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What is the risk of meeting a person COVID in a group, knowing the incidence rate?

Text updated on 2020-11-19

When you're in a group, you have to ask yourself how likely it is that a person carrying the coronavirus will be in that group. The group may be a work or family gathering, bus passengers, or store patrons. The more people there are, the greater the likelihood. If we know the number of positive people per 100,000 people (often called the "incidence rate"), it is fairly easy to calculate the likelihood of a person being positive in a group of a given size.

The incidence rate, estimated from the number of people who have had a positive PCR test for coronavirus, is published on official websites and reported by many websites and newspapers. In France, the weekly incidence rate available on official sites is the number of people testing positive in a region over 7 days. This weekly incidence of positive tests can be used as a rough estimate (see below) of the prevalence of COVID, i.e., the number of cases of COVID-19 at any given time in a region.

To estimate the risk of running into at least one person with COVID-19, we can use a very classical probability formula. You have to reason in reverse and calculate first Pthe probability that no one in the group is contaminated. If there is only one person in the group, then P=(1-Ti) with Ti the incidence rate (i.e., the official rate "per hundred thousand" divided by 100,000). If there are two people, then the probability that no one is infected becomes P= (1-Ti)2 . If N is the number of people in the group, then : P= (1-Ti)N.

Finally, the probability that at least one person in the group is contaminated is equal to 1-Por if you prefer percentages, 100 x (1-P)

In this calculation, it is assumed that all individuals have an equal chance of infection and that the probability of having COVID-19 for any individual is independent of the status of other individuals. However, this is not true: spouses are more likely to have COVID-19 than other members of a family, for example.

Several sites offer to do this calculation, either with the data entered by the user or from data "collected" on official sites. These sites are almost all generated by volunteers!

The result of this calculation does not express the risk of contracting the disease, which depends on other factors such as the duration of the event, the space in which it takes place, and precautionary measures such as masks and spacing. In combination with these factors, it allows a better assessment of the risk of contracting coronavirus in a given situation. See our questionnaire to assess your risk of contamination in each situation.

Nevertheless, this probability is only an estimate. It should be interpreted as an approximation of the real risk and used with caution, for two major reasons:

Elias Orphelin and Guillaume Rozier propose a simple calculator using the incidence rate entered by the user.

David Berger offers a "COVID risk calculator" for Belgium and Switzerland. This presents, for the Belgian provinces and the Swiss cantons, the risk (probability in %) of having at least one COVID-positive person in a group according to the size of the group and the age of the people, the number of days over which one wants to cumulate the official incidence, and the finding bias by which one wants to multiply this incidence.

Joshua Weitz and his colleagues created a COVID-19 Event Risk Assessment Planning Tool to visualize on a map of the United States the probability that at least one positive individual will be present at an event, depending on the number of people in the group and the bias on the incidence rate (to be multiplied by 5 or 10). The incidence rate is calculated over 10 cumulative days.

The ISI Foundation has developed a calculator that allows the probability of at least one COVID-positive individual being present at an event to be displayed on a map of Italy or Spain, depending on the number of people in the group, the number of days accumulated for the incidence (7 days or 10 days), and the percentage of infections detected.

FRANCE: estimation of the number of infectious persons based on the number of people admitted to intensive care units (French interface)
Florence and Denis Corpet propose a calculator based on the same formula P= (1-Ti)N. But they estimate the prevalence of contagious people from the number of entries into Intensive Care Units (ICU), a figure that is independent of the number of people tested and the quality of the tests. This calculator can be used for all countries. See the question How many people are contagious with COVID around me?

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In France, the official incidence rate is the number of positive tests per 100,000 inhabitants. It is calculated as follows: (100,000 * number of positive cases) / population size. The weekly rate is therefore the sum of the rates over 7 days, which makes it possible to smooth out the variations linked to the day of the week, particularly on Sundays when the data are very low compared to the rest of the week. This also allows the tests done over a week to be cumulated, thus increasing the share of the population tested. The rates are also standardized (direct standardization), by age (10-year age groups) and gender, with the population of metropolitan France in 2020 serving as the reference population. As of 29/08/2020, the indicators derived from laboratory data (SI-DEP) present incidence, positivity, and screening rates corrected according to the screening carried out in airports on the arrival of international flights.


The U.S. CDC considers the typical infectious period to be 10 days and makes the following recommendations. For most people with COVID-19, isolation and precautions can usually be discontinued 10 days after the onset of symptoms and disappearance of fever for at least 24 hours, without the use of fever-reducing drugs, and with improvement of other symptoms. For individuals who never develop symptoms, isolation and other precautions may be discontinued 10 days after the date of their first positive SARS-CoV-2 RT-PCR test. A limited number of individuals with a severe form may produce a coronavirus capable of replicating beyond 10 days which may warrant extending the duration of isolation and precautions for up to 20 days after symptom onset; consultation with infection control experts should be considered.


Analysis of 15,771 children between the ages of 1 and 18 living in Bavaria, Germany and participating in a public health screening program for type 1 diabetes. Serological tests detecting the presence of antibodies detect 6 times more infected children than reported cases.

Hippich, M., Holthaus, L., Assfalg, R., Gonzalo, J. M. Z., Kapfelsperger, H., Heigermoser, M., ... & Heck, S. (2020). Public health antibody screening indicates a six-fold higher SARS-CoV-2 exposure rate than reported cases in children. Med.

Analysis of 16,025 people between March and April, 2020 in ten regions of the United States. Serological tests that detect the presence of antibodies reveal 6 to 24 times more COVID-19 infections than the number of reported cases. It should be noted that PCR tests were not widely available at the time.

Havers, F. P., Reed, C., Lim, T., Montgomery, J. M., Klena, J. D., Hall, A. J., ... & Krapiunaya, I. (2020). Seroprevalence of antibodies to SARS-CoV-2 in 10 sites in the United States, March 23-May 12, 2020. JAMA internal medicine.

Between 25 May and 15 July, 2020, the Italian Ministry of Health conducted a large seroprevalence study of SARS-CoV-2 on a representative sample of 64,660 people. An overall prevalence rate of 2.5% was measured, with a peak in the region of Lombardy (7.5%) and in particular in the province of Bergamo (24%). As a result, the actual number of Italians who have been in contact with the virus would be almost 5 times higher than the officially reported figures.


Analysis of 105 index patients and their 392 contact cases within the household. The secondary attack rate for contacts who are spouses of index cases is 28% compared to 17% for other adult household members.

Li, W., Zhang, B., Lu, J., Liu, S., Chang, Z., Cao, P., ... & Chen, J. (2020). The characteristics of household transmission of COVID-19. Clinical Infectious Diseases.

Description of the "COVID-19 Event Risk Assessment Planning Tool" site.

Chande, A., Lee, S., Harris, M., Nguyen, Q., Beckett, S. J., Hilley, T., ... & Weitz, J. S. (2020). Real-time, interactive website for US-county-level COVID-19 event risk assessment. Nature Human Behaviour, 1-7.

Further reading

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

How many people are contagious with COVID around me?

How long is a person contagious?

Can a person without symptoms infect others?

How many people are infected without showing symptoms?

What strategies to detect contagious people at the entrance of a bar or an airplane?

SARS-CoV-2 and COVID-19, what's that? Some figures

Can we predict the evolution of COVID-19 ?