Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics

TL;DR

This paper introduces a bond percolation model for multitype networks with heterogeneous edge occupation probabilities, providing new insights into network phase transitions and epidemic modeling.

Contribution

It develops a general formalism for multitype networks with heterogeneity, unifies previous models, and improves epidemic contact network analysis.

Findings

Derives statistical properties and phase transition criteria for multitype networks.

Shows the formalism encompasses previous models based on probability generating functions.

Demonstrates improved modeling of epidemic dynamics with heterogeneity in contact networks.

Abstract

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes -- in which final state can be obtained by studying the underlying network percolation properties -- have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many non-trivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.