Analysis of Self-Similarity, Memory and Variation in Growth Rate of COVID-19 Cases in Some Major Impacted Countries

In the present work investigation of self-similarity as well as scaling analysis have been performed over daily number of new confirmed cases of COVID-19 in some major impacted countries viz. USA, Brazil, India, Russia, Spain, UK, Italy, Germany and France from their respective dates of first report of COVID-19 till June 30, 2020. To reduce uncertainty and irregular fluctuations in these present time series seven-point moving averages are taken and the entire analysis has been further performed over these seven-point moving average data. Scale invariance and self-similarity or self affinity manifests the fractal nature. For these time series, investigations of fractal nature have been performed by means of Higuchi method and corresponding fractal dimensions have been obtained. Also scaling analysis has been applied to understand the nature of the memory in these by means of Hurst exponent. Next, on the basis of these seven-point moving average data cumulative profiles of confirmed cases of COVID-19 for these countries have been generated. An effort has been made to understand the initial exponential growths in them. Study does not yield constant growth rates of infection; rather it shows time dependent profiles with variable functional representations at different windows of time for all these countries. Finally an effort has been made to predict the scenario for certain upcoming days for all the nine countries considered within a pre-assigned tolerance level continuing with the last obtained exponential growth rates. Results are not persistent in most of the cases. This might point towards a difficult scenario of prediction of future impacts in these countries.