Parametric analysis of early data on COVID-19 expansion in selected European countries

Martin Spousta

To evaluate the evolution of the spread of the disease as a function of time, one can study the time dependence of parameters b 1 , b 2 , and N 0 . This can be done by fitting the data in time windows or by fitting the data between the time of the beginning and a given time t. The former method is more susceptible to fluctuations of the data which may occur within the time windows while the latter method may be biased by the change of the parameters in time. We tested both of these methods as well as various sizes of the time window with the conclusion that fitting from the beginning leads to less fluctuating values of parameters which exhibit the same trends and tend to converge to the same values as the values of parameters analyzed by fits in time windows. From now on, we therefore evaluate the evolution of parameters b 1 , b 2 , and N 0 by fitting from the beginning up to a time t indicated on the x-axis of plots. The evolution of parameters b 1 , b 2 , and N 0 is shown in upper left and lower panels of Figure 1 . One can see that parameters are highly oscillating at the beginning but then for times greater than 20 days since the first registered The parameter b 1 can be interpreted as a parameter quantifying the uncontrolled spread of the disease. As such, it will be assumed that it is universal for all the European countries since they share approximately the same default density of interactions among inhabitants (cities of similar density, similar level of public transportation, similar default 2 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. cultural behavior). Consequently, for subsequent studies, the parameter b 1 was fixed to a value 0.32 representing a value preferred by a minimum χ 2 condition for the fit in the country with the most stable evolution which is Italy. The time evolution of N 0 and b 2 parameters in the case of fixed b 1 is shown in Figure 2 . One may identify several features seen from the behavior of parameters: