Analysis of a COVID-19 Epidemic Model with Seasonality

The statistics of COVID-19 cases exhibits seasonal fluctuations in many countries. In this paper, we propose a COVID-19 epidemic model with seasonality and define the basic reproduction number R-0 for the disease transmission. It is proved that the disease-free equilibrium is globally asymptotically stable when R-0 < 1, while the disease is uniformly persistent and there exists at least one positive periodic solution when R-0 > 1. Numerically, we observe that there is a globally asymptotically stable positive periodic solution in the case of R-0 > 1. Further, we conduct a case study of the COVID-19 transmission in the USA by using statistical data.