Reproduction coefficient

Jump to: navigation, search

Reproduction coefficient may refer to various quanitties:

Reproduction of photons in a cavity with active medium,

Reproduction of electrons in photomultiplier or in a Geiger counter

multiplication of number of neutrons in nuclear reactor,

multiplication of number of patients due to transmittance of some decease,


In particular, term Reproduction coefficient is applied to spreading of infection Covid19. The same quantity is denoted also with term Rnumber (or R number). This number is average number of new patients, who get ill due to contact with one ill person.


Sparse data on R


For Wuhan, 2020.01.24, R is estimated to range from 3.6 to 4 [1]

For China, since 2020.01.01 to 2020.02.07, R is estimated to range from 1.4 to 6.49, with mean 2.28 [2]


2020.09.18, in the UK R coefficient is estimated to be between 1.1 and 1.4 [3]



     Efficiency of masks [4]

Use of face masks is reported to reduce the coefficient R for one or two orders of magnitude.

Efficiency of medical mask is estiamted as

\(E = 1-R/R_0 \)
\(R_0\) is reproduction coefficient under condition, that the people do not use the face masks, and
\(R\) is the reproduction coefficient under condition, that all the people use masks in public places.

Various estimates for the efficiency are suggested in year 2020:

2020.04.19, intyroverts estimate of the efficiency to be 98.5% [5]

2020.04.23, estimate of the efficiency to be 97% [6].

2020.05.04, nashaniva estimates the efficiency of masks almost 100% ("В масках вероятность заражения снижается до минимума") [7].

2020.05.04, Саулюс Чаплинскас estimates the efficiency of masks to be 98.5% [8].

2020.06.02, Rachael Rettner suggests the estimate of the efficiency 85% [9][10].

2020.06.04, Ирина Иванова estimates the efficiency of masks more than 90% (probability of transfer reduces tens times, "при ношении масок риск заразиться коронавирусом снижается в десятки раз") [11][12].

2020.07.21, don24 repeats the same estimate, more than 90%. [13].

The authors usually do not indicate, how did they got the estimates of efficiency of mask, but there is important exception:

2020.09.02, Emma Fischer et al describe measurements of penetration of aerosol particles tgrough various masks at talking [14]:


Mask, name Description
1, “Surgical”* Surgical mask, three layers
2, “Valved N95” N95 mask with exhalation valve
3, “Knitted” Knitted mask
4, “PolyProp” Two-layer polypropylene apron mask
5, “Poly/cotton” Cotton-polypropylene-cotton mask
6, “MaxAT” One-layer Maxima AT mask
7, “Cotton2” Two-layer cotton, pleated style mask
8, “Cotton4” Two-layer cotton, Olson style mask
9, “Cotton3” Two-layer cotton, pleated style mask
10, “Cotton1” One-layer cotton, pleated style mask
11, “Neck Gaiter” One-layer polyester/spandex, 0.022 g/cm2
12, “Bandana”* Double-layer bandana, 0.014 g/cm2
13, “Cotton5”* Two-layer cotton, pleated style mask
14, “Fitted N95” N95 mask, no exhalation valve, fitted
“Swath” Swath of mask material, polypropylene
“None”* Control experiment, no mask


Assuming, that the aerosol is dominant mechanism of transmittance of the infection, the penetration coefficients approximates ratio \(R/R_0\) for each kind of mask. Roughly, the results by Fischer confirm the estimates above:

The medical face masks reduce amount of aerosol particles, spread by a patient, for an order of magnitude.

Second wave of covid19

Screenshot of the second wave of Covid19, number of daily new cases at UK in 2020 [15] 2020.09.30.CovidUKfragment.png


According to the estimates of the efficiency of masks, since the mass use of the face masks, the reproduction coefficient of Covid19 should be significantly below unity.
Since the 2020 spring, almost 100% of people wear masks in the public places.
So, the pandemic is supposed to decay exponentially.
Then, the "second wave" [16][17][15] of Covid19 cannot be attributed to the unwanted transfer of the infection from ill pacients to new victims.

The reasonable hypothesis explains the "second wave" as manifestation of the total hybrid Putin world war of the Russian officials against the Human civilization.

Under condition of total corruption of the top Russian officials, there are no mechanisms that would prevent them from using of bioweapon in this war; the aliases of the Russian usurper, like Boshirov and Petrov, intentionally spread the infection, in the same way, as they apply unstable nuclei of Po-210 or poison novichok for murdering.

This concept shows good agreement with reports about use of the Russian diplomatic post for contraband. Centners of cocaine, Po-210, Novichok, highly pure biopreparate and other weapon of mass murdering can be smuggled with the Russian diplomatic post.

The Pasechick institute and GNC Vektor are reported to manufacture bioweapon. These facilities are located in Russia. So, the intentional spreading of infection by the Russian terrorists appears as natural and reasonable hypothesis. This hypothesis shows good agreement with other evidences of terroristic activity of the Russian proxies. After to shout down the civil airplanes (see Katyn-2, MH17), to use the nuclear weapon (see Putin kiled Litvinenko), to use the chemical weapon (See 2018.03.04.Теракт, in Russian), one could expect, that the Russian terrorists will use the bioweapon too. It could be delivered with the diplomatic post; use of the Russian diplomatic post for contraband is also reported (see Кокаин в диппочте, in Russian).

Carriers of the Russian diplomatic passports appear as the main suspects in the terroristic attack on all the countries. The attack with bioweapon perfectly fits the general concept of the hybrid war. Within this concept, the civilized countries should consider ways to resist: search well the Russian diplomatic post and detend, interrogate the Russian officials, especially carriers of the diplomatic passports, as the primary suspects.


  1. Jonathan M. Read, Jessica R.E. Bridgen, Derek A.T. Cummings, Antonia Ho, Chris P. Jewell1. Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. January 24, 2020. We estimate the basic reproduction number of the infection (𝑅𝑅0) to be significantly greater than one. We estimate it to be between 3.6 and 4.0, indicating that 72-75% of transmissions must be prevented by control measures for infections to stop increasing. ..
  2. Ying Liu, Albert A Gayle, Annelies Wilder-Smith, Joacim Rocklöv. The reproductive number of COVID-19 is higher compared to SARS coronavirus. Journal of Travel Medicine, Volume 27, Issue 2, March 2020. PubMed, bioRxiv and Google Scholar were accessed to search for eligible studies. The term ‘coronavirus & basic reproduction number’ was used. The time period covered was from 1 January 2020 to 7 February 2020. For this time period, we identified 12 studies which estimated the basic reproductive number for COVID-19 from China and overseas. Table 1 shows that the estimates ranged from 1.4 to 6.49, with a mean of 3.28, a median of 2.79 and interquartile range (IQR) of 1.16.
  3. James Gallagher. Coronavirus: What is the R number and how is it calculated? 2020.10.01. .. On Friday 18 September, the government said the R number across the UK was estimated to be between 1.1 and 1.4, slightly up on the previous week. ..
  4. Introverts For Progressive Revolution. How the risk of contagion reduces when everyone wears a mask. // 2020.04.19.
  5. Introverts For Progressive Revolution. How the risk of contagion reduces when everyone wears a mask. // 2020.04.19.
  6. 4 April 2020 .. medical masks, which offer 97% protection are single-use masks..
  7. Эпидемиолог: Заражение происходит при 15-минутном контакте. В масках вероятность заражения снижается до минимума. 04.05.2020 / 09:59.
  8. Профессор: в масках вероятность заражения коронавирусом снижается до 1,5% ELTA, понедельник, 4 мая 2020 г. 09:26, Директор Центра инфекционных заболеваний и СПИДа профессор Саулюс Чаплинскас пояснил, что медицинские маски на больном и контактирующем с ним здоровом человеке снижают вероятность заражения всего до 1,5%. Профессор заметил, что коронавирусом можно заболеть, если в восприимчивый организм попадает достаточное количество вируса.// .. "Но если человек будет без маски, то вероятность заражения составляет 100%. Если маска будет только на здоровом человеке, вероятность заражения снижается до 70%. Если же маска будет на больном, то вероятность заражения будет всего 5%, если оба – всего 1,5%, – сказал Чаплинскас.
  9. Face masks may reduce COVID-19 spread by 85%, WHO-backed study suggests. June 02, 2020.
  10. Face masks may reduce COVID-19 spread by 85%, WHO-backed study suggests By Rachael Rettner - Senior Writer June 02, 2020 Here's how much face masks, social distancing and eye protection may help with preventing COVID-19 spread. .. The review found that keeping a distance of at least 3 feet (1 meter) from other people lowered the chances of coronavirus infection or spread by 82%, and keeping a distance of 6 feet (2 m) could be even more effective.
  11. рач: использование масок снижает риск заболеть COVID-19 в десятки раз. 03:43 04.06.2020 (обновлено: 05:00 04.06.2020) МОСКВА, 4 июн - РИА Новости. Основным путем передачи коронавирусной инфекции является воздушно-капельный - это происходит при кашле, чихании и разговоре, поэтому при ношении масок риск заразиться коронавирусом снижается в десятки раз, сообщила РИА Новости заведующая консультативно-профилактическим отделением Инфекционной клинической больницы № 1 московского департамента здравоохранения, врач-инфекционист Ирина Иванова.
  12. Врач: использование масок снижает риск заболеть COVID-19 в десятки раз. 4 июн. 2020 г.
  13. COVID-19: ношение маски снижает риск заражения в десятки раз 31 июля 2020 15:10. .. если сравнить помещение которое проветривается, к примеру автобус с открытыми окнами, и такое же, которое не проветривается, то лучше первое, там риск заразится меньше. Но ношение маски снижает его в разы, в десятки раз!» — отметил доктор.
  14. Low-cost measurement of face mask efficacy for filtering expelled droplets during speech Emma P. Fischer, Martin C. Fischer, David Grass, Isaac Henrion, Warren S. Warren and Eric Westman. Science Advances 02 Sep 2020: Vol. 6, no. 36, eabd3083 DOI: 10.1126/sciadv.abd3083
  15. 15.0 15.1 Coronavirus second wave: Which countries in Europe are experiencing a fresh spike in COVID-19 cases? Comments// By Mathieu Pollet • last updated: 05/10/2020 - 14:06 Countries across Europe are seeing a resurgence in COVID-19 cases after successfully slowing outbreaks early in the year.// Some countries — such as Albania, Bulgaria, Czech Republic, Montenegro, North Macedonia — are seeing higher case numbers than earlier in the year.// France, the UK, Poland, the Netherlands and Spain are likely dealing with the much-feared second wave and have started taking action to curb it.// While on the face of it infection numbers might be higher, it could be accounted for by the increase in testing - many countries didn't have the capacity to carry out tests in such a high volume earlier in the year.
  16. Beds converted for COVID-19 use at Tokyo hospital after 'second wave' of infections August 3, 2020 (Mainichi Japan). TOKYO -- A hospital in the capital has once again set aside beds normally used by regular inpatients for those infected with the COVID-19 virus in response to instructions by the Tokyo Metropolitan Government following a resurgence of infections.// Amid the "first wave" of infections, the Japanese Red Cross Musashino Hospital in the suburban Tokyo city of Musashino had converted a total of 30 beds, including 20 beds for regular patients and 10 high care unit beds, into those for use by patients infected with the novel coronavirus. After the state of infections settled down, in May the hospital left five intensive care unit beds for COVID-19 patients and restored the rest to regular use. However, following a request by the metropolitan government, which aims to secure a total of 2,800 beds, the hospital has once again converted 20 regular patient beds into those designated for COVID-19 patients.
  17. Second wave of virus has now hit Japan, COVID-19 panel expert says. THE ASAHI SHIMBUN August 20, 2020 at 15:51 JST. Japan is now “in the midst of a second wave” of COVID-19, warned an infectious disease expert on Aug. 19, in stark contrast to the central government. // The government has long stopped short of labeling the surge in new cases since early July as such.// “We were able to somehow overcome ‘the first wave’ after the state of emergency was declared," said Kazuhiro Tateda, the head of the Japanese Association for Infectious Diseases, speaking at the annual conference that began in Tokyo on Aug. 19. "But we are now in the midst of a second wave.”


Bioweapon, Corruption, Coronavirus, Covid19, Dippa, Boshirov and Petrov, Designate Russia as state sponsor of terrorism, Putin world war, Terror

ГНЦ Вектор, Институт Пасечника, Кокаин в диппочте, Коррупция, Новичок, Путинская мировая война,