COVID-19 cases prediction with negative group delays digital function

Abstract

The negative group delay (NGD) is an uncommon function enabling to propagate arbitrary waveform signals with time-advance behavior. The counterintuitive NGD function was initially experimented for anticipating typically fast and short duration electronic signals in micro- and milli-second time scale. The application of NGD function to large time scale signal attracts more and more the attention of data processing engineer. This paper aims to investigate on the ability of NGD function to predict time- dependent social data with someday time-advances. As practical case of study, an innovative application of NGD function for predicting disease cases is treated. The digital circuit theory enabling to understand the low-pass (LP) NGD canonical TF and the characterization approach is established. It is shown in which condition the first order difference equation represents a LP-NGD circuit. Then, the design method of typical LP-NGD predictor as numerical circuit is introduced in function of the expected time-advance. The NGD predictor time-variation property is theoretically initiated. The NGD time-advance varied from -7 days to -1/2 days is investigated with deterministic data prediction processing from 5-months bi- exponential waveform data. The predicted data with time-advance of about -4 days was confirmed by analytical computation and simulation. The LP-NGD digital predictor feasibility is validated with monthly COVID-19 randomly arbitrary data by computed and virtually tested results. It was investigated with sensitivity analysis that the prediction performance is better when the input signal is smoothed enough. As expected, prediction result showing very good correlation with input data is demonstrated.