We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.

我们提出了一种确定性模型，捕捉接触者追踪的基本特征，作为减轻传染病爆发的公共卫生非药物干预措施的一部分。通过在个体层面结合过程的机械公式，我们获得了一个积分方程（日历时间延迟和感染后时间提前），用于计算在任何时间点检测和隔离受感染个体的概率。然后将其与总发病率的更新方程相结合，形成一个封闭的系统，描述涉及接触者追踪的传播动态。我们根据病原体特征和接触者追踪实施限制来定义和计算基本有效繁殖数。当应用于 SARS-CoV-2 病例时，我们的结果表明，只有在速度和覆盖范围方面近乎完美的症状感染诊断和接触者追踪相结合才能实现控制，除非采取额外措施来减少总体社区传播。地方。在检测或追踪能力的限制下，根据感染的总体增长率和流行情况，暂时中断接触者追踪可能会导致不可逆转的失控，即使疫情之前已得到遏制。