Abstract
The pandemic of novel coronavirus disease 2019 (COVID-19) has been a severe threat to public health. The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak. In this paper, we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine, and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine. The model is established based on the combination of the compartmental model and individual-based model simulations, which results in a closed-form delay differential equation model. The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate. The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient. We applied the model to study the effectiveness of contact tracing and quarantine. The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model, however, it is not enough to describe the diverse response due to the stochastic effect. Based on model simulations, we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size, however, may not be enough to achieve zero-infectious in a short time, a combination of close contact quarantine and social contact restriction is required to achieve zero-infectious. Moreover, the effect of reducing epidemic size is insensitive to the period of quarantine, there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.