54: Coveille a structuring project for UTC-LMAC

It was in the context of the ongoing health crisis due to Covid-19 that the National Institute of Mathematical Sciences and their Interactions (INSMI), one of the ten CNRS institutes, decided to set up a platform to coordinate actions involving modelling Covid-19 phenomena.

54: Coveille a structuring project for UTC-LMAC

Forecasting and Monitoring Objectives for the Coveille Project

Six lecturer-cum-research scientists - forming three pairs - are involved in Coveille, a project to model the dynamics of the Covid-19 epidemic at several levels of granularity. The aim of Coveille is to be able to monitor the spread of the virus and warn of the risks of secondary surges.

What are the specific features of the Coveille Project? The involvement of lecturer-cum-research scientists with expertise in mathematical models and approaches, whether deterministic, stochastic or random, who will be supported, from January 2021, by two students on a final internship.

How will the Coveille project unfold? "It consists of three phases: the first involves classical statistical analysis, with Miraine and Ghislaine, the second, with Florian and Ahmad, establishes ordinary differential equations; as for Salim and myself, in a third phase, we will add randomness to the deterministic equation," explains Nikolaos Limnios, a university full professor.

Coveille's research is based on two lines of research, the first dealing with deterministic and random modelling, estimation and quantitative forecasting, and the second with identifying classes of interacting individuals. However, these two axes are in no way disjointed and the success of the project will, they are aware, depend on a permanent dialogue between the three pairs.

The first phase led by Ghislaine Gayraud, university professor, a specialist in mathematical statistics and Miraine Davila Felipe, lecturer, specialist in probability? "With Coveille, we want to develop tools that would allow us to describe the evolution of the pandemic at different levels. Indeed, the great difficulty in epidemics in general, and for Covid in particular, is due to the heterogeneity of the population in terms of age and social background, for example. This, from a mathematical point of view, poses a major challenge. Ghislaine and I are more specifically interested in the contact network of individuals. Our aim is to model the social network through which Covid is likely to spread," explains Miraine Davila Felipe.

"The idea is not to predict who will or will not be infected in the long term, but to be able to monitor and identify clusters within the population based on individuals' contacts. In short: we are more interested in the network of relationships through which the virus will spread than in the transmission itself", adds Ghislaine Gayraud.

What are some characteristic of the models and deterministic approaches of the second phase? "We are working on models that do not take into account the random aspect. In fact, in the deterministic approaches where the theme of "inverse problems" and numerical analysis in general are addressed, we consider that we know very well the parameters used to build the models. Modelling that applies, among others, to mechanics or biology. In this field, several projects have thus been carried out with the Amiens University Hospital, notably on the detection of cancer cells in the human body based on measurements of the electrical brain activity of patients, or the characterisation for epilepsy, a project carried out by the region and on which we collaborated with the mathematics department of the University of Amiens", explains Ahmad El Hajj, university professor and head of the deterministic team.

Prof. Florian De Vuyst, director of LMAC, agrees: "It is indeed a question of characterising a tumour, for example, at a certain place in the body, on the basis of signals or measurements that are not images in the strict sense of the word. This is what we call "inverse problems". In short, it is possible to transform signals that cannot be directly interpreted into intelligible data that can be used to establish a diagnosis”.

Concerning Covid-19, we have the expertise, by taking a direct model of the SARS-CoV-2 virus, to determine infectivity, incubation and death rates, recovery time, etc." These are all epidemiologically relevant variables that can be calculated from observable data such as the number of infected people, hospitalized people, etc. "With Covid-19, we have the expertise, using a direct model of the virus, to determine the infectivity, incubation and death rates, the recovery time, etc. ", he adds.

So what are the possible hazards that could be taken into account in the case of Covid? Based on the previous data available, for example on individuals susceptible to infection, asymptomatic individuals, those with severe symptoms, those with undeclared symptoms and finally those cured or deceased, Florian and Ahmad will propose a deterministic SEIR (Susceptible–Infected–Removed) model enriched with categories that best reflect the reality of the current epidemic. To this model, we are going to assign random disturbances such as the rate of infectivity or the percentage of severely infected people that depend on several factors and cannot be totally controlled in a deterministic way", explains Nikolaos Limnios.

The objectives set for such models? "The first objective is to determine the dynamics and evolution of the virus in the population. However, the development of stochastic models is mainly a response to the need for forecasting. It is a question of being able to say that, if we have a number of patients N at time T, we will have, for example: N X 2 patients at T+10. A reliable forecast is a valuable tool for decision support. In the case of Covid, it would make it possible to decide on the containment of this or that territory or to resize the capacity of hospitals, for example," concludes Salim Bouzebda, university professor, head of the stochastic team.