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.