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Lethality, mortality, excess mortality, R0, kappa: what are we talking about?

Text updated on 2020-06-21

Learn what each of these terms means to understand the risks associated with a SARS-CoV-2 coronavirus infection and the dynamics of the spread of COVID-19.

Case-fatality rate: risk of dying from the COVID-19 disease for a person infected with SARS-CoV-2. This rate is calculated by dividing the number of people who died from COVID-19 by the total number of people infected with the virus. This rate depends on several factors including age, physical and medical conditions (obesity, diabetes, hypertension, immunosuppression, etc.) and gender. For more information on the estimated lethality of the COVID-19 virus, see What is the risk of dying from this COVID-19 for an infected person?.

Mortality rate: risk of dying at a given time. This rate is calculated by dividing the number of people who died by the total number of people in a given region and over a defined period of time.

Excess mortality compared to a previous period. Mortality data for March and April in France show an excess mortality compared to the same period in 2019. Although not all deaths are attributable to COVID-19 , it is reasonable to believe that excess mortality is largely due to this disease.

R0, baseline reproductive number or initial transmission rate of the coronavirus: number of people infected on average by a person infected with SARS-CoV-2 in a population that has never been in contact with this coronavirus before. If the R0 is 3, for example, this means that one person infected with the coronavirus will infect an average of 3 people, and these 3 people will in turn infect 3 others. This will result in the rapid spread of the virus. If R0 is less than 1, it means that an infected person will infect on average less than one person and the epidemic will eventually die out. The lower the R0, the more likely it is that the epidemic will disappear quickly. The R0 is also used to calculate the minimum proportion of people in a population that must be immunized for the epidemic to begin to decline and disappear. This is because an immunized person will not be infected and will not infect others. If enough people in the population are immunized, then an infected individual will infect on average less than one person. This is called herd immunity. Although the concept of R0 is fairly simple to understand, its estimation is complex and varies widely across studies for COVID-19. Prior to containment, estimates of R0 ranged from 1.95 to 6.49. While R0 depends on the infectivity of the pathogen, it also depends on population density and individual behaviour. For more information on how to lower the average reproduction rate or R, see How to succeed in deconfinement?.

R or Re or Rt, effective reproduction number or average reproduction rate: the number of people infected on average by a person infected with SARS-CoV-2 at a given time.

Dispersion factor k (kappa): a parameter that measures the variability of the reproduction rate within the population. When k is high, the number of people infected by each infected individual (secondary infections) is approximately the same for all infected individuals: this is the situation observed during the Spanish flu epidemic in 1918. On the contrary, when k is low and close to 0, the number of people infected by each infected individual is very variable: most individuals infect very few others, but a few infect many. The epidemic then tends to spread through so-called "super-propagation" events, where one infected person transmits the virus to many contacts. For example, when k = 0.1 and R0 = 3, 73% of infected people infect less than one person, while 6% of infected people will infect more than 8 people. The epidemic then progresses in a discontinuous manner, by outbreaks (in English, "clusters"). This discontinuous mode of spread was observed during the SARS epidemic (R0 = 2; k = 0.16) and, to a lesser degree, the MERS epidemic (R0 = 0.6; k = 0.25). It is still too early to know the k of COVID-19 with certainty, but it would be around 0.1 - 0.4. For more information, see Why are superspreader events crucial to understanding the COVID-19 epidemic ?

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This study shows the effect of age, diabetes, and hypertension on the severity of COVID-19 and the case rate of hospitalized patients in and around New York.

Richardson, S., Hirsch, J. S., Narasimhan, M., Crawford, J. M., McGinn, T., Davidson, K. W., ... - Cookingham, J. (2020). Presenting characteristics, comorbidities, and outcomes among 5700 patients hospitalized with COVID-19 In the New York City area. Jama.

This study shows the effect of sex on the severity of COVID-19 and the fatality rate in patients with COVID-19

Jin, J. M., Bai, P., He, W., Wu, F., Liu, X. F., Han, D. M., ... - Yang, J. K. (2020). Gender differences in patients with COVID-19 Focus on severity and mortality. Frontiers in Public Health, 8, 152.

Public Health France data for the weeks of March 23-29 2020 and March 30 to April 5 show that all causes of mortality at the national level in France is significantly higher than the mortality expected over this period. At the national level, excess mortality is estimated at +16% and +34%, respectively, for these two weeks. This increase in overall mortality is particularly marked in the Greater East and Ile-de-France regions.

Public Health France, Weekly Epidemiological Point of April 16, 2020

Data from the Regional Observatory of Health Ile de France (France) revealed a very high excess mortality in the department of Seine Saint Denis, with the largest change in mortality in Ile de France compared to the same period in 2019 (up 69.4% between March 1 and 31 2020 and 118.4% between March 1 and April 10 2020). In comparison, mortality in Paris increased by 89.8%. In this department, the densest of Ile de France but also the poorest, housing is often small (for 1/4 of the population of Seine Saint Denis, the area per capita is 14m2 compared to 17m2 in Paris) and occupied by larger families (42.1% of dwellings are occupied by 3 or more people, compared to 21.8% in Paris), making social distance more difficult to implement. It is also in this department compared to the other departments of Ile de France that resides the largest number of workers exposed to situations at risk (hospital workers, nursing assistants, cashiers, delivery drivers) with more travel than in other departments (more than 50% of the inhabitants of the Seine Saint Denis work in another department in comparison with only 24.4% of Parisians working in another department). Finally, often in connection with difficult social conditions, the prevalence of certain pathologies (diabetes, chronic disease, overweight) is higher than in other departments. The social and health inequalities suffered by the Seine Saint Denis population explains the high mortality in Seine Saint-Denis compared to other departments of Ile de France.

Mangeney, C., Bouscaren, N.,Telle-Lamberton, M., Saunal, A., Féron, V.La excess mortality during the epidemic of COVID-19 in the departments of France, Regional Health Observatory Ile de France, April 2020.

Data on human mortality are available from the human mortality project (https://www.mortality.org/) website, which reveals discrepancies between the reported figures of victims of the COVID-19 and excess mortality in each country. Many newspapers such as The Economist have described these deviations with 10% reported for Belgium, -5% for France, -40% for the Netherlands, -43% for Austria among others.

The Economist excess mortality database:

Data from the United Kingdom's Office of National Statistics (ONS) show similar results to French data from the Ile de France Regional Health Observatory. Comparison of the mortality rate between March 1 and April 17 2020 in disadvantaged areas in terms of wages, employment, health, education level, environment etc. and in privileged areas, shows that the risk of dying from COVID-19 in disadvantaged areas is 2.1 times higher than in favoured areas.

Deaths involving COVID-19 by local area and socioeconomic deprivation: deaths occurring between March 1 and April 17 2020, Office for National Statistics, May 1 2020.

A study that compares the R0 of published studies on SARS-CoV-2 prior to the implementation of containment measures. The average R0 is estimated at 3.28.

Liu, Y., Gayle, A. A., Wilder-Smith, A., Rocklev, J. (2020). The reproductive number of COVID-19 is higher compared to SARS coronavirus. Journal of travel medicine.

A U.S. study estimates that R0 was at 5.7 in Wuhan while its estimate was much lower in small European cities at the beginning of the epidemic.

Sanche, S., Lin, Y. T., Xu, C., Romero-Severson, E., Hengartner, N., & Ke, R. (2020). High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerging Infectious Diseases, 26(7).

Epidemiological study on the population of the home or "cluster" of Oise where many cases were infected in a high school, estimating R0 to 3.3.

Salje, H., Kiem, C. T., Lefrancq, N., Courtejoie, N., Bosetti, P., Paireau, J., ... & Le Strat, Y. (2020). Estimating the burden of SARS-CoV-2 in France.

A study of outbreaks or "clusters" in Hong Kong (corresponding to 1,037 people tested positive) carried out in May 2020 estimates that 20% of cases of contamination are responsible for 80% of local transmission. Social exposures produce more secondary cases than family or work interactions. The k dispersal factor is estimated at 0.45 (95% CI: 0.30-0.72).

Adam, D., Wu, P., Wong, J., Lau, E., Tsang, T., Cauchemez, S., ... - Cowling, B. (2020). Clustering and superspreading potential of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Hong Kong. PREPRINT

Interest of the kappa dispersal factor in modeling the propagation dynamics of certain infectious diseases. The k dispersal factor for SARS was estimated at 0.16 (90% confidence interval 0.11-0.64).

Lloyd-Smith, J. O., Schreiber, S. J., Kopp, P. E., Getz, W. M. (2005). Superspreading and the effect of individual variation on disease emergence. Nature, 438(7066), 355-359.

Simple explanations in French about the kappa setting and the importance of super propagating situations.

Korsia-Meffre, S. (2020). COVID-19 "The only thing that matters is where it falls" or how to avoid a possible second wave. Vidal

A University of Chicago study shows that it COVID-19 spreads faster in cities with higher population densities.

Berman, M. G., Bettencourt, L. M., & Stier, A. J. (2020). COVID-19 attack rate increases with city size. MedRxiv. PREPRINT

Further reading

What is the risk of dying from this COVID-19 for an infected person?

How many people are actually infected relative to the number of confirmed COVID-19 cases?

How many people are infected without showing symptoms?

Why are superspreader events crucial to understanding the COVID-19 epidemic?

What is a superspreader event for COVID-19 ?