Epidemic models with digital and manual contact tracing
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915726765326336 |
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| author | Britton, Tom Zhang, Dongni |
| author_facet | Britton, Tom Zhang, Dongni |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12869 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Epidemic models with digital and manual contact tracing Britton, Tom Zhang, Dongni Probability Populations and Evolution 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. |
| title | Epidemic models with digital and manual contact tracing |
| topic | Probability Populations and Evolution |
| url | https://arxiv.org/abs/2211.12869 |