Modification 1: I misexpressed the English expression for the sum of expected infected people; the scales for the figures are in anyway correct. I described the right order.
Modification 2: I found a bag for sorting of labels. The graph lines are all the more same, but description for the analyses are changed. Additionally, I utilized 16 countries with longer time points.
The PzDom model, proposed in arXiv:1603.00959v8 [q-bio.PE], exhibits a set of indicators to analyze population dynamics. This model is further developed in https://doi.org/10.1101/780882 and https://doi.org/10.20944/preprints201911.0055.v1. Now we name this extended version of a PzDom model as "exPzDom". In the uploaded code of Julia language describing exPzDom (https://github.com/sadachi79/exPzDom), Re(s), "expected sums", Re(v), RRR, E(l) and "threshold" are calculable.
I applied this code to the data of new cases for SARS-CoV-2 infected from 2/24/2020 to 5/21/2020 in 16 countries of the high ranks.
"threshold" is a threshold caclulated by D/lambda_J, where D is a speed of increase for an individual and lambda_J is a Jeans wavelength-like parameter. If the value is smaller than 1, the population would converge, while the value larger than 1 results in divergence. Further information is available in https://doi.org/10.20944/preprints201911.0055.v1.
By this indicator, obviously U.S.A. is in bad situation with diverging growth of COVID-19, and India, Brazil and Russia are following.
Re(v) is in non-Archimedean sense, larger values mean potentials for the increase in population; smaller values vice versa. Further information is available in https://doi.org/10.1101/780882. Please also refer https://doi.org/10.1371/journal.pone.0179180.
By this indicator, obviously U.S.A. is in bad situation with diverging growth of COVID-19, and Brazil, Russia, Peru, India, Mexico, Saudi Arabia are following. Rest of them seem to be getting out of the situation.
Re(s) is an indicator related to a covariance of the denoted data, and 0 < Re(s) < 1 means the population is decreasing, while 1 < Re(s) < 2 means increasing, within the category of Gaussian fluctutation. Re(s) = 1 is a neutral situation. Re(s) > 2 means an explosive increase/decrease of population. Further information is available in arXiv:1603.00959v8 [q-bio.PE].
By this indicator, explosions until mid-March are over. Explosions in individual countries such as Spain, U.K., and Russia are observed during April. China seems to have a prominent output of escaping the situation as Re(s) > 3.
E(l) is a number of external symmetry of an observed group. Further information is available in https://doi.org/10.1101/780882.
In previously posted reports for analyses in Japan in this blog (described in Japanese), E(l) ~ 10 is a safer course, E(l) ~ 15 is not good, and E(l) ~ 20 is terrible. Top 8 countries still seem to be in terrible course, while next 8 countries once settled down to a safer course, followed by reentering to not good situations.
"expected sums" is an expected further increase from the particular time point utilized for a calculation. It is caclculable by (∑N)*Im(s)^(-"Number of data groups"), where ∑N is a sum of all the population numbers at a particular time point. Further information is available in arXiv:1603.00959v8 [q-bio.PE].
It seems that tens to hundreds of thousand of people in each country still have potentials for infection.
Discussions for these evaluators are welcomed.
