On COVID-19 outbreaks predictions: Issues on stability, parameter sensitivity, and precision

Abstract

We formulate ill-posedness of inverse problems of estimation and prediction of Coronavirus Disease 2019 (COVID-19) outbreaks from statistical and mathematical perspectives. This is by nature a stochastic problem, since e.g., random perturbation in parameters can cause instability of estimation and prediction. This leaves us with a plenty of possible statistical regularizations, thus generating a plethora of sub-problems. We can mention as examples stability and sensitivity of peak estimation, starting point of exponential growth curve, or estimation of parameters of SIR (Susceptible-Infected-Removed) model. Moreover, each parameter has its specific sensitivity, and naturally, the most sensitive parameter deserves a special attention. E.g., in SIR model, parameter β is more sensitive than parameter γ. In a simple exponential epidemic growth model, parameter b is more sensitive than the parameter a. We also discuss on statistical quality of COVID-19 incidence prediction, where we justify an exponential curve considering the microbial growth in ideal conditions for epidemic. The empirical data from Iowa State, USA, Hubei Province in China, New York State, USA, and Chile justifies an exponential growth curve for initiation of epidemics outbreaks.