Nonlinear Prediction for the COVID-19 Data Based on Quadratic Kalman Filtering

ABSTRACT

Considering the application of prediction techniques to support the decision-making process during a dynamic environment such as the one faced during the COVID-19 pandemic, demands the evaluation of several different strategies to compare and define the most suitable solution for each necessity of prediction. Analyzing the epidemic time series, for example, the number of new confirmed cases of COVID-19 per day, classic compartmental models or linear regressions may not provide results with enough precision to support managerial or clinical decisions. The application of nonlinear models is an alternative to improve the performance of these models. The Kalman Filter (KF) is a state-space model that is used in several applications as a predictor. The filter algorithm requires low computational power and provides estimates of some unknown variables given the measurements observed over time. In this chapter, the KF predictor is considered in the analysis of five countries (China, United States, Brazil, Italy, and Singapore). Similarly to the ARIMA methodology, the results are evaluated based on three criteria R2 Score, MAE (Mean Absolute Error), and MSE (Mean Square Error). It is important to notice that the definition of a predictor for epidemiological time series shall be carefully evaluated and more complex implementations do not always represent a better prediction on average. For the proposed KF predictor, there were specific time-series samples with no satisfactory result, achieving a negative R2 Score, for example, while, on the other, other samples achieved higher R2 Score and lower MAE and MSE, when compared to other linear predictors. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.