Comparison of Growth Patterns of COVID-19 Cases through the ARIMA and Gompertz Models. Case Studies: Austria, Switzerland, and Israel

Abstract

On May 19, 2020, data confirmed that coronavirus 2019 disease (COVID-19) had spread worldwide, with more than 4.7 million infected people and more than 316,000 deaths. In this article, we carry out a comparison of the methods to calculate and forecast the growth of the pandemic using two statistical models: the autoregressive integrated moving average (ARIMA) and the Gompertz function growth model. The countries that have been chosen to verify the usefulness of these models are Austria, Switzerland, and Israel, which have a similar number of habitants. The investigation to check the accuracy of the models was carried COVID-19 Growth Patterns Comparison: ARIMA and Gompertz Models Rambam Maimonides Medical Journal 2 July 2020  Volume 11  Issue 3  e0022 out using data on confirmed, non-asymptomatic cases and confirmed deaths from the period February 21-May 19, 2020. We use the root mean squared error (RMSE), the mean absolute percentage error (MAPE), and the regression coefficient index R 2 to check the accuracy of the models. The experimental results provide promising adjustment errors for both models (R 2 >0.99), with the ARIMA model being the best for infections and the Gompertz best for mortality. It has also been verified that countries are affected differently, which may be due to external factors that are difficult to measure quantitatively. These models provide a fast and effective system to check the growth of pandemics that can be useful for health systems and politicians so that appropriate measures are taken and countries' health care systems do not collapse.

A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve

“…In other words, the result of the estimation is essentially independent of the choice of M in this case. Finally, to bound the values of c 1 = 0.01 and c 2 = 0.2, we take into account the highest and the lowest values found in Spain and other countries, as it is seen in [34,35,37]. Those values are also reasonable with the observed range in Figure 1 described in [33].…”

“…Finally, for constructing the prior distribution of the parameter c we will assume to be independent of the other parameters. This fact can be empirically seen in [34,35,37] where authors describe different estimates of c in several countries. Moreover, Figure 7 described in [33] based on data from 73 countries shows a spread over more than one order of magnitude.…”

“…Moreover, the Gompertz curve have been widely used in epidemiology and virology to explain the behaviour of many biological processes, see for example [29][30][31][32]. Concerning to the COVID-19 we refer the readers to [33][34][35][36][37][38]. Finally, we also recommend readers see [39] where authors propose a generalized Gompertz growth model.…”

Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in México

“…In this work, Eqs. (12)(13)(14)(15) are presented as proof to demonstrate the coupling of the coefficients obtained during the learning process to the ANN model (Eq. 5), as well as illustrating that using three neurons in the hidden layer, ten coefficients are generated.…”

“…The authors emphasize that a simple model can be effective by using only the observed data, without applying some type of external covariate. Perez et al [ 14 ] compared an autoregressive integrated moving average (ARIMA) and a Gompertz function growth model in the COVID-19 cases applied for Austria, Switzerland and Israel. The results show that both models have a correlation index higher than 0.999, predicting that the end of the pandemic is close in the three countries.…”