Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations.

By Vittoria Colizza, Alessandro Vespignani. Journal of Theoretical Biology, 2007

459 citations recorded by the source corpus.

The spatial structure of populations is a key element in the understanding of the large-scale spreading of epidemics. Motivated by the recent empirical evidence on the heterogeneous properties of transportation and commuting patterns among urban areas, we present a thorough analysis of the behavior of infectious diseases in metapopulation models characterized by heterogeneous connectivity and mobility patterns. We derive the basic reaction-diffusion equations describing the metapopulation system at the mechanistic level and derive an early stage dynamics approximation for the subpopulation invasion dynamics. The analytical description uses a homogeneous assumption on degree block variables that allows us to take into account arbitrary degree distribution of the metapopulation network. We show that along with the usual single population epidemic threshold the metapopulation network exhibits a global threshold for the subpopulation invasion. We find an explicit analytic expression for the invasion threshold that determines the minimum number of individuals traveling among subpopulations in order to have the infection of a macroscopic number of subpopulations. The invasion threshold is a function of factors such as the basic reproductive number, the infectious period and the mobility process and it is found to decrease for increasing network heterogeneity. We provide extensive mechanistic numerical Monte Carlo simulations that recover the analytical finding in a wide range of metapopulation network connectivity patterns. The results can be useful in the understanding of recent data driven computational approaches to disease spreading in large transportation networks and the effect of containment measures such as travel restrictions.

Subfields: Modeling and Simulation, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/417f8057a081c37a76edb5b95ed865510a64f9aa

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Citations in the corpus

Non-pharmaceutical interventions during the COVID-19 pandemic: A review (2020, background): “This introduces another threshold typically called invasion threshold [146].”
Modelling dynamical processes in complex socio-technical systems (2011, background): “Only infeasibly tight mobility restrictions, reducing global travel fluxes by 90% or more, would be effective 84,91,92 .”
COVID-19 lockdown induces disease-mitigating structural changes in mobility networks (2020, background): “The threshold is higher in the metapopulation model compared to the well-mixed description, an expected effect caused by the heterogeneity of the system [30].”
Statistical physics of vaccination (2016, background): “These analyses have shown that though the condition R0 > 1 still guarantees that the epidemics is not self-extinguishing and that there are patches here and there in the network where the infection is circulating, in order to have global macroscopic spread a second threshold has to be overcome [142,”
Modeling human mobility responses to the large-scale spreading of infectious diseases (2011, background): “Recently, analytical solutions have been found for Markovian diffusion processes [1].”