Some insights on the COVID-19 pandemic from Fisher information.

We explored the application of Fisher information to the study of pandemics and illustrated the insights that can be gained using the COVID-19 pandemic, as a test case. To do so, we applied the Fisher information theory previously applied to periodic systems, to non-periodic dynamic systems. The resulting mathematical machinery was then used to compute the Fisher information measure, as the amount of information extracted from the time series for COVID-19 confirmed infections and deaths. The analysis was performed for the World as a whole and five nation-states: India, USA, Japan, Germany, and Chile. Several insights resulted from the study: (1) the information content of the time series varied widely for different time periods, over the course of the pandemic, (2) it is advisable not to fit model parameters or make policy decisions based on data from time periods with low Fisher information, (3) the most information about a wave of infections comes towards the end of the wave where the time series data has the most information about the dynamics of the pandemic, and (4) the quality of the time series data significantly affects the Fisher information value, and, therefore, what can be learned from studying the time series.