Sideward contact tracing in an epidemic model with mixing groups

TL;DR

This paper introduces a stochastic epidemic model incorporating sideward contact tracing within mixing groups, using macro-branching processes to analyze the early epidemic phase and derive the effective reproduction number.

Contribution

It develops a novel macro-branching process framework to account for sibling dependencies in contact tracing within mixing groups, providing new insights into epidemic thresholds.

Findings

Derived an expression for the effective macro-reproduction number.

Showed how the reproduction number depends on group size and tracing parameters.

Numerical analysis illustrates the impact of various factors on epidemic spread.

Abstract

We consider a stochastic epidemic model with sideward contact tracing. We assume that infection is driven by interactions within mixing events (gatherings of two or more individuals). Once an infective is diagnosed, each individual who was infected at the same event as the diagnosed individual is contact traced with some given probability. Assuming few initial infectives in a large population, the early phase of the epidemic is approximated by a branching process with sibling dependencies. To address the challenges given by the dependencies, we consider sibling groups (individuals who become infected at the same event) as macro-individuals and define a macro-branching process. This allows us to derive an expression for the effective macro-reproduction number which corresponds to the effective individual reproduction number and represents a threshold for the behaviour of the epidemic. Through numerical examples, we show how the reproduction number varies with the distribution of the mixing event size, the mean size, the rate of diagnosis and the tracing probability.