Novel uses of three-parameter logistic models and first-derivative models for the Coronavirus Disease (COVID-19) epidemic in the United States, in three distinct scenarios

Abstract

Background: Forecasting the current coronavirus disease (COVID-19) epidemic in the United States necessitates novel mathematical models for accurate predictions. This paper examines novel uses of three-parameter logistic models and first-derivative models through three distinct scenarios that have not been examined in the literature as of July 14, 2020.Methods: Using publicly available data, statistical software was used to conduct a non-linear least-squares estimate to generate a three-parameter logistic model, with a subsequently generated first-derivative model. In the first scenario a logistic model was used to examine the natural log of COVID-19 cases as the dependent variable (versus day number), on July 11 and May 1. Independent t-test analyses were used to test comparative coefficient differences across models. In the second scenario, a first-derivative model was derived from a base three-parameter logistic model for April 27, examining time to peak mortality and decrease in case fatality rate. In the third scenario, a first-derivative model of mortality through July 11 as the dependent variable, versus confirmed cases, was generated to look at case fatality rate relative to increasing cases.Results: All models generated were statistically significant with R2 > 99%. The logistic models in the first scenario best predicted time to growth deceleration in the natural log of cases in the U.S. (slowing of exponential growth), estimated at March 11, 2020. For the May 1 data, independent t-test analyses of comparative coefficients across models were useful to track improvements from implemented public health measures. The first-derivative model in the second scenario on April 27, when the epidemic was more controlled, showed peak mortality around April 12-13, with a case fatality rate of < 1,000 deaths and trending down. The first-derivative model in the third scenario estimated a near-zero case fatality rate to occur at 4 million confirmed cases. It has not been affected by fluctuations in mortality from June 29 through July 11.Conclusion: Three-parameter logistic models and first-derivative models have utility in predicting time to growth deceleration, and case fatality rates relative to cases. They can objectively assess improvements of implemented epidemiologic measures and have applicable public health safety implications.