论文标题
具有数字和手动接触跟踪的流行模型
Epidemic models with digital and manual contact tracing
论文作者
论文摘要
我们分析了一个马尔可夫爵士流行模型，该模型在该模型中自然恢复或被诊断出来，从而导致隔离和潜在的接触追踪。我们的重点是考虑到其独立使用和与手动跟踪的组合，通过跟踪应用程序进行数字触点跟踪。我们证明，随着人口大小$ n $的增长，流行过程会收敛到限制过程，与典型的流行病模型不同，由于接触跟踪创建的依赖关系，这与典型的流行模型不同。但是，通过将待传递的个体分组为宏个人，我们得出了多类分支过程解释，从而可以计算复制数$ 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跟踪手动跟踪的$ P_C $。
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.
