Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks

Abstract

We use the annealed formulation of complex networks to study the dynamical behavior of disease spreading on both static and adaptive networked systems. This unifying approach relies on the annealed adjacency matrix, representing one network ensemble, and allows to solve the dynamical evolution of the whole network ensemble all at once. Our results accurately reproduce those obtained by extensive numerical simulations showing a large improvement with respect to the usual heterogeneous mean-field formulation. Moreover, by means of the annealed formulation we derive a new heterogeneous mean-field formulation that correctly reproduces the epidemic dynamics.

5 pages, 3 Figures. Final version published in Physical Review E (Rapid Comm.)

References in corpus (6)

• Critical phenomena in complex networks
• The entropy of randomized network ensembles
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Entropies of complex networks with hierarchically constrained topologies
• Routes to thermodynamic limit on scale-free networks
• Reply to the Comment on the paper "Non-mean-field behavior of the contact process on scale-free networks"

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