Unknown uncertainties in the COVID-19 pandemic: Multi-dimensional identification and mathematical modelling for the analysis and estimation of the casualties.

• We extend the SpID-N model with comprehensive unknown uncertainties. • We construct the ARX, ARMAX, and OE based extended SpID-N models. • We learn optimal rates to learn the unknown parameters and uncertainties. • We extensively analyse the developed models and predicted future casualties. Insights about the dominant dynamics, coupled structures and the unknown uncertainties of the pandemic diseases play an important role in determining the future characteristics of the pandemic diseases. To enhance the prediction capabilities of the models, properties of the unknown uncertainties in the pandemic disease, which can be utterly random, or function of the system dynamics, or it can be correlated with an unknown function, should be determined. The known structures and amount of the uncertainties can also help the state authorities to improve the policies based on the recognized source of the uncertainties. For instance, the uncertainties correlated with an unknown function imply existence of an undetected factor in the casualties. In this paper, we extend the SpID-N (Suspicious-Infected-Death with non-pharmacological policies) model as in the form of MIMO (Multi-Input-Multi-Output) structure by adding the multi-dimensional unknown uncertainties. The results confirm that the infected and death sub-models mostly have random uncertainties (due undetected casualties) whereas the suspicious sub-model has uncertainties correlated with the internal dynamics (governmental policy of increasing the number of the daily tests) for Turkey. However, since the developed MIMO model parameters are learned from the data (daily reported casualties), it can be easily adapted for other countries. Obtained model with the corresponding uncertainties predicts a distinctive second peak where the number of deaths, infected and suspicious casualties disappear in 240, 290, and more than 300 days, respectively, for Turkey. [ABSTRACT FROM AUTHOR]