Time dependent reproduction number (Rt) is one of the most popular parameters to track the impact of COVID-19 pandemic. However, especially at the initial stages, Rt can be highly underestimated because of remarkable differences between the actual number of infected people and the daily incidence of people who are tested positive. Here, we present the analysis of daily cumulative number of hospitalized (HP) and intensive care unit (ICU) patients both in space and in time in the early phases of second wave COVID-19 pandemic across eight different European countries, namely Austria, Belgium, Czech Republic, France, Italy, Portugal, Spain, and United Kingdom. We derive simple model equations to fit the time dependence of these two variables where exponential behavior is observed. Growth rate constants of HP and ICU are listed, providing country-specific parameters able to estimate the burden of SARS-COV-2 infection before extensive containment measures take place. Our quantitative parameters, fully related to hospitalizations, are disentangled from the capacity range of the screening campaign, for example the number of swabs, and they cannot be directly biased by the actual number of infected people. This approach can give an array of reliable indicators which can be used by governments and healthcare systems to monitor the dynamics of COVID-19 epidemic.