  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.
