COVID-19 reproduction number estimated from SEIR model: association with people's mobility in 2020

This paper is an exploratory study of two epidemiological questions on a worldwide basis. How fast is the disease spreading? Are the restrictions (especially mobility restrictions) for people bring the expected effect? To answer the first question, we propose a tool for estimating the reproduction number of epidemic (the number of secondary infections $R_t$) based on the SEIR model and compare it with an non-model $R_t$ estimation. To measure the $R_t$ of COVID-19 for different countries, real-time data on coronavirus daily cases of infections, recoveries, deaths are retrieved from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. To assess the effectiveness of mobility restrictions for the COVID-19 pandemic in 2020, the correlations between the $R_t$ and people's mobility (based on the Apple mobility index) are presented. The correlations were considered for 12 countries and for most of them, the correlations are negative. This shows a delay in the implementation of mobility restrictions - the countries imposed them in response to growth of new COVID-19 cases, rather than preventively.