A contact-network-based formulation of a preferential mixing model

Heterogeneity in the number of potentially infectious contacts and connectivity correlations ("like attaches to like", i.e., assortatively mixed or "opposites attract", i.e., disassortatively mixed) have important implications for the value of the basic reproduction ratio R (0) and final epidemic size. In this paper, we present a contact-network-based derivation of a simple differential equation model that accounts for preferential mixing based on the number of contacts. We show that results based on this model are in good qualitative agreement with results obtained from preferential mixing models used in the context of sexually transmitted diseases (STDs). This simple model can accommodate any mixing pattern ranging from completely disassortative to completely assortative and allows the derivation of a series of analytical results