The COVID-19 (novel coronavirus disease 2019) pandemic has tremendously impacted global health and economics. Early detection of COVID-19 infections is important for patient treatment and for controlling the epidemic. However, many countries/regions suffer from a shortage of nucleic acid testing (NAT) due to either resource limitations or epidemic control measures. The exact number of infective cases is mostly unknown in counties/regions with insufficient NAT, which has been a major issue in predicting and controlling the epidemic. In this paper, we propose a mathematical model to quantitatively identify the influences of insufficient detection on the COVID-19 epidemic. We extend the classical SEIR (susceptible-exposed-infections-recovered) model to include random detections which are described by Poisson processes. We apply the model to the epidemic in Guam, Texas, the Virgin Islands, and Wyoming in the United States and determine the detection probabilities by fitting model simulations with the reported number of infected, recovered, and dead cases. We further study the effects of varying the detection probabilities and show that low level-detection probabilities significantly affect the epidemic; increasing the detection probability of asymptomatic infections can effectively reduce the the scale of the epidemic. This study suggests that early detection is important for the control of the COVID-19 epidemic.
Keywords: COVID-19; detection probability; epidemic scale; nucleic acid testing.