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