Regional Prediction of COVID-19 in the United States Based on the Difference Equation Model

The novel coronavirus pneumonia 2019 (COVID-19) has swept the globe in just a few months with negative social and psychological consequences for public health. So far, the United States has been one of the countries most affected by the epidemic. In this study, 51 states in the United States are divided into 10 state clusters according to relevant factors, and a difference equation model with spatio-temporal dynamic characteristics is established to predict the transmission dynamics of COVID-19 in the 10 state clusters and obtain data on regional aggregation levels (the United States). The study showed that the Pearson Correlation Coefficient between the actual data and the predicted data in the 10 state clusters is between 0.6 and 0.96 (mean R$^{2}$=0.8448), and the mean absolute error (MAE) of the newly confirmed cases in each cluster is between 300 and 1650 (mean MAE=878) and the average forecasting error rate (AFER) of the total confirmed cases in each cluster is between 0.9$\%$ and 3$\%$ (mean AFER=1.57$\%$). These results show that the difference equation model can well predict the changes in the recent confirmed cases of infectious diseases such as COVID-19.