Building a network with assortative mixing starting from preference functions, with application to the spread of epidemics

Compartmental models of disease spread have been well studied on networks built according to the Configuration Model, i.e., where the degree distribution of individual nodes is specified, but where connections are made randomly. Dynamics of spread on such “first order” networks were shown to be profoundly different compared to epidemics under the traditional mass action assumption. Assortativity, i.e., the preferential mixing of nodes according to degree, is a second order property that is thought to impact epidemic trajectory. We first show how assortative mixing can come about from individual preferences to connect with others of lower or higher degree, and propose an algorithm for constructing such a network. We then investigate via simulation how this network structure favors or inhibits diffusion processes, such as the spread of an infectious disease.