Feb 26, 2021

Distinguishing Four Waves in the Covid-19 Pandemic Spread During the Last Year – Examining the Effects of Vaccination on the Last Wave

Corona waves

The graphs showing new daily corona cases and new daily deaths exhibit distinct and separate peaks in all countries over the last year of the pandemic, corresponding to several waves of Covid-19 infection (see Worldometers under individual countries). In many countries, the 1st wave occurred around April, the 2nd around August, the 3rd around November 2020, and the 4th around January 2021 (see Table 1).

The 2nd wave mostly exhibited very low values of infected and dead. Some countries rather differed in some of the dates; for example, Israel had the 3rd wave in September to October, Belgium had the 4th wave in November, etc. The last, 4th wave now mostly continues to descend toward quite low values, and possibly toward the epidemic break; in some countries, including France, Italy, Czechia, and Belgium, the 4th wave is tailing, and the values continue to keep quite high. Most victims belong to the 3rd wave, many also to the 4th one (in some countries closely overlapping with the 3rd one, e.g., in Sweden), and in some countries to the 1st one (e.g., Belgium, Sweden).

The waves sometimes overlap and are difficult to distinguish. A long tail may indicate another wave; for example, the tail after the 4th wave in Czechia may indicate a 5th wave. Some countries differ; for example, Brazil seems to show two broad peaks, and India has one broad peak covering the period from April 2020 to February 2021. China, that has obviously never reported real data, shows only one small peak placed in February 2020. Of course, the shapes of the waves reflect the officially reported values and need not exactly show the real spread. However, the four-peaks pattern can be seen even on the whole world summary values. 

Reviewing the pandemic results

Table 1 shows deaths per million people, ranging from the highest values of nearly 2000 (BE, CZ, GB), down to a half (DE) or a third (IL) in the European domain. The Far East countries, including, e.g., JP, KR, TW or AU, show much lower values (60, 31, 40 or 35, respectively) probably because of their geographic isolation and early closure. The values from non-democratic countries are not reliable; the mean world value is 321 deaths per million, which says nothing about the real situation; China, the country of the virus origin, reports 3 dead per million.

The most important parameter is of course the fraction of the infected population. Curiously, none of 200 countries of the world, and the WHO neither, cared to regularly obtain this value. Several isolated attempts to serologically estimate this value occurred mainly during the early stage of the pandemic. From the beginning it seemed very probable that the total number of people who had been infected was somewhere between 5 times to 100 times higher than the number of positively reported cases, often about 10 times (here). As for now, the most probable factor to multiply the reported cases to obtain the infected fraction is between 6 and 10. Table 1 shows rough estimation of the infected population fractions in several countries for the factor equaling 8.

It seems probable that between ¼ and ¾ of the population have already been infected by Cocid-19 in various developed countries, except for the mentioned isolated Far East countries.

Differences among the countries

Strict measures have been applied in nearly all countries that are included in Table 1, and it is difficult to explain the difference between Germany and neighboring Czechia. The fact is that the measures have been most liberal in Sweden, and the death per million in Sweden is lower than in seven of ten Western countries in the table. Among the factors affecting the differences are the ways of registering and reporting the deceased and diseased, protection of the endangered groups, namely senior citizens, and of course the general behavior habits resulting from the local culture. Different viral strains or mutants might have some effects too; similar timing of the waves in different countries suggests that the latter factor might be involved.

Some differences can be explained by the population age distribution. More than 90% deaths belong to the age group of 65+; Sweden has 20% population in this group, while Israel only 10%, so that Israel would be expected to have only half of the Swedish mortality, which is exactly what Table 1 demonstrates (614/1262 = 0.49). Of course, the politicians like to ascribe the lower values to their wisdom.

Covid-19 decline and vaccination

By 23 February 2021, the share of people who received at least one dose of a vaccine is 52% in Israel, 27% in the UK, 13% in the US, and 4% in Germany, Spain, Italy, and France (here). In most countries, the values of new corona cases and new deaths now decline. The question is what the relation of the decline and the vaccination is.

The numbers of new cases and new deaths started to decrease in most countries between the end of December 2020 and the end of January, as the dates of the 4th peak maxima show in Table 1. The vaccination against Covid-19 started in many countries toward the end of 2020. Thus, the two events touch in time but do not overlap. Table 2 shows ten first countries of Table 1 with their 4th peak maximum date, and with their population fraction being vaccinated by at least one dose till said date.

The graph of daily new cases in Israel shows a decreasing trend from around January 20, when 1/3 of the population has been vaccinated by the first dose of the Pfizer vaccine, and the graph of daily new deaths shows a decreasing trend from around January 27, when ½ of the population has been vaccinated. Most people received only the first dose of two doses separated by 3 weeks. The first dose confers 50% to 80% protection, but only several weeks after delivery, and most of the vaccinated people had got the dose very closely to the peak maximum date. In any case, the effects of the vaccination on the 4th peak decreasing trend would naturally be assumed.

To evaluate how prominent the decreasing trend the last peak exhibits in the countries, the percent decrease of the new cases and the new deaths by February 16, relatively to the date of the peak maximum, was calculated (if the peak maximum has 200 new daily cases, and Feb 16 has 50 new cases, the % decrease is 150/200=75% decrease). The decrease is between about 50 and 80%, except for Czechia and France where, moreover, the values stagnate (see also Table 1, the column “4th peak ending”).

It might be expected that high infected population fraction will result in the epidemic ending (collective or herd immunity), and indeed, the estimated % of the infected population well correlates with the case and death % decrease (see the last two columns of Table 2). In case of Germany, Czechia and France, the correlation is weak. As for Czechia, it seems that the population is thoroughly infected (more than 30% tests are positive), so that no measures have any effects, and the virus will end its work in the whole susceptible population; the epidemics may hopefully be over quite soon, after infecting the last remaining susceptible victims; if that is true, no vaccination would be needed there. France, still having many uninfected susceptible people (if the estimation is correct), might expect a fight like that in Czechia, but the vaccination may help in finishing the matter more peacefully. Germany may have managed to keep a larger part of the population uninfected (if the estimation is correct), but surely the country would have to fight some more waves in the future, if not being helped by the vaccination. 

Reviewing the vaccination timetable clearly shows that the fractions of the population who had been vaccinated were too low to explain the decreasing trends of the case and death numbers  in all countries except for Israel (see Table 2). This holds for the whole world (see Table 1). For example, India exhibits clear decline in the numbers of new cases and deaths, while only 0.8% population has got the first vaccine dose and 0.1% the second dose by February 23 (here). 


The total world values for new daily Covid-19 cases and new daily deaths show decline. The last Covid-19 wave exhibits a clear decrease toward minimal new cases and deaths values for example in Switzerland, Spain, and Germany. The new deaths go to zero in Sweden. Also, populated countries like Brazil and importantly India, show a clear decline of the values. The trend started incidentally at the same time as the current vaccination efforts started, but before any substantial part of the population was vaccinated. The only exception is Israel, where a third or a half of the population got the first vaccine dose (a small part of the population got the second dose) when the decline started to be perceptible, so that the vaccination might or might not affect the decline there.

It is not clear whether another Covid-19 wave would come without the vaccination or not. In some countries, like Czechia, the epidemic would probably end even without vaccination, due to a large segment of the infected population; the epidemic might continue till attaining herd immunity in many other countries, such as France and even Germany; in East Asian countries and Australia, the epidemic would hardly stop without continuing hermetic closure or without the vaccination.

Anyway, the world decline of the new Covid-19 cases and deaths that started in January was interestingly not a result of the vaccination.

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