A simple mathematical tool to forecast COVID-19 cumulative case numbers

Mathematical models are known to help determine potential intervention strategies by providing an approximate idea of the transmission dynamics of infectious diseases. To develop proper responses, not only are more accurate disease spread models needed, but also those that are easy to use.

As of July 1, 2020, we selected the 20 countries with the highest numbers of COVID-19 cases in the world. Using the Verhulst-Pearl logistic function formula, we calculated estimates for the total number of cases for each country. We compared these estimates to the actual figures given by the WHO on the same dates. Finally, the formula was tested for longer-term reliability at t = 18 and t = 40 weeks.

The Verhulst-Pearl logistic function formula estimated the actual numbers precisely, with only a 0.5% discrepancy on average for the first month. For all countries in the study and the world at large, the estimates for the 40th week were usually overestimated, although the estimates for some countries were still relatively close to the actual numbers in the forecasting long term. The estimated number for the world in general was about 8 times that actually observed for the long term.

The Verhulst-Pearl equation has the advantage of being very straightforward and applicable in clinical use for predicting the demand on hospitals in the short term of 4-6 weeks, which is usually enough time to reschedule elective procedures and free beds for new waves of the pandemic patients.