Performance of Richard and Logistic Time Series Models in Predicting COVID-19 New Cases

Abstract

A growth curve is a non-linear model to capture the growth process. Growth curves have been applied in many sectors, especially in the health sector. It can capture the growth of bacteria or cancer cells. Recently, the growth curve widely used to capture the future situation of the pandemic situation because of COVID-19 that spread all around the world. The Logistic growth curve is a growth curve that has characteristics such as taking very slowly at the early growth process, then rising sharply, and then slowing as it approaches the maximum carrying capacity. Another growth curve is the Richard growth curve which has a more flexible form than the Logistic growth curve to form the s-line in the cumulative curve. The first derivative of growth curves can be transformed into linear equations and hence, it can be modelled using time series analysis. This research interest is to evaluate performance of time series models based on Logistic and Richard growth curves in predicting new cases of COVID-19. This research used two types of data to evaluate the models. First, it is based on simulation methods to evaluate the bias, RMSE, and variance of the parameter estimates. Furthermore, the RMSEP of forecasting based on testing data is also calculated by means of simulation. The result showed that the Richard model tended to have a small bias and RMSE of parameter estimates when compared to Logistic model if the period of the training data was prolonged. However, if the data is generated from Logistic growth curve bias and RMSE of Logistic model are smaller than Richard model. These results were also shown by the RMSEP calculated based of the testing data. Regarding the evaluation of the variance of the parameter estimate, the result showed that Logistic growth curve tended to produce smaller variance when compared to the variance of Richard growth curve. The second evaluation is based on empirical dataset, in this case the weekly new cases of COVID-19 in Jakarta have been used. Using this empirical data the Richard growth curve performed better than the Logistic growth curve. This has been indicated by the RMSE and MAPE of predicting the training data. Moreover, this was also shown by RMSEP and MAPE calculated based on testing data in which the Richard growth curve tended to produce smaller values than the Logistic growth curve. This situation also has been shown by the 95% prediction interval of forecasting the testing data in which the prediction interval based on Richard model has included more testing data than the prediction interval based on Logistic model.