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.
First, individually on the platform MODCOV19, then with the call for expression of interest launched by Marie-Christine Ho Ba Tho, Director of Research at UTC. Immediately, 3 “pairs” of lecturer-cum-research scientists were formed around the Coveille project.
The first two, consisting of Ghislaine Gayraud, professor, Miraine Davila Felipe, lecturer, and Nikolaos Limnios and Salim Bouzebda, both professors, are particularly interested in stochastic models and tools.
In other words, models where factors of randomness are introduced. The last “pair”, with Florian De Vuyst and Ahmad El Hajj, both professors, works on deterministic mathematical models and approaches.
So, what is the aim of COVEILLE? It is to model the dynamics of the Covid-19 epidemic at different levels of granularity of data analysis. In short, models which will be used to help monitor the spread of the SARS-CoV‑2 virus and the risks of secondary upsurges.
After 15 years as a university professor — 8 years at the engineering school, Ecole Centrale Paris in the laboratory of mathematics applied to systems, followed by an additional 7 years at the École normale supérieure de Cachan in the Centre of mathematics and their Applications — Florian De Vuyst came to UTC in 2017, a year before taking over the direction of UTC-LMAC in January 2018.
“Currently, LMAC has 13 lecturer-cum- research scientists, 2 associate professors, 2 ATERs and some 15 PhD students. Within the lab, we work of course on purely theoretical aspects but also on algorithms and more practical applications”, explains Florian De Vuyst. As a host team, LMAC is also a member of the Fédération de mathématiques des Hauts-de-France (FMHF), a CNRS research federation.
What are the specialities of the two research teams? “EPIA works on the problems of “inverse problems”, “partial differential equations” or “numerical model reduction”. Pure deterministic modelling with practical applications in many fields. We can mention the detection of anomalies, medical imaging, fluid mechanics or road traffic, for example. The S2 team is particularly interested in stochastic modelling, characterised by the introduction of randomness, mathematical statistics, data analysis or even machine learning. Theoretical fields which lead to models allowing, among other things, the extraction of knowledge, forecasting under uncertainty, detection of changes in trend, robust estimation, etc. Models applicable, in particular, in the fields of health, physical systems such as mechanics — the study of cracks in a material, for example — the reliability of complex systems, or simply human activity”, he stresses.
What can we see as a LMAC’s strong point? “It is the existence of two teams, one with a socalled “deterministic” approach, i.e., working on so-called “continuous”, homogenised models, and the other with a stochastic approach which is interested in finer samples or scales of time and space. This makes it possible to describe a reality in two different but often complementary ways and to give elements of response in different ways and with different criteria”, details Florian De Vuyst. Far from the image of disembodied mathematics, the UTC-LMAC teams collaborate on concrete applications, particularly with health institutions and industry. “The EPIA team has notably worked with the Amiens University Hospital. The objective was to detect anomalies in the brain or other parts of the body based on the response of living tissue to different types of waves emitted by medical devices. In short, the aim is to reverse the perspective of unintelligible observations or measurements in order to make them intelligible. The team is also collaborating, within the framework of Cifre PhD theses, with the manufacturer Renault on a project to optimise vehicles. A first task related to the problem of making the vehicle lighter while maintaining the same performances or “services”. A second, to come, will concern the reduction of drag, i.e., the so-called CX coefficient, due to air friction. This translates into lower energy consumption,” he explains.
Finally, LMAC has been involved in collaboration with other UTC laboratories. “A joint collaborative platform has been set up with Adnan Ibrahimbegovic of the UTC-Roberval laboratory and a senior member of the Institut universitaire de France. The aim? To work together on joint projects dedicated to digital mechanics. We are also working with the BMBI, particularly with Anne-Virginie Salsac, on problems related to microcapsules and their transport in blood vessels. The main objective is to enable innovation in medicine. In particular, we have a PhD student under co-supervision who is pursuing a thesis on model reduction techniques”, concludes Professor De Vuyst.
It was after a call for expressions of interest (CEI) that three pairs, presenting jointly skills in deterministic and stochastic approaches and tools, were formed within LMAC to work on Coveille. “I’m the most recently arrived colleague at UTC in 2019. The fact that my colleagues chose me to lead this project touches me enormously, because they are showing, by this gesture, a great mark of confidence in me”, assures Miraine Davila Felipe.
It was while she was teaching at the University of Havana, Cuba, that the idea of coming to France first occurred to her. What triggered this? “Well, I met French research scientists from the École polytechnique visiting my university and was won over by the quality of mathematical research in France. This motivated me to apply for a Master 1 in Applied Mathematics at the same school. I was selected and won a scholarship. I continued with a joint Master 2 at Ecole Polytechnique and Paris VI — Sorbonne University — in mathematics applied to biology. This enabled me, during an internship at Télécom Paris, to gain initial experience in epidemiology. In particular, I worked on methods for estimating rare events in the case of communicable diseases, which could possibly lead to crisis situations from a public health point of view,” she explains.
Hence her interest in epidemiology. She then went on to complete her PhD within a multidisciplinary team of biologists, mathematicians, statisticians and probabilists, led by a professor from Paris VI at the Collège de France.
The theme of this thesis? “I worked on phylodynamic models, a relatively recent field of research. The aim is to study the spread of diseases in the population using the genetic data of the pathogen — virus or bacterium. These are models used particularly for diseases such as flu’, HIV or Ebola, characterised by a high mutation rate of the pathogens involved. Finding different genetic sequences of a given pathogen in patients allows us to reconstruct the transmission tree. In a nutshell: to say who infected whom over time, provided we have enough data to reduce uncertainty,” says Miraine Davila Felipe.
This is a new field of research that makes it possible, for example, to estimate the date of the beginning of the epidemic and which research scientists are trying to apply to Covid-19. In this, they are helped by the emergence of sampling techniques that are fairly quick and inexpensive compared to what existed previously. “Currently on Covid-19, there is a site on which nearly 10 000 patient genetic sequences are stored. It should be noted that each individual hosts a certain number of viruses, with, however, always one that is over-represented. In general, it is the one that is most likely to be transmitted. Hence the possibility, thanks to the signature left by the virus, of reconstructing, with the help of statistics, phylogenetic trees of transmission. Of course, there are still many uncertainties, but this nevertheless allows us to make estimates in relation to the evolution of epidemics. We can thus estimate the reproduction rate of the virus or R0,” she points out.
This is a field of research that she explored further during her post-doc at the Institut Pasteur from 2017–18 and then as a temporary teaching and research associate at the University of Nanterre, which she has been pursuing since her arrival at the UTC. “I have developed this type of model from a mathematical point of view and have obtained fairly robust theoretical results from an epidemiological point of view. The idea is to couple two very different but highly correlated variables: the dynamics of the epidemic at the population level, through the curves of patients over time, and the genetic dynamics of the virus thanks to mathematical transmission trees. We thus have dual sourced information”, concludes Miraine Davila Felipe.
Finally, this is a field of research that she intends to apply, with other colleagues, at Coveille, a transverse project based on the modelling of Covid-19.
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.
