Epidemic models with digital and manual contact tracing

2022/11/23 by Britton, Tom, Zhang, Dongni
#FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.12869

Abstract

We analyze 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 combination with manual tracing. We prove that as the population size n grows large, the epidemic process converges to a limiting process, which, unlike 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^(ind), which, contrary 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 app-users π_c required for R=1 is higher than the critical fraction manually contact traced p_c for manual tracing.

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