Abstract
In this paper, we investigate the epidemic spreading on random and regular networks through a pairwise-type model with a general transmission rate to evaluate the influence of the node-weight distribution. By using block matrix theory, an epidemic threshold index is formulated to predict the epidemic outbreak. An upper bound of the epidemic threshold is obtained by analyzing the monotonicity of spectral radius for nonnegative matrices. Theoretical results suggest that the epidemic threshold is dependent on both matrices and with the first matrix being related to the mean-field model while the second one reflecting the heterogeneous transmission rates. In particular, for a linear transmission rate, this study shows the negative correlation between the heterogeneity of weight distribution and the epidemic threshold, which is different from the results for existing results from the edge-weighted networks.
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