Abstract
<h3>Abstract</h3> This paper presents a simple mathematical model that answers how much testing and tracing we need to do to suppress new surges of COVID-19 infections after reopening. We derived the model by modifying the SEIR model taking into the effects of testing and tracing. The following equation is one of the essential outcomes of the model: Where <i>ρ</i> is the percentage of infectious people that have to be detected per day, <i>R<sub>0</sub></i> is the basic reproduction number, S/N is the percentage of the susceptible population over the entire population, <i>D</i> is the length of the infectious period, and <i>η</i> is the percentage of close contacts that have to be traced. If the above equation is satisfied, we can bring the effective reproduction number <i>R<sub>e</sub></i> to below 1 to get the transmission suppressed. This model demonstrates that together with social-distancing measures such as wearing masks in public, with a reasonable amount of testing and tracing, we may suppress the COVID-19 transmission for good. For example, if social distancing measures can bring <i>R<sub>0</sub></i> to below 1.2, for <i>D</i> being 10 days, in places where 15% people have developed antibodies, we can suppress the transmission by detecting only 0.13% of the infectious population daily while tracing 50% of their close contacts. The model provides intuitive insights and quantitative guidance for policymakers and public health practitioners to deploy the testing and tracing resources optimally.
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