The total number of cases by COVID-19 until May 8, 2020, for the United States of America was 1,215,571, in Spain it was 221,447, in Belgium it was 51,420 and in Austria it was 15,673.
The variation of the time in days to go from one range to another ranged between 3 and 46. The values of the speed of the range (dy⁄dt) were between 4.6 and 21549.7 For all countries, these values will show the speed with which the change in the number of infected occurs for the moment in which the change in range occurs, but only for that point, in such a way that when comparing these values among the analyzed countries, it is observed that this measure It allows establishing differences in how fast or not the change in the range occurred, showing the differences in the dynamics of the number of infected between countries. Thus, the countries with a dynamic that has shown an increase in the number of infected, such as Spain and the United States, obtained the highest values, while the other 2 countries with the least tendency to increase their number of infected obtained the lowest values for the passage from range 2 to 3, and thereafter, the other range changes, which are the changes of greatest interest, since in a pandemic rank 1 will be easily overcome (see table 1).
The areas evaluated for each of the ranges with equation 1 ranged from 48,899 to 280,953 for the United States of America, between 4,369 and 1,056,204 for Spain, between 4,673 and 229,418 for Belgium and between 2,888 and 101,820 for Austria. While the derivative of SAPT varied between 3,079 and 123,157 for all countries (See table 1). In this way, the derivative of SAPT temporarily differentiates space as it changes in each of the countries.
From these results, it is possible to observe how the SAPT changes in each of these countries, as they increase the days before the day in which the change in rank occurred, showing the differences between countries, with the number of days elapsed. from the beginning of the epidemic until the change of rank occurs. For example, the comparison between the areas of the four countries in range 3 shows that the area of the pandemic in Belgium is 1.3 and 1.8 times greater than in the United States of America and Spain, respectively; while for SAPT in Austria, the ratio is 1.5 compared to SAPT in the United States and Belgium. One explanation for this is that Belgium took 11 days more than Spain to go to rank 3. In this way it can be seen that the heights of the triangles of all countries to go to rank 3 are practically the same, what changes are the days elapsed to move from one rank to another; so the difference between areas will show us how fast or slow the number of people infected with COVID-19 will occur in one country compared to the others. In other words, it is possible from the SAPT analysis to observe how the pandemic spreads as it changes its range, which allows us to differentiate between the dynamics of the epidemic for any country, anytime, anywhere.
The ratio of change between the number of cases of COVID-19 and the time it takes to move from one range to another, allows evaluating the speed of infection as it spreads in different countries. For example, the comparison between Austria and Belgium shows that the spread of infection has a higher speed in Austria because it only lasted 17 days at level 2, while Belgium was 36 days. But then, Belgium changes its level which is reflected in its speed, reaching Austria in rank 3. In this way, the derivative of the area of each right triangle (dA⁄dt), also allows evaluating the speed of change of the infection energy range, completely differentiating the dynamics of pandemic and COVID-19 infection, between countries.
In light of these results, it can be seen that the methodology has the ability to mathematically differentiate the pandemic dynamics between countries, finding a unique way to calculate the speed of the epidemic from the areas and differential equations.