Non-Linear Fitting of Sigmoidal Growth Curves to predict a maximum limit to the total number of COVID-19 cases in the United States

Abstract

In the present work is used non-linear fitting of the "Gompert" and "Logistic" growth models to the number of total COVID-19 cases from the United States as a country and individually by states. The methodology allowed us to estimate that the maximum limit for the total number of cases of COVID-19 patients such as those registered with the World Health Organization will be approximately one million and one hundred thousand cases to the United States. Up to 04/19/20 the models indicate that United States reached 70% of this maximum number of "total cases" and the United States will reach 95% of this limit by 05/14/2020. The application of the nonlinear fitting of growth curves to the individual data of each American state showed that only 25% of them did not reach, on 04/19/20, the percentage of 59% of the maximum limit of "total cases" and that 17 of the 50 states still will not have reached 95% of that limit on 05/14/20.

Universality in COVID-19 spread in view of the Gompertz function

“…1, we also show f S (x) and df S (x)/dx by blue curves. As already noticed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and is discussed later, the asymmetry is clearly found in dN (t)/dt…”

“…The indicator K takes a value between zero and unity, is not affected by the weekly schedule of the test, and is found to decrease almost linearly as a function of time in the region 0.25 < K < 0.9 provided that there is only a single outbreak affecting the infection. In order to understand the linearly decreasing behavior of K, Nakano and Ikeda proposed the "constant damping hypothesis" in their paper [26], and Akiyama proved that the hypothesis of exponential decrease in discrete time shows the Gompertz curve in continuous time [27], independently of other works [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Since the indicator K is expected to be useful to predict the date when the restrictions can be relaxed as K(t) 0.05, it would be valuable to analyze its solution, the Gompertz function, in more detail.…”

“…Recently, a double exponential function called the Gompertz function is found to catch the features of N (t) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The Gompertz function appears when the infection probability per infected people exponentially decreases as a function of time.…”

COVID-19 Forecasts for Cuba Using Logistic Regression and Gompertz Curves

“…[25] Bauckhage used the logistic and Gompertz models to obtain predictions for Germany for mid-April 2020, [26] while Rodrigues-Silva used these models to obtain predictions for the state of Goias in Brazil [27] and Dutra used them to estimate the number of persons affected by COVID-19 for various US states and the whole country. [28] Attanyake fi tted logistic, Gompertz and other exponential models to data corresponding to the impact of COVID-19 in Sri Lanka, Italy and Hubei, a province in central China. [29] Ahmadi adjusted the Gompertz, Bertalanffy and cubic polynomial models to forecast pandemic dynamics for April 2020 in Iran.…”