Recursive contact tracing in Reed-Frost epidemic models

TL;DR

This paper extends Reed-Frost epidemic models to include recursive contact tracing and asymptomatic transmission, analyzing phase transitions and effectiveness on different networks through simulations.

Contribution

It generalizes previous models to finite populations and networks, providing numerical analysis of contact-tracing phase transitions and their universality classes.

Findings

Clear contact-tracing phase transition observed

Finite-size scaling matches percolation universality class

Quantifies effectiveness of recursive contact tracing

Abstract

We introduce a Reed-Frost epidemic model with recursive contact tracing and asymptomatic transmission. This generalizes the branching-process model introduced by the authors in a previous work [arxiv:2004.07237] to finite populations and general contact networks. We simulate the model numerically for two representative examples, the complete graph and the square lattice. On both networks, we observe clear signatures of a contact-tracing phase transition from an "epidemic phase" to an "immune phase" as contact-network coverage is increased. We verify that away from the singular line of perfect tracing, the finite-size scaling of the contact-tracing phase transition on each network lies in the corresponding percolation universality class. Finally, we use the model to quantify the efficacy of recursive contact-tracing in regimes where epidemic spread is not contained.