A New Adaptive Logistic Model for Epidemics and the Resurgence of COVID-19 in the United States

The Adaptive Logistic Model (ALM) of epidemics incorporates the results of infection mitigation effects on the course of an epidemic, and well describes the histories of the COVID-19 epidemics in many countries, including the United States. In particular, it is much more successful than is a basic logistic model. However, in the U.S. these mitigation efforts have recently been relaxed in many places, resulting in the second peak in infections that started in late May of 2020. In this paper the ALM is modified to account for the relaxation of these mitigation effects, leading to the Adaptive Logistic Model 2 (ALM-2). The ALM-2 is then used to understand quantitatively the second peak of COVID-19 cases. The ALM-2 is also successfully applied to the data on deaths even though they do not yet show a second peak.