On short-term trends and predictions for COVID-19 in France and the USA: comparison with Australia

In Europe and the USA daily new COVID-19 cases have recently been occurring in record numbers, which has created an alarming situation. The CDC in conjunction with several University groups gives forecasts for each county in the USA for several weeks at a time, but they have very large confidence intervals typified by the most recent national prediction of between 310,000 and 710,000 new cases for the week ending November 21, 2020. We have examined recent data for France and the USA over 10, 15 and 20 days. Using such data with simple fitting techniques, which do not require knowledge of any parameters, it has been possible to predict new case numbers fairly accurately for a week or more. A best-fitting polynomial of high order was only useful for a few days, after which it severely overestimated case numbers. A more detailed analysis with confidence intervals was performed for polynomials of orders one to six, which showed that lower order polynomials were more useful for prediction. Using the packages PCHIP and a POLYFIT (with degree one) in MATLAB gave smooth curves from which future case numbers could be reasonably well estimated. With PCHIP the average errors over 7 days were remarkably small, being -0.16% for France and +0.19% for the USA. A comparison is made between the temporal patterns of new cases for France, the USA and Australia. For Australia the second wave has dwindled to close to zero due to hard lock down conditions, which are discussed.