis of data on travel to school or work (grouped by all hierarchical administrative levels, from the national level down to the municipality level). The inset shows the explicit representation of individuals in the model enabling the simulations of the most important contacts for diseases transmission, i.e. household, school, and workplace contacts. The spatial spread of the epidemic is determined by i) transmission in the general population at the national scale and ii) transmission in schools and workplaces at a more local scale. Bottom: 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. Geographic 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

Disease compartmental structure. Diagram flow of the infection transmission structure adopted by both models. The transition from the susceptible class to the latent class is induced by the interaction between the susceptible individuals and the infectious individuals (see text).

Figure 3

Comparison of the epidemic incidence and size. Incidence profiles and epidemic size for GLEaM and the agent-based model at the global level. Time is expressed in days since the first importation of infected individuals in Italy. Results for three values of the reproductive number are shown from left to right: R₀ = 1.5, R₀ = 1.9, R₀ = 2.3. Average profiles (lines) and 95% CI (shaded areas) are shown.

Figure 4

Activity peaks difference in the two models. Histogram of the activity peak difference (T_GLEaM - T_AB) (measured in days) between GLEaM and the agent-based model at the global level. The histogram is obtained by comparing each pair of stochastic realizations in the two models and considering negative and positive differences when the GLEaM activity peak occurs before or after the agent-based model, respectively. Results for three values of the reproductive number are shown from left to right: R₀ = 1.5, R₀ = 1.9, R₀ = 2.3.

Figure 5

Epidemic profiles and geography. Geographic variation of the epidemic profiles for GLEaM and the agent-based model at the level of the major urban areas in Italy: a) profiles for a selected number of Italian subpopulations distributed from North to South and in the Islands. Time is expressed in days since the first importation of infected individuals in Italy. Average profiles for the scenario with R₀ = 1.9 are shown; b) difference of the epidemic size as a fraction the population size (top row) and peak shift measured in days (bottom row) between GLEaM and the agent-based model at the level of GLEaM geographical census areas as functions of: the latitude of the geographical census area (left); its population size (center); and the traffic of the airport associated to the geographical census area (right). Results for R₀ = 1.9 are shown.

Figure 6

Geotemporal spreading pattern of the epidemic. Comparison of the spatial epidemic evolution in GLEaM (top) and in the agent-based model (bottom) at three different snapshots of the simulation for R₀ = 1.9. From left to right snapshots show: 127 days, 148 days, and 176 days after the first importation of infected individuals in Italy. Maps reproduce the average number of cases at the resolution scale of the Italian municipalities.

Figure 7

Cumulative cases in different age brackets. Comparison of epidemic size by age group between GLEaM and the agent-based model for three values of the reproductive number: R₀ = 1.5 (left), R₀ = 1.9 (center), and R₀ = 2.3 (right).