##### < Modelization

# How many people are contagious with COVID around me?

Text updated on 2020-11-19

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What is the risk of meeting a contagious person on the street or in a meeting? Here is a calculation based on the number of entries in resuscitation that estimates the number of infectious people around you.
**

On the street, in a meeting, in a classroom, or in a store, you may have wondered how many infectious COVID people were around you. Unfortunately, you can't tell by observing people because many people who are contagious have no symptoms. Moreover, this number changes from one day to the next and depending on the region.

**Why is an estimate based on the incidence rate unsatisfactory**?

A simple estimate of the risk of encountering a contagious person uses the **incidence rate**. By definition, this rate is the proportion of new positive individuals in a population at a given point in time. See the question **What is the risk of crossing a COVID-positive person in a group, knowing the incidence rate?**. However, this rate, which is often published on official websites, is estimated from the number of positive tests, which depends directly on the number of people tested. It is therefore very sensitive to the conditions that led people to be tested or not. For example, in France in March and April 2020, very few people were tested, and the incidence curve rose very little while the number of people hospitalized increased a lot. In France, testing increased significantly from the beginning of August to the end of October 2020, and the incidence rate increased similarly. In the first week of November 2020, both rates decreased simultaneously(SI-DEP data). Finally, each time a new testing center opens in a city, the incidence rate increases.

We decided to estimate the number of infectious persons based on the number of resuscitation admissions, which is not dependent on the testing policy. By following our reasoning, you can become **familiar with the epidemiological estimates and understand why each estimate has its limitations**.

**What does our estimator give?**

We estimate that at the beginning of November 2020, in Toulouse, we crossed 2 infected passerby per thousand, and 5 in Lyon. One thousand people: this corresponds to the number of passerby in an hour in a busy street, the passengers of a full subway train, or the students of a large college. The probability that, in a group of 25 people, at least one was infected was 5% in Toulouse, and 12% in Lyon. Beware, our estimates are not perfect: they are within an order of magnitude (see the paragraph "limits" at the bottom of the page). To see today's estimate, click to open the table showing the **number of infectious people** in Paris, Marseille, Lyon and Toulouse, in the street and in meetings. This table is updated every day. Another table, also based on ICU entries, gives the number of infected people per 1,000 people in the street for 30 French departments: **Thirty cities in France, classified by infectious density**.

**How to estimate the number of COVID-19 holders?**

Making an estimate is a bit like baking a cake: to make it good, you need good ingredients and a good recipe. The ingredients here are the data and parameters of the model. The data changes every day and according to the region, and they need to be updated. The parameters are related to the virus and the disease: they are found in scientific articles and they don't change much. The recipe is the way to combine these data and parameters, using mathematical formulas, into a spreadsheet that displays the expected results directly. This is the cake we share online.

**Here is already the list of ingredients: data and parameters**

**The number of admissions to intensive**care units (**ICU)**published in France includes all critical care services (intensive care in the strict sense + intensive care + continuing care). It represents reliable data as long as these units are not saturated, independent of the number of PCR tests performed, and available for each French department on Réa-GéoDES. Many countries also publish this data, gathered on OurWorldInData (ICU data for Intensive Care Units).- The
**size of the population**is also a given. It is the number of inhabitants of the town, region, or country in question, which can be found on official websites (INSEE for France). - The
**number of days between first symptoms and entry into the**ICU is seven, according to an international meta-analysis by Grasselli, JAMA but, more recently, a French study observed a delay of eight days (COVID-ICU, Intensive Care Medicine). **Lethality**: In order to extrapolate from the ICU data to the number of infected persons we must know the number of deaths. The proportion of lethality of ICU patients is 42% worldwide, according to Armstrong, Anaesthesia. A more recent study of Intensive Care Units in France, Belgium, and Switzerland (COVID-ICU, Intensive Care Medicine) shows that the proportion of lethality in the ICU has decreased and is 31%, on average. This parameter can change according to the admission criteria in the ICU and the quality of care. The proportion of lethality of infected persons (Infection Fatality Rate) varies between 0.37 and 0.75% depending on the study (see question**What is the risk of dying from COVID-19 for an infected person?**), we estimate it at 0.5% in France according to Salje, Science. This proportion depends very much on the population age pyramid according to Levin, medRxiv and must therefore be adapted to the country in question.**Duration of contagiousness**: A patient is contagious between 7 and 21 days, but the average duration is 7 days after the first symptoms, or 9 days in all, since contagion begins two days before symptoms. Viral RNA is found for longer in nasopharyngeal swabs, but is no longer infectious according to Wölfel, Nature.**Asymptomatic**: 42.5% of infected persons are asymptomatic according to Lavezzo, Nature in the exhaustive survey of an Italian commune by PCR test. A survey conducted in June 2020 among English households found it to be 76.5% asymptomatic(Petersen, Clin. Epidemiol.). We, therefore, use here the average of the two, 60%. The asymptomatic people are the only ones we are likely to come across, because patients are confined to their homes or to the hospital.

**Here is the recipe to combine these ingredients: steps of the calculation**

- Let's start with yesterday's ICU admissions, released today. The ICU admissions curve shows oscillations related to weekends (smaller numbers on Sunday). To amortize them, instead of using the daily entries, we use their 7-day moving average.
- Those who enter the ICU had symptoms of COVID an average of 8 days earlier, and they began to be contagious 2 days before symptoms, 10 days before entering the ICU. We can therefore deduce from yesterday's ICU entries how many people became contagious 11 days ago.
- Lethality rates are used to move from the number of admissions to the ICU to the number of new infectious cases. Multiply the number of ICU patients by their lethality (31%), which gives the number of deaths. Divide this number of deaths by the case-fatality of the infected persons (0.5%) to obtain an estimate of the number of infected persons.
- Each patient remains infectious for about 9 days: we therefore add up the new infectious persons over 9 days to know the number of infectious persons, the prevalence, on the ninth day.
- These calculations give us the number of people who were contagious 11 days ago. How do we know that number today? We assume that this number will continue to evolve as it has for the past week. We therefore extrapolate the exponential curve fitted to the data for the last 7 known days from 11 days into the future, because the contagion is exponential.
- Then divide this number of infected people by the population size of the department or region to obtain the infection rate as a percentage. This assumes that all new ICU patients come from the region, which is not always the case.
- Finally, in the street, it is not the sick that we interact with as they are confined to their homes or are being treated in the hospital. We come across asymptomatic people: some are not yet sick but are already contagious, others who will never have symptoms. We, therefore, multiply the number of infectious people by the percentage of asymptomatic people, to estimate how many contagious people we are likely to come across.

For those who prefer the equations, see the Calculator below and the text to the right of the results on Coronavirus Carriers in Paris, Lyon, Marseille, Toulouse, and France.

**Do the math for YOUR city or country!**

You can estimate yourself the number of people infected in your city, region, or country today, if you have ICU entry data for two weeks. Just enter these numbers as well as the population size in the Calculator below (data for France: Réa-GéoDES; for other countries: OurWorldInData).
It takes a bit of time because it is necessary to input the entries of Réa over 15 days into this interactive table in order to calculate the regression. And don't forget to include the population size! This calculator also allows you to change the values of the parameters if you want to test how this changes the results.
Click to see this **CALCULATOR Covid** (read only. To use, copy or download it).

- If you have a Google account, copy this calculator into your Google Drive with COPY
- Otherwise, open the calculator and then, at the top left of the page, click "File" then "Download" to recover it on your hard drive in Excel or OpenDocument format.

**What are the limitations of this estimator?**

This estimator is not a sophisticated model like those used by epidemiologists who advise governments by projecting the evolution of the epidemic over several weeks: it simply answers a simple question, for the very day of the calculation. Here are some of its limitations.

- This estimator takes many parameters into account. If these parameters are misestimated in the scientific literature, the final estimate will be biased. For example, if the true case-fatality rate of the infected was 0.4% instead of 0.5% (used here), the number of infectious persons would be underestimated by 20%.
- Another limitation is that the case-fatality rate varies according to age and country. During the summer, it was mostly young people who were infected, and this may have lowered the actual case-fatality rate. See the question
**The management of patients with COVID-19 has it gotten any better?** - Another limitation is the validity of the input data from the ICU. Resuscitation is not necessarily counted in the same way in different countries. There is resuscitation in the strict sense of the term, reserved for patients with multiple vital failures, intensive care for those with a single failure, and continuous monitoring of those at risk of vital failure (in France, the three cases are grouped together in the ICU value). In France, all hospitalized persons are tested for SARS-CoV-2 and are counted in the ICU even if they have gone to hospital for a reason other than COVID-19. This may lead to a slight overestimation of the ICU value.
- Finally, the number of infectious persons is extrapolated over 11 days from the data. If the extrapolation curve was wrongly estimated, this would lead to significant errors in the number of contagious people on the street. This extrapolation is a weakness of the model, especially when there are very few entries in the ICU: in a small region or if the epidemic is almost contained, on a curve with almost zero slope, the appearance of a cluster of contagion would be modelled by a very fast growing exponential, whereas if it is identified and well monitored, it will be quickly controlled.

This calculation also presents the limits detailed in the question **What is the risk of interacting with a COVID person in a group, knowing the incidence rate?**.

In conclusion, the calculations presented here give a rough idea of the number of contagious people around us. This number should not be taken as an exact value, but rather as within an order of magnitude. The original version of this model is presented on the website of its authors, Florence & Denis **Corpet: How many infectees are in my town?**

__Sources__

A multicenter cohort study on hospitals in France, Belgium, and Switzerland followed more than 4,000 patients admitted to intensive care units between the end of February and early May 2020. Mortality (estimated at 90 days) of ICU patients fell steadily from 42 to 25% during this period (Table S5), with an average case-fatality rate of 31%. The mean time between the first symptoms and entry into the ICU was eight days in this study for patients who eventually died from COVID-19 (Table 1, line 13, coL4).

COVID-ICU group, for the REVA network and the COVID-ICU investigators. (2020) Clinical Characteristics and Day-90 Outcomes of 4,244 critically ill adults with COVID-19a prospective cohort study... Intensive Care Medicine DOI: 10.1007/s00134-020-06294-xThis large-scale Italian study evaluates risk factors for mortality among intensive care unit patients in Lombardy, Italy. We used it mainly to find out that there are seven days between the first symptoms of a person who is going to die from Covid-19 and entry into resuscitation (Table 3, line 16, col.3, of the article).

Grasselli, G., Greco, M., Zanella, A., Albano, G., Antonelli, M., Bellani, G., ... & Cattaneo, S. (2020). Risk factors associated with mortality among patients with COVID-19 in intensive care units in Lombardy, Italy. JAMA internal medicine, 180(10), 1345-1355.In a review and meta-analysis of 24 observational studies, the English authors follow the fate of patients in intensive care units (ICU) in Asia, Europe, and North America. We used the percentage of mortality of patients in European intensive care units, 48.44% out of seven studies (Fig.3 of the article), whereas at the global level it is 41.65%.

Armstrong, R. A., Kane, A. D., & Cook, T. M. (2020). Outcomes from intensive care in patients with COVID-19: a systematic review and meta-analysis of observational studies. Anaesthesia,75(10), 1340-1349.Thomas PUEYO published on "Medium" on March 12, 2020 an article viewed over 26 million times. With a simple model, he demonstrates that a catastrophe is imminent. In mid-March, he called on heads of state and business leaders to act very quickly to limit contagion. The exponential growth in the number of sick people was seriously threatening the whole world. The equations in his model were classical, hardly debatable, and available in an online table. We used his basic ideas and the simplest of his equations, but not his epidemic model, which we believe no longer applies today. Thomas Pueyo is an engineer, his paper, which he alone signed, is not published in a scientific journal.

https://medium.com/tomas-pueyo/coronavirus-agissez-aujourdhui-2bd1dc7838f6The article by Salje et al. describes the state of the epidemic in France during the first wave, and proposes a case-fatality rate of 0.5% of infected persons, which we have retained in our calculations (with the correction of June 26, 2020, published on the Science website).

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. Science.Levin et al. show in their meta-analysis that the case-fatality rate depends very strongly on the age of the patients, and will therefore be different in older (e.g., European) and younger (e.g., African) populations. This is why the interactive calculator we propose allows to change all parameters, including the case-fatality rate.

Levin, A. T., Hanage, W. P., Owusu-Boaitey, N., Cochran, K. B., Walsh, S. P., & Meyerowitz-Katz, G. (2020). Assessing the Age Specificity of Infection Fatality Rates for COVID-19: Systematic Review. Meta-Analysis, and Public Policy Implications. medRxiv, 2020(2023.20160895).The online journal Coronavirus Fact-Checking Taskforce (https://zici.fr/49) discusses the duration of infectivity in the section "Infectious period: what is its duration?". It is, by definition, the number of days when infectivity is more than 50% of its maximum. Thus defined, it lasts nine days. Among the studies that allow this number to be put forward is that of Wölfel et al. which shows that viral RNA from nasopharyngeal samples can no longer infect cells in culture after 8 days.

Wölfel, R., Corman, V. M., Guggemos, W., Seilmaier, M., Zange, S., Müller, M. A., ... & Hoelscher, M. (2020). Virological assessment of hospitalized patients with COVID-2019. Wölfel Nature, 581(7809), 465-469.In the Italian municipality of Vo' (3,400 inhabitants), almost the entire population was tested by PCR twice, at the end of February and at the beginning of March 2020, for coronavirus carriage. 42.5% of the people infected with the virus were asymptomatic carriers.

Lavezzo, E., Franchin, E., Ciavarella, C., Cuomo-Dannenburg, G., Barzon, L., Del Vecchio, C., ... & Abate, D. (2020). Suppression of a SARS-CoV-2 outbreak in the Italian municipality of Vo'. Nature, 584(7821), 425-429.In England, the results of a large survey conducted in June 2020 on 36,000 non-hospitalized people show that 115 had a positive PCR test on the day of collection, and that 88 people who tested positive were asymptomatic on that day, or 76.5%. If we look specifically at those with COVID-19 symptoms, this percentage rises to 86% on the day of the test.

Petersen, I., & Phillips, A. (2020). Three Quarters of People with SARS-CoV-2 Infection are Asymptomatic: Analysis of English Household Survey Data. Clinical Epidemiology, 12, 1039.