[Paper Review] A framework for epidemic spreading in multiplex networks of metapopulations

David Soriano‐Paños, Laura Lotero+2 more|arXiv (Cornell University)|Feb 12, 2018

COVID-19 epidemiological studies51 references21 citations

TL;DR

This paper proposes a multiplex network framework to model epidemic spreading in metapopulations with heterogeneous, recurrent mobility patterns. By representing different agent classes (e.g., socio-economic groups) as layers in a multiplex network, the authors derive analytically tractable Markovian equations that accurately predict epidemic thresholds and spatio-temporal dynamics, validated against Monte Carlo simulations across synthetic and real-world networks including Medellín, Colombia.

ABSTRACT

We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of the spreading process with extensive Monte Carlo simulations. Our results are in excellent agreement with the simulations. We also derive an exact expression of the epidemic threshold on this general framework revealing a non-trivial dependence on the mobility parameter. Finally, we use this new formalism to address the spread of diseases in real cities, specifically in the city of Medellin, Colombia, whose population is divided into six socio-economic classes, each one identified with a layer in this multiplex formalism.

Motivation & Objective

• To develop a general theoretical framework for modeling epidemic spreading in structured metapopulations with heterogeneous, recurrent mobility patterns.
• To overcome limitations of mean-field approximations and random diffusion assumptions in traditional metapopulation models.
• To incorporate realistic, class-specific mobility patterns (e.g., daily commutes) into epidemic modeling using multiplex network formalism.
• To derive analytically tractable equations for epidemic dynamics (SIS and SIR) that capture both macroscopic and microscopic spreading patterns.
• To validate the framework against extensive Monte Carlo simulations and apply it to a real-world case study (Medellín, Colombia)

Proposed method

• Represent metapopulations as multiplex networks where nodes are geographical patches and layers correspond to distinct agent classes with unique mobility patterns.
• Model the movement-interaction-return (MIR) process: agents move between patches according to class-specific origin-destination matrices, interact locally in well-mixed patches, and return to their home patches.
• Formulate Markovian evolution equations for SIS and SIR dynamics on each layer (monoplex case), capturing time-evolving infection probabilities.
• Generalize the monoplex equations to multiplex metapopulations by constructing a supra-matrix M that combines mobility, local population size, and infection dynamics across layers.
• Derive the epidemic threshold as the inverse of the largest eigenvalue of the supra-matrix M, enabling analytical prediction of outbreak onset.
• Validate the framework by comparing analytical predictions and simulation results for both synthetic ER and scale-free networks, and for a real mobility dataset from Medellín

Experimental results

Research questions

• RQ1 How does the inclusion of class-specific mobility patterns affect the epidemic threshold in a metapopulation?
• RQ2 Can a multiplex network framework accurately capture both macroscopic and microscopic epidemic dynamics in structured populations with recurrent mobility?
• RQ3 What is the analytical expression for the epidemic threshold in a multiplex metapopulation with heterogeneous mobility and population composition?
• RQ4 How does the interplay between different mobility layers influence the overall epidemic risk compared to individual layers?
• RQ5 To what extent can the proposed Markovian formalism replace computationally expensive Monte Carlo simulations in epidemic risk assessment?

Key findings

• The proposed multiplex metapopulation framework accurately reproduces epidemic dynamics, including the onset of epidemics, at both macroscopic and microscopic levels, with excellent agreement between analytical predictions and Monte Carlo simulations.
• The epidemic threshold is determined by the largest eigenvalue of a supra-matrix M that encodes mobility patterns, local population sizes, and infection dynamics across layers, revealing a non-trivial dependence on the mobility parameter.
• The framework reveals a phenomenon of epidemic detriment in the full multiplex structure—where the overall epidemic risk is lower than in individual layers—indicating that layer interplay can suppress disease spread.
• For the real-world case of Medellín, Colombia, the model successfully captures the impact of distinct mobility patterns across socio-economic classes, showing that the full multiplex structure leads to different epidemic outcomes than individual layers.
• The analytical framework enables efficient computation of epidemic thresholds without relying on simulations, offering a time-saving alternative for risk assessment and policy testing.
• The Markovian equations derived are general and can be extended to more complex mobility patterns and refined epidemic models in future work.