A mathematical method to describe the relative weight of two infections of different transmissibility is presented and applied to discuss the incidence of Omicron and Delta in two case studies (Italy and Argentina).
by Dr Galileo Violini
The Omicron variant has been discovered on November 19, 2021 by Dr. Sikhulile Moyo’s group at the Botswana-Harvard AIDS Institute Partnership, on a specimen collected on November 9,1 although anomalies in some samples had been noticed a few days earlier at a private laboratory in South Africa.2 On November 24, the discovery was reported to the World Health Organization (WHO), who on the 26, declared it a variant of concern.3 Since then, the variant has been rapidly developing worldwide. It has reached some 150 countries/territories4 and, in several cases, it has given origin to a tremendous increase in daily contagions.
The effect of this new variant on the consequences of the development of the pandemic is controversial. Its low lethality, about 115 cases out of more than 550,000 confirmed cases,4 and the lesser necessity of long-term hospitalisation and intensive care make the most serious effects of the infection less serious than those of all the previously observed variants5 and has been interpreted as a possible first signal that the end of the tunnel may be near; COVID-19 may become an endemic infection that will no longer affect the lives of the world population.6 However, it is possible that these characteristics are a consequence of the current vaccination campaign, even if appalling differences in vaccination across different countries7 have collectively administered more doses than the world population. A comprehensive South African study showed that in case of hospitalisation for severe diseases, there was no significant difference between Delta-infected and possible Omicron-infected people,8 which could be due as well as to ethnic-demographic factors of resilience that suggested care in the extrapolation of these results to other countries.9,10 In any case, despite these features, the WHO has joined the cautious attitude of Imperial College5 warning about the risk that the Health System may be unable to face the pressure of a possible tsunami of largely increased infections.11
Elsewhere, we pointed out an interesting indication that seems to come from the first countries where the Omicron variant has been detected.12 We observed that it seems that they are now in the stage of a decreasing diffusion of the variant, which seems to exhibit a peak much narrower than those associated with previous variants of the virus. This result has just received confirmation from the statement of the South African Government that “All indicators suggest the country may have passed the peak of the fourth wave at a national level,” so it could release some restrictions established to fight the Omicron burst.13
The estimate of the actual development of the outbreak is a major problem of public health policy. Biology provides tools for it, but these tools are more useful than a forecast for the understanding of what happened sometime before. Just an example: La Repubblica, a major Italian newspaper, today, January 1, 2022 published a big title, “The Higher Health (Italian) Institute, ISS: Delta variant remains at 79% of cases, but Omicron runs”.14 The news is correct, but the quoted ISS report refers to December 20, 2021, and its update is announced for next January 3. Actually, as we shall show, standard Physics techniques allow to make a fast order of magnitude estimate of the diffusion of a rapidly developing variant, and, incidentally agree with the historical December 20 data.
The number of confirmed cases of the presence of the variant in a country is determined through laboratory analysis over only a small number of the possible cases of infection of which it is responsible. The first signal of the possibility that a specimen belongs to the Omicron variant, is the missing of a specific gene.3 However, that signal, the S-gene dropout, does not necessarily prove that the analysed specimen corresponds to the variant, and more advanced genomic tests are required to prove it. Not all laboratories are equipped to perform this identification.
In practice, the number of confirmed cases is by orders of magnitude smaller than the estimated incidence of the variant. As a matter of fact, the largest number of confirmations comes from the UK (45 per cent) and Denmark, Germany, and the US (12 per cent). An interesting piece of data to underscore is that only one death occurred in the US and a fraction of only 3 per 10,000 in the other three countries.4
The purpose of this note is to present a non-biological approach to the problem of identifying Omicron cases among those identified as COVID. The idea is of a typical interdisciplinary origin. In Physics, it is common that the problem of identifying a background is mixed with the phenomenon one wants to study.
In this case, one can consider the pre-existing situation as a background to which, at a certain moment, is superimposed on a peaked burst due to Omicron. This can be done if one can take advantage of different features that may allow distinguishing Omicron’s effect from the background.
Immediately before the Omicron burst, the most diffused variant was Delta, a variant of large lethality, which is not the case with Omicron. Therefore, a first indication that a new burst is to be attributed to Omicron is the observation that it is not accompanied by a death burst. Of course, the usual time lapse between the period considered for the infection and the death must be taken into account.
This feature was indeed noticed immediately in the South African countries where the variant was first observed. As a matter of fact, during the Omicron burst, in South Africa, the increase in death has been marginal.13 In November and December 2021, the number of reported COVID deaths has been stable, around 150-200, despite the two-order-of-magnitude increase of the infections. Even this estimate may be short of identifying all Omicron-infected South Africans for several reasons, although it is true that the situation may be different in countries where, in the last few days, broad testing campaigns have been carried out.
Our quantitative approach to estimate at a certain moment the Omicron incidence is based on the assumption that the infection is due to Omicron itself, with a rapid increase of the contagions, and to a less transmissible background that most probably is generally due to the Delta variant, that was almost everywhere the dominant one before the appearance of Omicron.
Thus, one can follow the evolution of the cases prior to the appearance of Omicron and extrapolate it. Due to the narrow peak of Omicron, the variation of extrapolation in the peak’s times is small and, if one assumes that the difference between the observed incidence and the Delta extrapolated one is due to Omicron, the relative incidence of the two variants can be easily evaluated.
As an example, we shall present the application of this technique to two country cases. Obviously, the method can be applied to any country, provided that the trend of the Delta background can be easily identified. However, this is not necessarily true, because it may happen that prior to the possible Omicron peak, the curve of the cases exhibited a peak. As an example of this situation, one may mention the Dominican Republic, where a peak, whose maximum had been reached on November 15, ended two weeks later.15
Two countries having a flat Delta background in October to November are Italy and Argentina. Thus, we shall study them as examples of the application of the proposed method.
We shall present in detail the case of Italy and summarise the results referring to Argentina.
For Italy, we considered the six half months between October 1 and December 30 and present in Table 1 the average COVID-death data in intervals of half month.
As Table 1 shows, during the period we considered, there was a death increase that obviously in the first month and a half was not related to Omicron, whose first case in Italy was detected on November 28 and traced to an arrival from Mozambique ten days earlier.
The size of this increase is such as to double the death average in a month, both in the case of no-Omicron month and Omicron-month.
The pattern is totally different when one considers the contagions between October 1 and December 30. We fitted the data assuming either a linear or an exponential form for the curve, although we expect that over such a short period does not make much difference.
In the first two months, the growth of contagions and deaths (scaled by two weeks) followed a similar pattern until the explosion of the last days led to a great change in the exponent of the exponential.
The obvious likely explanation of this change is that the outbreak due to Omicron started to appear. In order to estimate the ratio of Omicron/Delta cases we extrapolated the November behaviour of contagions and evaluated the expected accumulated value at December 30. The difference between the actual value and the extrapolated one gives an estimate of the accumulated effect of the Omicron variant, whereas that between the extrapolated value and the accumulated value on November 30 offers an estimate of the Delta cases.
Actually, we made two extrapolations, one using the fit for the period Nov. 16 – Nov. 30 and one for the period Nov. 1 - Nov. 30.
From the contagions between Nov. 16 and Nov. 30, the estimated value of the accumulated thousands of contagions on December 30 is 5361 (linear extrapolation) or 5390 (exponential extrapolation).
As one would have expected, since the Delta contagions in November had been growing (as the deaths indicate), if we had used the fit to the data of the whole month of November, slightly lower values would have been obtained, namely 5275 (linear extrapolation) or 5290 (exponential extrapolation).
Thus, out of the currently accumulated thousands of contagions, 5981, those that can be attributed to Omicron are between 600,000 (first extrapolation) and 700,000 (second extrapolation), whereas those due to the Delta would be about 250,000 (first extrapolation) and about 350,000 (second extrapolation).
This allows us to estimate that the fraction of Omicron cases is currently of the order of 70 per cent of the total cases. Of course, this figure is affected by some uncertainty, whose main source is the possibility that the recent data about positive test cases may include double-counting of people eager to celebrate New Year’s Eve with gatherings that would require a negative COVID test.
One could argue that it is well known that the number of detected contagions depends on the number of tests and for that reason, it is usually preferred to follow the development of the pandemic referring to indicators such as hospitalisations, intensive care, and deaths.
Given the delay lapse between contagions and fatalities, it is too early to make use of the described method to understand the relative weights of Delta and Omicron in the peak of the last few days. However, one can try to get rid of the variability of the number of tests, referring to the ratio of positive cases with respect to the tests.
If one extrapolates the observed ratio between October 15 and November 30 to the last week and compares the extrapolation with the observed values of the ratio, then the estimated average incidence of Omicron between December 26 and December 30 turns out to be about 63 per cent, in fair agreement with the previous result.
This calculation also provides an estimate for the situation on December 20, with 5 per cent Delta and 25 per cent Omicron, which is in very good agreement with the estimate of the ISS.14
A similar test was carried out for Argentina, a country where, after a long period of relatively few contagions, in the last few days registered a burst. In the first 10 days of December, the daily cases have steadily been of the order of 2000, but after a week with about 4-5,000 cases per day, there has been a strong increase, reaching the record value of 42,000 contagions on the 29th.
The same calculation would suggest the presence of about 160,000 Omicron cases among those that appeared after December 13, against 190,000 cases of the variants dominating in the first half of the month. However, it should be noted that these Omicron cases arose mostly in the last few days.
As a final remark, one could observe that a recent South African study suggests that Omicron may not only evade antibody immunity by vaccination and previous infection, but also enhance 4.4 times immunity against Delta variant.16 This would imply that our estimates of the ratio may be slightly overestimated, especially if projected on longer terms the Delta fraction of the cases, but it is clearly a second-order effect.
After the completion of this article an interview of Professor Battiston to La Repubblica17 arrived at similar conclusion about the relative incidence of the two variants. His method of calculation is different from ours18 but the basic idea, which is becoming broadly accepted in Italy, is the same - the two contagions run independently from each other.19 Moreover the expected new ISS report has been published. It confirms the rapid diffusion of Omicron although without a quantitative estimate.20
- Associated Press. (2021, December 4). Scientist Says Omicron Was a Group Find. VOA. Retrieved from https://www.voanews.com/a/scientist-says-omicron-was-a-group-find/6339275.shtml.
- Sguazzin, A. (2021, November 30). How a Missing Gene Led South African Scientists to Find Omicron. Bloomberg. Retrieved from https://www.bloomberg.com/news/articles/2021-11-30/how-south-african-scientists-found-the-troubling-omicron-strain.
- World Health Organization. (2021, November 26). Classification of Omicron (B.1.1.529): SARS-CoV-2 Variant of Concern. World Health Organization. Retrieved from https://www.who.int/news-room/questions-and-answers/item/coronavirus-disease-(covid-19)-variants-of-sars-cov-2
- Omicron Tracker. Newsnodes. (n.d.). Retrieved from https://newsnodes.com/omicron_tracker/
- Ferguson, N., Ghani, A., Hinsley, W., & Volz, E. (2021, December 22). Report 50 - Hospitalisation risk for Omicron cases in England. Imperial College London. Retrieved from https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-50-Severity-Omicron/
- Leichman, A. K. (2021, December 23). Covid pandemic may be nearing end, experts suggest. ISRAEL21c. Retrieved from https://www.israel21c.org/covid-pandemic-may-be-nearing-end-suggest-experts/
- Violini, G. (2021, April 6). Can the planet wait for COVID Immunity in Africa? eTurboNews. Retrieved from https://eturbonews.com/2993067/can-the-planet-wait-for-covid-immunity-in-africa/
- Wolter, N., Jassat, W., Walaza, S., Welch, R., Moultrie, H., Groome, M., ... & Cohen, C. (2021). Early assessment of the clinical severity of the SARS-CoV-2 Omicron variant in South Africa. medRxiv.
- Francis, E. (2021, December 17). South Africa says vaccines and past infections could be reason Omicron variant cases appear milder. The Washington Post. Retrieved from https://www.washingtonpost.com/world/2021/12/17/covid-omicron-south-africa-vaccinations
- Doucleff, M., & Wood, D. (2021, December 17). Omicron may be less severe in South Africa. That may not be the case for the U.S. NPR. Retrieved from https://www.npr.org/sections/goatsandsoda/2021/12/17/1065315661/omicron-may-be-less-severe-in-south-africa-that-may-not-be-the-case-for-the-u-s
- World Health Organization. (2021, December 29). WHO Director-General’s opening remarks at the press conference - 29 December 2021. World Health Organization. Retrieved from https://www.who.int/director-general/speeches/detail/who-director-general-s-opening-remarks-at-the-press-conference---29-december-2021
- Violini, G., & De Jesús Salvador, W. (2021, December 29). Ómicron y cuarta dosis – Ciencia y emotividad. Acento. Retrieved from https://acento.com.do/opinion/omicron-y-cuarta-dosis-ciencia-y-emotividad-9019120.shtml
- ABC News. (2021, December 31). South Africa says its Omicron COVID-19 outbreak has peaked as restrictions begin to ease. ABC News. Retrieved from https://www.abc.net.au/news/2021-12-31/south-africa-omicron-peak-passed/100733016
- la Repubblica. (2021, December 31). Covid, il report dell’Iss: da lunedì Lombardia, Piemonte, Lazio e Sicilia in giallo. Raddoppia l’incidenza dei casi, sale l’occupazione delle terapie intensive. la Repubblica. Retrieved from https://www.repubblica.it/cronaca/2021/12/31/news/covid_dati_iss-332211752/?ref=RHTP-BH-I322793271-P3-S1-T1
- Google. (n.d.). Dominican Republic COVID Statistics. Google. Retrieved from https://www.google.com/search?q=Dominican%2BRepublic%2BCovid &rlz=1C1ONGR_esDO928DO928&oq=Dominican%2BRepublic%2BCovid&aqs=chrome.. 69i57j69i59j0i512l3j0i457i512j0i512j69i60.13687j0j4&sourceid=chrome&ie=UTF-8
- Khan, K., Karim, F., Cele, S., San, J. E., Lustig, G., Tegally, H., ... & Sigal, A. (2021). Omicron infection enhances neutralizing immunity against the Delta variant. medRxiv.
- Fraioli, L. (2021, December 27). Battiston: "Nuove regole davanti a Omicron o ci sarà un lockdown di fatto". la Repubblica. Retrieved from https://www.repubblica.it/cronaca/2021/12/27/news/battiston_ripensare_quarantena_ e_tracciamento_o_ci_ ritroveremo_in_un_lockdown_non_voluto_-331724614/
- Battiston, R. Private communication.
- Fraioli, L. (2022, January 9). Battiston: “Non illudetevi che Delta sia scomparsa. Circola ancora e fa paura.” la Repubblica. Retrieved from https://www.repubblica.it/cronaca/2022/01/09/news/battiston_non_illudetevi_che_delta_ sia_ scomparsa_circola_ancora_e_fa_paura_-333123373/
- Ministero della Salute, Istituto Superiore di Sanità. (n.d.). (rep.). Monitoraggio Fase 2 Report settimanale | Report 86 Sintesi nazionale (pp. 1–25). Retrieved from https://www.iss.it/documents/20126/0/Report+86+Sintesi+Nazionale+monitoraggio+ fase+2+%281%29.pdf/ d2dd9a2a-24b6-ec3a-9bba-c92ebf9edddf?t=1641575348975.
About the Author
Dr Galileo Violini Former professor of Theoretical Physics (University of Rome La Sapienza and University of Calabria); Author of 250 publications (science policy, high-energy phenomenology, physics teaching, epidemiology) and, with N. Queen, of “Dispersion theory in high-energy physics”; Co-founder and Emeritus Director, Centro Internacional de Fisica, Bogota, Colombia; John Wheatley Award of the American Physical Society (APS); Spirit of Abdus Salam Award of ICTP and Salam-Family; Former UNESCO’s Representative in Iran; Former Director of an EU program at Universidad de El Salvador; Advisor of several Latin American countries; APS Fellow and Former Member-at-large of the APS Forum of International Physics; Doctorate honoris causa, Ricardo Palma University, Lima.