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. 

This plat­form, MODCOV19, was set up under full lock­down in France. Quite nat­u­ral­ly, sev­er­al lec­tur­er-cum-research sci­en­tists from the UTC-LMAC Lab. (the Com­piègne Applied Math­e­mat­ics Lab­o­ra­to­ry), inter­est­ed in the prob­lem, were mobilised. 

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. 

A full uni­ver­si­ty pro­fes­sor, Flo­ri­an De Vuyst has been Direc­tor of the Com­piègne Lab­o­ra­to­ry of Applied Math­e­mat­ics (UTC-LMAC) since 2018. With more than 30 per­son­nel – lec­tur­er-cum- research sci­en­tists, asso­ciate pro­fes­sors, tem­po­rary teach­ing and research attachés (ATER), doc­tor­al and post-doc­tor­al stu­dents – UTC-LMAC has two teams. The first, EPIA, is devot­ed to “inverse prob­lems and numer­i­cal analy­sis”; the sec­ond, S2, to “sto­chas­tic sys­tems”. Cur­rent­ly, 6 lec­tur­er-cum­re­search sci­en­tists, are mobilised on Cov­eille, a mod­el­ling project linked to the Covid-19 epidemic. 

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. 

Miraine Davi­la Felipe is a senior lec­tur­er at UTC-LMAC Com­piègne Applied Math­e­mat­ics Lab­o­ra­to­ry (LMAC). She is a mem­ber of the S2 team ded­i­cat­ed, in par­tic­u­lar, to sto­chas­tic mod­els and tools. In oth­er words: mod­els where a degree of ran­dom­ness is intro­duced. She is lead­ing the Cov­eille Project, a mod­el­ling project based on COVID-19. 

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. 

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. 

Le magazine

Novembre 2023 - N°61

Activité physique, nutrition & santé

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