Predicting epidemic threshold of correlated networks: A comparison of methods

Being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control. Real-world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present-day theoretical methods. Quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential. We use a susceptible–infected–removed (SIR) model to examine four widely-used theoretical methods – the heterogeneous mean-field (HMF), quenched mean-field (QMF), dynamical message passing (DMP), and connectivity matrix (CM) methods – to predict the outbreak threshold of a correlated network. The potential topological structure of correlated network impacts on prediction accuracy of these four methods. We emphasize that the quantitative changes of degree correlation, degree distribution exponent and network size strongly affect the outbreak of SIR spreading dynamics, and compare the simulation results with the theoretical ones obtained from these four methods. The extensive experiments in synthetic networks show that (a) the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size; (b) the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size; (c) the increasing network sizes decrease outbreak threshold but do not affect outbreak size; (d) as for four theoretical methods, CM and DMP are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations. The experimental results in 50 real-world networks also prove the above conclusions.