title: The Scaling of Human Contacts and Epidemic Processes in Metapopulation Networks.
abstract: We study the dynamics of reaction-diffusion processes on heterogeneous metapopulation networks where interaction rates scale with subpopulation sizes. We first present new empirical evidence, based on the analysis of the interactions of 13 million users on Twitter, that supports the scaling of human interactions with population size with an exponent γ ranging between 1.11 and 1.21, as observed in recent studies based on mobile phone data. We then integrate such observations into a reaction- diffusion metapopulation framework. We provide an explicit analytical expression for the global invasion threshold which sets a critical value of the diffusion rate below which a contagion process is not able to spread to a macroscopic fraction of the system. In particular, we consider the Susceptible-Infectious-Recovered epidemic model. Interestingly, the scaling of human contacts is found to facilitate the spreading dynamics. This behavior is enhanced by increasing heterogeneities in the mobility flows coupling the subpopulations. Our results show that the scaling properties of human interactions can significantly affect dynamical processes mediated by human contacts such as the spread of diseases, ideas and behaviors.
authors.affiliation: Computational Epidemiology Laboratory, ISI Foundation, via Alassio 11/C, 10126, Torino, Italy.
authors.forename: Michele
authors.initials: M
authors.lastname: Tizzoni
authors.affiliation: Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston MA 02115 USA.
authors.forename: Kaiyuan
authors.initials: K
authors.lastname: Sun
authors.affiliation: Computational Epidemiology Laboratory, ISI Foundation, via Alassio 11/C, 10126, Torino, Italy.|Dipartimento di Fisica, Universitá degli Studi di Torino, via Giuria 1, 10126, Torino, Italy.
authors.forename: Diego
authors.initials: D
authors.lastname: Benusiglio
authors.affiliation: Laboratoire de l'Informatique du Parallélisme, INRIA-UMR 5668, IXXI, ENS de Lyon, 69364 Lyon, France.
authors.forename: Márton
authors.initials: M
authors.lastname: Karsai
authors.affiliation: Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston MA 02115 USA.
authors.forename: Nicola
authors.initials: N
authors.lastname: Perra
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D020407:Internet; D008962:Models, Theoretical; D011157:Population Dynamics