Year: 2025
Type: article
Abstract: We analyse a Markovian SIR epidemic model where individuals either recover naturally or are diagnosed, leading to isolation and potential contact tracing. Our focus is on digital contact tracing via a tracing app, considering both its standalone use and its combination with manual tracing. We prove that as the population size n grows large, the epidemic process converges to a limiting process, which, unlike with typical epidemic models, is not a branching process due to dependencies created by contact tracing. However, by grouping to-be-traced individuals into macro-individuals, we derive a multi-type branching process interpretation, allowing computation of the reproduction number R . This is then converted to an individual reproduction number $R^\mathrm{(ind)}$ , which, in contrast to R , decays monotonically with the fraction of app-users, while both share the same threshold at 1. Finally, we compare digital (only) contact tracing and manual (only) contact tracing, proving that the critical fraction of app-users, $\pi_{\mathrm{c}}$ , required for $R=1$ is higher than the critical fraction manually contact-traced, $p_{\mathrm{c}}$ , for manual tracing.
Source: Advances in Applied Probability
DOI: 10.1017/apr.2025.15
Authors: Tom Britton, Dongni Zhang
Institution: Stockholm University
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Funder: Vetenskapsrådet
OpenAlex ID: W4411151197