Repeat Contacts and the Spread of Disease: An Agent Model with Compartmental Solution

TL;DR

This paper enhances the traditional SIR disease spread model by incorporating repeat contacts and stochastic encounter probabilities, revealing how contact dynamics influence outbreak trajectories and final case counts.

Contribution

It introduces a novel agent-based contact model with a compartmental solution, demonstrating the impact of contact stale rates on disease spread and outbreak extinction.

Findings

Order of magnitude differences in case counts based on contact stale rates

Faster contact renewal leads to quicker outbreak decline

Early rapid extinction is possible but difficult once missed

Abstract

Using a probability of novel encounter derived from a physical model, we augment the SIR compartmental model for disease spread. Scenarios with the same initial trajectories and identical $R_0$ values can diverge greatly depending on the speed at which our circles of acquaintances grow stale - leading to order of magnitude differences in final case counts. A momentum effect arises from variation in the mean time since infection, and this feeds back into new infection rate and faster decline in the late stages of an outbreak. Rapid extinction of an outbreak can occur in the early stages, but once this opportunity is missed the effect is diminished and then, only herd immunity can help.