New approach of non-linear fitting to estimate the temporal trajectory of the COVID-19 cases / New approach of non-linear fitting to estimate the temporal trajectory of the COVID-19 cases

Carlos Maximiliano Dutra, Fabiane Moreira Farias, Carlos Augusto Riella de Melo


COVID-19 was declared, in March 2020, as a pandemic by the World Health Organization, and has since called attention to the monitoring given by the Internet and other means of communication for statistical data related to the number of cases of infected patients in healthcare systems, number of recovered and number of deaths with daily update of new and accumulated data. Some studies have been developed to estimate the temporal evolution of data related to COVID-19 to try to predict incidence and lethality scenarios, among other information about this disease. This work aims to determine when and how it is possible to use the non-linear fitting of the sigmoidal growth functions to estimate the evolution of COVID-19 cases over time. To achieve the proposed objective, a series of fittings of the sigmoidal growth functions "Gompertz" and "Logistic" were made in eight countries that have already reached the stable plateau phase of the total number of registered cases of the disease: Australia, Austria, China, Croatia, New Zealand, South Korea, Switzerland and Thailand. The parameters for the data set of the total number of cases until 05/02/2020 were determined as: (i) maximum limit for the accumulated number of cases, (ii) the inflection point, and (iii) the growth rate. Based on the inflection point of the adjusted Gompertz function, were made fittings of the first case until we have the adjustment for the data up to 20 days after the tipping point. The temporal variation of the maximum limit of the total number of cases was analyzed, and it was found that this parameter for the same adjustment period is always higher in the Gompertz function than in the Logistic function and that over time they converge to the same limit to fit the recorded data. From this convergence, it is possible to anticipate the estimation of the maximum limit of total cases of the complete series of data by interpolation between the values of this parameter in the adjusted functions Gompertz and Logistic. It should be identified through successive non-linear adjustments throughout the acquisition of the day-to-day data, when the smallest relative difference occurs between the maximum limit of total cases of the Gompertz model and the theoretical value obtained by multiplying by 2.7 the total number of cases up to the day of adjustment of the data, assuming that this day corresponds to an inflection point. This reference point is one of the inflection points of the different possible adjustments of the Gompertz function as the daily data of total numbers of COVID-19 cases are obtained. At this point, interpolation is then performed between the maximum limit values of the number of cases of the adjusted functions to estimate the maximum limit of the complete series. Having this value and considering the data of two points in the growth curve (the reference point and its neighbor) it is possible to estimate the other parameters of inflection point and growth rate that best adjusts the data already recorded and the maximum limit to be reached. Thus, it was possible to estimate the Gompertz model function that describes the temporal evolution of the total number of cases accumulated in the countries with relative error below 15% recovering the entire historical series of disease evolution recorded by the observed data that were not part of the model; and through the derivative of the Gompertz function one can also establish a model that described the trend of the time series of new cases.  Thus, this new approach proved to be effective in predicting the temporal trajectory of COVID-19 cases through daily monitoring via non-linear regression of Gompertz and Logistic models until it exceeds the Gompertz inflection point and there is convergence between the maximum limits of number of accumulated cases that allows us to determine the parameters of the model for a non-linear adjustment representative of the entire historical temporal series of evolution of COVID-19 cases in that city, state or country.


Covid19, predicted, estimated, coronavirus, gompertz, logistic, model, epidemiology

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Ahmadi, A., Fadaei, Y., Shirani, M., Rahmani, F. Modeling and Forecasting Trend of COVID-19 Epidemic in Iran until May 13, 2020. Cold Spring Harbor Laboratory Press. URL: . Accessed May 14, 2020.

Bliznashki, S. A Bayesian Logistic Growth Model for the Spread of COVID-19 in New York. Cold Spring Harbor Laboratory Press. URL: . Accessed May 14, 2020.

Chan, J.F.W. et al. A familial cluster of pneumonia associates with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster. The Lancet. 2020. v. 395, m. 10223, p. 514-523. [Medline: 31986261]

Peirlinck, M., Costabal, F., Linka, K., Kuhl, E. Outbreak dynamics of COVID-19 in China and the United States. Cold Spring Harbor Laboratory Press. URL: . Accessed May 14, 2020.

Mondal, S.; Ghosh, S. Possibilities of exponential or Sigmoid growth of Covid19 data in different states of India. Cold Spring Harbor Laboratory Press. URL: . Accessed May 14, 2020.

Teleken, J.T., Galvão, A.C., Robazza, W.S. Comparing non-linear mathematical models to describe growth of diferente animals. Acta Sci., Anim. Sci. 2017 jan./Mar., v. 29, n.1, p. 73-81. [Doi: ] . Accessed May 14, 2020.

World Health Organization. Novel Coronavirus (2019- nCoV) Situation Report – 1. Janeiro 2020.URL: Accessed May 14, 2020.



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