Low prevalence, quasi-stationarity and power-law behavior in a model of contagion spreading

Department of Physics, College of Sciences, Shiraz University - Shiraz 71454, Iran

^(a) montakhab@shirazu.ac.ir

Received: 21 June 2012
Accepted: 4 August 2012

Abstract

While contagion (information, infection, etc.) spreading has been extensively studied recently, the role of active local agents has not been fully considered. Here, we propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local probabilistic dynamics occurring at various nodes. Transmission occurs only after the quality-based fitness of the contagion has been evaluated by the local agent. We study such spreading dynamics on Erdös-Rényi as well as scale free networks. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. Low prevalence is seen for a wide range of contagion quality for arbitrary large networks. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. These properties, while absent in standard theoretical models, are observed in recent empirical observations.