Forecast U.S. Covid-19 Numbers by Open SIR Model with Testing

The U.S. Covid-19 data exhibit a high-frequency oscillation along a low-frequency wave for outbreaks. There is no model to account for it. A modified SIR model is proposed to explain this spiking phenomenon. It is also used to best-fit the data and to make forecast. For the simulated duration of 590 days, the model is capable of achieving a 0.5 percent mean squared relative error (MSRE) fit to the seven-day average of the daily case number. The outright 28-day prediction by the model generates a 20 percent MSRE for the cumulative case total due to a persistent underestimation of the data by the model. With the proposed correction to the aberration, the model is able to keep the 28-day cumulative case total forecast within 10 percent MSRE of the data.