Effective Network Size Predicted From Simulations of Pathogen Outbreaks Through Social Networks Provides a Novel Measure of Structure-Standardized Group Size

Collin M. McCabe, Charles L. Nunn

The transmission of infectious disease through a population is often modeled assuming that interactions occur randomly in groups, with all individuals potentially interacting with all other individuals at an equal rate. However, it is well known that pairs of individuals vary in their degree of contact. Here, we propose a measure to account for such heterogeneity: effective network size (ENS), which refers to the size of a maximally complete network (i.e., unstructured, where all individuals interact with all others equally) that corresponds to the outbreak characteristics of a given heterogeneous, structured network. We simulated susceptible-infected (SI) and susceptible-infected-recovered (SIR) models on maximally complete networks to produce idealized outbreak duration distributions for a disease on a network of a given size. We also simulated the transmission of these same diseases on random structured networks and then used the resulting outbreak duration distributions to predict the ENS for the group or population. We provide the methods to reproduce these analyses in a public R package, "enss." Outbreak durations of simulations on randomly structured networks were more variable than those on complete networks, but tended to have similar mean durations of disease spread. We then applied our novel metric to empirical primate networks taken from the literature and compared the information represented by our ENSs to that by other established social network metrics. In AICc model comparison frameworks, group size and mean distance proved to be the metrics most consistently associated with ENS for SI simulations, while group size, centralization, and modularity were most consistently associated with ENS for SIR simulations. In all cases, ENS was shown to be associated with at least two other independent metrics, supporting its use as a novel metric. Overall, our study provides a proof of concept for simulation-based approaches toward constructing metrics of ENS, while also revealing the conditions under which this approach is most promising.