Classification of COVID-19 anomalous diffusion driven by mean squared displacement

In this study, we classify the COVID-19 anomalous diffusion in two categories of countries based on the mean squared displacement (MSD) of daily new cases, which includes the top four countries and four randomly selected countries in terms of the total cases. The COVID-19 diffusion is a stochastic process, and the daily new cases are regarded as the displacements of diffusive particles. The diffusion environment of COVID-19 in each country is heterogeneous, in which the underlying dynamic process is anomalous diffusion. The calculated MSD is a power law function of time, and the power law exponent is not a constant but varies with time. The power law exponents are estimated by using the bi-exponential model and the long short-term memory network (LSTM). The bi-exponential model frequently use in magnetic resonance imaging (MRI) can quantify the power law exponent and make an easy prediction. The LSTM network has much better accuracy than the bi-exponential model in predicting the power law exponent. The LSTM network is more flexible and preferred to predict the power law exponent, which is independent on the unique mathematical formula. The diffusion process of COVID-19 can be classified based on the power law exponent. More specific evaluation and suggestion can be proposed and submitted to the government in order to control the COVID-19 diffusion.