Application of the Logistic Model to the COVID-19 Pandemic in South Africa and the United States: Correlations and Predictions

We apply the simple logistic model to the four waves of COVID-19 taking place in South Africa over the period 2020~January~1 through 2022 January 11. We show that this model provides an excellent fit to the time history of three of the four waves. We then derive a theoretical correlation between the growth rate of each wave and its duration, and demonstrate that it is well obeyed by the South Africa data. We then turn to the data for the United States. As shown by Roberts (2020a, 2020b), the basic logistic model provides only a marginal fit to the early data. Here we break the data into six "waves," and treat each one separately. For four of the six the logistic model is useful, and we present full results. We then ask if these data provide a way to predict the length of the ongoing Omicron wave in the US (commonly called "wave 4," but the sixth wave as we have broken the data up). Comparison of these data to those from South Arica, and internal comparison of the US data, suggests that this last wave will die out by about 2022-January-20.