Post-doctoral position in mathematics: vaccination on large graphs

The candidate will, in collaboration with the project members,
develop some or all of the following questions.

Optimal vaccination: back to finite dimension
For a certain class of models, it is known that optimal vaccinations are the ones that target the most connected individuals. However, identifying these individuals may not be so easy if the underlying graph is unknown. One can then use a statistical procedure to estimate connectedness, and build a strategy from this estimation. The goal will then be to see how much is lost by this approximation, and how far the corresponding strategies are from optimality.

- Vaccination depending on time
The previous works of the team on this subject focus on the vaccination models "at time zero", where vaccination modifies the underlying graph by removing nodes, and the infection model is then run on the modified, but fixed, graph: we will try and generalize our results to time-dependent vaccinations.

- Other epidemiological models
The previous questions will first be studied on the SIS model, but may then be also considered on other disease transmission models like SIR or SEIR.

The Covid-19 pandemy, evolving on a social network of approximately 8 billions nodes, showed the importance of epidemiological modelling. Many models exist and many simulations are made, but their robustness may not be entirely clear when they are applied on such large and heterogeneous graphs. Rigorous mathematical analysis of disease propagation models on large graphs helps discerning general principles that could, in the long run, inform vaccination policies.

The aim of this project is to pursue the analysis of such models, building on the theory of graphons, viewed as continuous approximations of large dense graphs. The main goal is to get a better understanding of how vaccination strategies can be adapted to the heterogeneity of the network.

The candidate will work in LAMA, UMR 8050, Univ. Gustave Eiffel (Champs-sur-Marne campus, east of Paris). The work will be in collaboration with researchers from two places: J.-F. Delmas (Ecole des Ponts ParisTech, CERMICS) and P.-A. Zitt (Univ. Gustave Eiffel, LAMA) in Champs-sur-Marne ; P. Frasca (CNRS, GIPSA-lab) and F. Garin
(INRIA, GIPSA-lab), in Grenoble. Meetings between the two teams will principally be held online, after a kick-off meeting.