Comparative Forecasts of Confirmed COVID-19 Cases in Botswana Using Box-Jenkin's ARIMA and Exponential Smoothing State-Space Models

Abstract

The recent outbreak of coronavirus (COVID-19) disease had forced Botswana to work robustly to “flatten the curve” of the pandemic to prevent the medical care system capacities from being overwhelmed. However, disappointingly, the accurate forecasting of infectious diseases remains a global challenge. This study adopts machine learning–based time series models known as auto regressive integrated moving average (ARIMA) and exponential smoothing state space (ETS) to model forecasts of confirmed COVID-19 cases in Botswana over a 60-day period. Findings show confirmed COVID-19 cases in Botswana steadily rising from April 2020, with short-term plateaus in early August 2021, and dropping gradually in late August 2021. This trend is effectively described using an additive model in seasonal trend decomposition method by Loess (STL). In scrutinizing the model’s forecast accuracy, findings show that the ARIMA model outperforms the ETS model by depicting the smallest accuracy measure of mean absolute error (MAE) of 36.63, root mean squared error (RMSE) of 70.03, and mean absolute percentage error (MAPE) of 7.36. However, when the models are compared based on metrics of execution time and memory utilization, results showed that ETS outperformed ARIMA with an execution time of 0.239 seconds and memory usage of 22,427 Kilobytes. Residual analysis was performed on forecasts errors of both ARIMA and ETS models, and findings showed that in most time lag intervals, residuals were independent, random, and depicted no autocorrelation. In scrutinizing the generated forecasts from both ARIMA and ETS models, results showed that given the environmental variables remain constants, i.e., government interventions and other environmental factors, confirmed COVID-19 cases in Botswana are expected to degrade in the next 60 days. The ARIMA model forecasted around 2,300 confirmed cases to be expected by September 28, 2021 and around 1,500 confirmed cases by October 26, 2021. The ETS model forecasted around 1,300 confirmed cases by September 28, 2021 and 1,100 cases by October 28, 2021. These findings should help raise social awareness at disease-monitoring institutions and government regulatory bodies, where they could be used to provide support for productive health decisions and propose policy improvement for better management of the COVID-19 disease in Botswana.