After the blockade that many nations suffered to stop the growth of the incidence curve of COVID-19 during the first half of 2020, they face the challenge of resuming their social and economic activity. The rapid airborne transmissibility of SARS-CoV-2, and the absence of a vaccine, calls for active containment measures to avoid the propagation of transmission chains. The best strategy to date, popularly known as test-track-treat (TTT), consists in testing the population for diagnosis, tracking the contacts of those infected, and treating by quarantine all these cases. The dynamical process that better describes the combined action of the former mechanisms is that of a contagion process that competes with the spread of the pathogen, cutting off potential contagion pathways. Here we propose a compartmental model that couples the dynamics of the infection with the contact tracing and isolation of cases. We develop an analytical expression for the effective case reproduction number $R_c\left(t\right)$ that reveals the role of contact tracing in the mitigation and suppression of the epidemics. We show that there is a trade-off between the infection propagation and the isolation of cases. If the isolation is limited to symptomatic individuals only, the incidence curve can be flattened but not bent. However, if contact tracing is applied to asymptomatic individuals too, the strategy can bend the curve and suppress the epidemics. Quantitative results are dependent on the network topology. We quantify the most important indicator of the effectiveness of contact tracing, namely, its capacity to reverse the increasing tendency of the epidemic curve, causing its bending.

中文翻译：

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病毒传播与接触者追踪：两个相互竞争的传染过程

在许多国家在2020年上半年遭受封锁以阻止COVID-19发病率曲线增长之后，它们面临着恢复其社会和经济活动的挑战。SARS-CoV-2在空中的快速传播能力以及疫苗的缺乏，要求采取积极的收容措施，以避免传播链扩散。迄今为止，最好的策略是称为测试跟踪治疗（TTT），包括测试人群以进行诊断，跟踪受感染者的联系以及隔离所有这些病例。更好地描述前者机制的综合作用的动力学过程是与病原体传播竞争，切断潜在的传染途径的传染过程。在这里，我们提出了一个隔离模型，将感染的动态与接触者追踪和病例隔离相结合。我们为有效案例复制数开发了一个解析表达式${\mathrm{[R}}_C（Ť）$揭示了接触追踪在缓解和抑制流行病中的作用。我们表明，在感染传播和病例隔离之间需要权衡。如果隔离仅限于有症状的个体，则发病曲线可以变平但不能弯曲。但是，如果将接触跟踪也应用于无症状个体，则该策略可以弯曲曲线并抑制流行病。定量结果取决于网络拓扑。我们量化了接触追踪有效性的最重要指标，即其逆转流行曲线的增加趋势并导致其弯曲的能力。