Global information measure based on fractional entropy with application for COVID-19 pandemic

This article presents a new measure to analyze the random behavior in multivariate time series. This study extended the range of entropy choices from Shannon, Rényi and Tsallis to fractional case. Furthermore, it is proposed explicit expressions of the Mutual Information Matrix (MIM) based on fractional entropy to analyze the nonlinear interactions between time series. Fractional entropy depends on a fractional parameter, and it is more sensitive to temporal non-linear dynamics than other methods related to classical entropies. Additionally, the eigenvalues of MIM based on fractional entropy are used to obtain a global information measure, which it represents the total mutual information among the entire time series can be quantified. To illustrate the obtained results, four models (Poisson, sinusoidal, coupled logistic maps and controlled vector autoregressive) are simulated and results are discussed. Finally, Covid-19 pandemic data time series from various testing centers in Baghdad (Iraq) was used to validate the behavior of proposed measures. Results demonstrate that the proposed global measure is more effective in predicting the nature of Covid-19 spread, which may assist governments in planning for its containment.