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Edge-based percolation methods can be used to analyze disease transmission oncomplex social networks. This allows us to include complex social heterogeneityin our models while maintaining tractability. Here we review the seminal workson this field by Newman et al (2001); Newman (2002, 2003), and Miller et al(2012). We present a systematic discussion of the theoretical background behindthese models, including an extensive derivation of the major results. We alsoconnect these results relate back to the classical literature in random graphtheory Molloy and Reed (1995, 1998). Finally, we also present an accompanying Rpackage that takes epidemic and network parameters as input and generatesestimates of the epidemic trajectory and final size. This manuscript and the Rpackage was developed to help researchers easily understand and use networkmodels to investigate the interaction between different community structuresand disease transmission.

Disease Transmission on Random Graphs Using Edge-Based Percolation