Know more

Our use of cookies

Cookies are a set of data stored on a user’s device when the user browses a web site. The data is in a file containing an ID number, the name of the server which deposited it and, in some cases, an expiry date. We use cookies to record information about your visit, language of preference, and other parameters on the site in order to optimise your next visit and make the site even more useful to you.

To improve your experience, we use cookies to store certain browsing information and provide secure navigation, and to collect statistics with a view to improve the site’s features. For a complete list of the cookies we use, download “Ghostery”, a free plug-in for browsers which can detect, and, in some cases, block cookies.

Ghostery is available here for free:

You can also visit the CNIL web site for instructions on how to configure your browser to manage cookie storage on your device.

In the case of third-party advertising cookies, you can also visit the following site:, offered by digital advertising professionals within the European Digital Advertising Alliance (EDAA). From the site, you can deny or accept the cookies used by advertising professionals who are members.

It is also possible to block certain third-party cookies directly via publishers:

Cookie type

Means of blocking

Analytical and performance cookies

Google Analytics

Targeted advertising cookies


The following types of cookies may be used on our websites:

Mandatory cookies

Functional cookies

Social media and advertising cookies

These cookies are needed to ensure the proper functioning of the site and cannot be disabled. They help ensure a secure connection and the basic availability of our website.

These cookies allow us to analyse site use in order to measure and optimise performance. They allow us to store your sign-in information and display the different components of our website in a more coherent way.

These cookies are used by advertising agencies such as Google and by social media sites such as LinkedIn and Facebook. Among other things, they allow pages to be shared on social media, the posting of comments, and the publication (on our site or elsewhere) of ads that reflect your centres of interest.

Our EZPublish content management system (CMS) uses CAS and PHP session cookies and the New Relic cookie for monitoring purposes (IP, response times).

These cookies are deleted at the end of the browsing session (when you log off or close your browser window)

Our EZPublish content management system (CMS) uses the XiTi cookie to measure traffic. Our service provider is AT Internet. This company stores data (IPs, date and time of access, length of the visit and pages viewed) for six months.

Our EZPublish content management system (CMS) does not use this type of cookie.

For more information about the cookies we use, contact INRA’s Data Protection Officer by email at or by post at:

24, chemin de Borde Rouge –Auzeville – CS52627
31326 Castanet Tolosan CEDEX - France

Dernière mise à jour : Mai 2018

Menu Logo Principal Oniris

Home page

Epidemiological modelling and its use to manage COVID-19

Insights into mechanistic models, by the DYNAMO team

Over the next few weeks, we will present some key elements of epidemiological modelling through short educational articles. These articles will help you to better understand and decipher the assumptions underlying the epidemiological models that are currently widely used, and how these assumptions can impact predictions of the spread of pathogens, particularly SARS-CoV-2. The objective is to discover the advantages and limitations of mechanistic modelling, an approach that is at the core of the DYNAMO team's work. The examples of models will be inspired by models used in crisis, but sometimes simplified to make them accessible.

#2 – What does this model predict ?

To go from the diagram to the model predictions, you need to define :

  • the initial conditions, i.e. how individuals in the population are distributed between the different health states at the beginning of the simulation (at t , the first time step);
  • the values of model parameters.

In the absence of accurate information, as is often the case at the beginning of an epidemic, it is assumed that the epidemic starts with the arrival of a (single) infected individual in a fully susceptible population. Here we consider the arrival of an asymptomatic individual (A) in a population of constant size N. As a reminder (see article #1), individuals in the population are grouped by health status according to whether they are susceptible (S), asymptomatic (A), symptomatic (I), recovered (R), or dead (M). Initially S(t ) = N-1, A(t ) = 1, I(t ) = 0, R(t ) = 0 et M(t ) = 0.

The values of the parameters were chosen to be consistent with the available knowledge on the propagation of SARS-CoV-2, so that on March 16 (with t  = January 1st) there were 148 cumulative deaths (the death toll in France on that date). Of course, this rudimentary model is not intended to be used in the current situation. The figures are mainly there to illustrate our point. Some parameter values may even seem surprising, such as the transmission rate of I's here lower than that of A's. It should not be forgotten, however, that some of the I's see their contacts decrease when they are ill !





Population Size

70 million


Proportion of symptomatic infected at risk of dying



A-transmission rate (per individual per day)



I-transmission rate (per individual per day)



Average time in A (days)



Average time in I (days)



I mortality rate (per day)


Parameter values used to obtain a cumulative number of 148 deaths as of March 16,
the epidemic starting following the arrival of individual A in the susceptible population on January 1st.


Under the assumptions we listed in article #1, and for the initial conditions and parameter values used, the model will predict the headcount by health status over time, as well as the flows between states. It is therefore possible to construct multiple outputs (which the model will calculate for us) depending on what we are interested in. Thus, the epidemic curve provides the date of the epidemic peak, the proportion of individuals affected simultaneously (i.e. prevalence, 20% of the population at the date of the epidemic peak here), the duration of the epidemic (80-100 days here), or the date of reaching a threshold of cumulative number of cases or deaths.

Pourcentage d'individus par état de santé

Epidemic dynamics predicted by the SAIRM model described in article #1,
whose parameters are calibrated as shown in the table above, and with 
as initial conditions 1 asymptomatic individual introduced into a susceptible population,
without any measures to control the epidemic. The grey vertical dotted line indicates March 16.

Let us now zoom in on the period from January 1st (t=0) to March 16 (t=76). We see very little variation in the number of individuals by health status during this period, which marks the beginning of the epidemic in France. We can nevertheless look at the number of new daily cases (also called incidence of infection, i.e. the sum of the flows from state S to states A and I) and the number of deaths (numbers in state M for the cumulative number of deaths; daily flow from state I to state M for the number of new deaths per day).

Nombre de décès cumulés par jour

Evolution of the cumulative number of deaths since the introduction of the virus into the population up to March 16.

Article#3 will discuss the predictive quality of models.