Spread of epidemic disease on networks.
Mark Newman,Mark Newman +1 more
TLDR
This paper shows that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks.Abstract:
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.read more
Citations
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The Structure and Function of Complex Networks
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
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Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
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Catastrophic cascade of failures in interdependent networks
Sergey V. Buldyrev,Sergey V. Buldyrev,Roni Parshani,Gerald Paul,H. Eugene Stanley,Shlomo Havlin +5 more
TL;DR: In this paper, the authors develop a framework for understanding the robustness of interacting networks subject to cascading failures and present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks.
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Epidemic processes in complex networks
TL;DR: A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear.
References
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Michelle Girvan,Mark Newman +1 more
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The Mathematics of Infectious Diseases
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.