Estimating the epidemic threshold on networks by deterministic connections

Abstract

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

Dynamics of social contagions with heterogeneous adoption thresholds: crossover phenomena in phase transition

“…Understanding the spreading mechanisms behind behavior has the potential to not only help us design better anti-virus strategies [7], but also shed new insights into the control of social unrest [1]. Moreover, different from biological contagions (such as epidemic spreading) [8][9][10][11][12][13], social contagions display one inherent characteristic: social reinforcement effect [7,14], which usually plays a vital role in the final status of contagions.…”