Disease Transmission on Random Graphs Using Edge‐Based Percolation

ABSTRACT 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 begin by reviewing the seminal works on this field in previous studies by Newman et al. (2002, 2003) and Miller et al. (2012). We present a unified discussion of the theoretical background behind these models, including a detailed derivation of some of the major results. We also demonstrate the connections between these studies and the classical literature in random graph theory as detailed in 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 were developed to help researchers easily understand and use network models to investigate the interaction between different community structures and disease transmission.