Dynamical Dorfman Testing with Quarantine

TL;DR

This paper explores a dynamic group testing strategy using Dorfman's method combined with quarantines within an SIR model to efficiently identify infections and control disease spread, analyzing cost trade-offs and optimal group sizes.

Contribution

It introduces a dynamic Dorfman testing framework with quarantine measures, analyzing optimal group sizes and comparing performance with existing non-adaptive methods.

Findings

Optimal first-stage group size differs between dynamic and static models.

Dynamic testing with quarantine reduces infection spread more effectively.

Proposed method outperforms non-adaptive testing in dynamic scenarios.

Abstract

We consider dynamical group testing problem with a community structure. With a discrete-time SIR (susceptible, infectious, recovered) model, we use Dorfman's two-step group testing approach to identify infections, and step in whenever necessary to inhibit infection spread via quarantines. We analyze the trade-off between quarantine and test costs as well as disease spread. For the special dynamical i.i.d. model, we show that the optimal first stage Dorfman group size differs in dynamic and static cases. We compare the performance of the proposed dynamic two-stage Dorfman testing with state-of-the-art non-adaptive group testing method in dynamic settings.