Tracking dynamics of superspreading through contacts, exposures, and transmissions in edge-based network epidemics

TL;DR

This paper develops an exact mathematical framework to track how superspreading behavior evolves during an epidemic on static contact networks, revealing that superspreading peaks early and control strategies should be implemented promptly.

Contribution

It introduces three novel metrics within an edge-based modeling framework to quantify superspreading dynamics throughout an epidemic, with proven behaviors and timing insights.

Findings

Superspreading peaks at less than half the epidemic duration.

Contact-based control is most effective early in an outbreak.

Metrics provide insights for epidemiological parameter estimation.

Abstract

Infectious disease superspreading caused by heterogeneity in contact behavior has been observed to be an important determinant of epidemic dynamics and size in both empirical and theoretical settings. However, it has also been observed that the importance of this type of superspreading changes throughout an epidemic, generally in a decreasing manner as infections cascade from individuals with many contacts to those with fewer contacts. We provide an exact mathematical formulation of this phenomenon in strongly-immunizing (SIR) epidemics on static contact networks. Building on the edge-based modeling framework, we construct three metrics to track how superspreading changes through the course of an epidemic, respectively measuring infected nodes' contacts, exposures, and transmissions: (1) the mean degree of infected nodes, (2) the mean number of susceptible neighbors of infected nodes, and (3) the mean number of secondary cases that will be caused by newly infected nodes. We prove results about the behaviors of these metrics, highlighting the fact that their peak times all occur at less than half the time it takes for population-level infection prevalence to peak. This suggests that the importance of superspreading will be low when an epidemic is already near its peak, so contact-based control strategies are best employed as early in an outbreak as possible. We discuss implications for accurately measuring epidemiological parameters from incidence, mobility, contact tracing, and transmission data.