Dangerous connections: on binding site models of infectious disease dynamics

TL;DR

This paper develops a hierarchical model for infectious disease spread on networks, analyzing individual, binding site, and population levels to derive key epidemiological metrics.

Contribution

It introduces a novel multi-level modeling framework that links individual binding site dynamics to population-level disease outcomes.

Findings

Derived formulas for $R_0$, $r$, and final size.

Characterized endemic equilibrium conditions.

Provided a tractable analysis method for network-based epidemic models.

Abstract

We formulate models for the spread of infection on networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of Physiologically Structured Population Models, the formulation starts on the individual level. Influences from the `outside world' on an individual are captured by environmental variables. These environmental variables are population level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of conditionally independent components: each individual has a fixed number of `binding sites' for partners. The Markov chain dynamics of binding sites are described by only a few equations. In particular, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population-level quantities are obtained by averaging over individuals in the population. Thus we are able to characterize population-level epidemiological quantities, such as $R_0$, $r$, the final size, and the endemic equilibrium, in terms of the corresponding variables.