Reaction–diffusion processes and metapopulation models in heterogeneous networks

By Vittoria Colizza, Romualdo Pastor-Satorras, Alessandro Vespignani. 2007

828 citations recorded by the source corpus.

Dynamical reaction–diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities—such as density, potentials and particles—diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction–diffusion process (given by the reaction steps B→A and B+A→2B) defined on networks with heterogeneous topology and no limit on the nodes’ occupation number. We investigate the effect of network topology on the basic properties of the system’s phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/02864b4041bb924d3c5c3ec02458fc9ed32da885

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Sociology and Political Science

In Statistical and Nonlinear Physics

Citations in the corpus

Random walks and diffusion on networks (2016, methodology): “Node-centric CTRWs have been used in, for example, some empirical-data-driven metapopulation disease-spreading models [208, 209].”
Saving Human Lives: What Complexity Science and Information Systems can Contribute (2014, neutral): “(19) and most sophisticated models, such as the GLEAM simulation framework possess an underlying mathematical machinery of similar nature [115, 120, 132, 133].”
Natural human mobility patterns and spatial spread of infectious diseases (2011, neutral): “These types of models have been employed in numerous recent studies [2,14,24,25].”
Modelling dynamical processes in complex socio-technical systems (2011, background): “Another interesting example is that of simple epidemic processes, such as the SIR model in a metapopulation context 79,82–90 .”
Vital nodes identification in complex networks (2016, background): “They did not consider the relationship between a real percolating process and the percolated state or discuss how to determine a node’s percolated state, but showed an example that in a metapopulation epidemic model [180, 181], for a network of township, the percolated state of a town would be the p”
Discrete-time Markov chain approach to contact-based disease spreading in complex networks (2009, background): “Restricting the scope of epidemiological models to those based in two states [1, 3, 4] −susceptible (S) and infected (I)−, the current theory concentrates on two specific situations, the contact process [23–28] (CP) and the reactive process [29–31] (RP).”
Node centrality in weighted networks: Generalizing degree and shortest paths (2010, background): “Freeman’s (1978) measures are only designed for binary networks.”
Critical phenomena in complex networks (2007, background): “Colizza et al. (2007) showed that ρc and the critical behavior do not depend on the degree distribution.”
Spatial Networks (2010, background): “The fact that reducing travel is not an efficient strategies was also confirmed in theoretical and numerical studies [41, 89, 92, 95].”
Learning Latent Block Structure in Weighted Networks (2014, background): “Vertices represent the n = 500 busiest airports in the United States, and each of the m = 5960 directed edges is weighted by the number of passengers traveling from one airport to another [10].”