Comparison of phenomenological growth models in predicting cumulative number of COVID-19 cases in East Java Province, Indonesia

Abstract

In this paper, five phenomenological (Richards, a generalized Richards, Blumberg, Tsoularis & Wallace, and Gompertz) models are implemented to predict the cumulative number of COVID-19 cases. The five phenomenological models are in the form of ordinary differential equations with a few number of model parameters.  The model parameters of each model were calibrated by fitting the model with the reported cumulative number of COVID-19 cases in East Java Province from March 25 until October 31, 2020 via nonlinear least square method. We compare the performance of the five phenomenological models by measuring four performance metrics, namely the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination (R²) and the Akaike information criterion (AIC).  When calibrating the cumulative number of cases, the five models perform very well, which are indicated by their high coefficient of determination (R²>0.999). However, a comparison of the four- performance metrics shows that Tsoularis & Wallace performed the best followed by a generalized Richards model. The prediction for the final size of the COVID-19 epidemic in East Java according to the Tsoularis & Wallace model is K=78 002. Both Richards and Gompertz models tend to underestimate the final size of the epidemic, while the Blumberg model tends to overestimate. The five models estimate the peak of the COVID-19 epidemic in East Java has been occurred on August 13-14, 2020. Using the predicted cumulative number of cases, we determine the daily new cases of COVID-19 in East Java. Based on the four-performance metrics, it appears that the five phenomenological models predict new daily cases of COVID-19 equally well.