Scarabel Francesca, Pellis Lorenzo, Ogden Nicholas H, Wu Jianhong
LIAM-Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, Toronto, Ontario, Canada.
Fields-CQAM Laboratory of Mathematics for Public Health, York University, Toronto, Ontario, Canada.
R Soc Open Sci. 2021 Apr 7;8(4):202091. doi: 10.1098/rsos.202091.
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.
我们提出了一个确定性模型，该模型捕捉了接触者追踪的基本特征，将其作为公共卫生非药物干预措施的一部分，以减轻传染病的爆发。通过在个体层面纳入过程的机制性表述，我们得到了一个积分方程（在日历时间上延迟，在感染后的时间上提前），用于描述感染个体在任何时间点被检测和隔离的概率。然后，这与总发病率的更新方程相结合，形成一个封闭系统，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繁殖数和有效繁殖数。当应用于严重急性呼吸综合征冠状病毒2（SARS-CoV-2）的情况时，我们的结果表明，除非采取额外措施减少总体社区传播，否则只有在速度和覆盖范围方面几乎完美的有症状感染诊断和接触者追踪组合才能实现控制。在检测或追踪能力的限制下，接触者追踪的暂时中断可能会根据感染的总体增长率和流行率，导致即使疫情先前已得到控制也会出现不可逆转的失控情况。
