Research Themes
Here is a brief presentation of my main research
topics.
Structured Models and Delay Equations.
Structured equations are partial differential equations in which the
main variable depends upon several "structures": time, for evolution
equations, but also space, age, size, maturity, and so on.
I focus on properties of hyperbolic structured partial differential
equations, usually age-structured equations, and in particular on their
stability (local, asymptotic). Age-structured hyperbolic systems can
sometimes reduce, by integration over the age variable, to delay
differential equations. Study of delay equation stability, either for
discrete delays or distributed delays, or several delays, or state-dependent
delays, is one of my main concerns about delay equations, especially
the existence of bifurcations and the study of the bifurcations.
Multi-scale Modelling of Erythropoiesis. The
term erythropoiesis denotes a set of process controlling differentiation,
proliferation and maturation allowing the production of red blood cells.
Hematopoietic stem cells produce, by division, cells committed to a
differentiation pathway (the red lineage), yet immature (progenitors)
that will produce, in turn, by differentiation and maturation red blood
cells.
I am interested in multi-scale modelling of erythropoiesis, that is
the development of erythropoiesis models accounting for events at the
molecular level (competition between proteins to trigger either
differentiation, death, or proliferation) and at the cell population
level. The models I focus on are deterministic and represented by
systems of structured nonlinear partial differential equations (the
structure variable being either age or maturity), or delay differential
equations (the delay appears through cell cycle durations usually).
This work is funded by the Agence Nationale de la Recherche,
through the project ProCell
that I supervise.
Multi-scale Modelling of Immune Response. In
collaboration with immunologists from the U851 INSERM (Jacqueline Marvel,
Christophe Arpin), and with Olivier Gandrillon, biologist
at the CGMC UMR 5534
(University Lyon 1), I am actually working on modelling of the CD8
immune response.
Confronted to a pathogen, the immune system reacts and the
adaptive immune response activates naive CD8 T cells, that proliferate
and acquire cytotoxic functions (they become effector cells, also known
as killer cells), and eliminate the pathogen. After reaching a peak, the
number of CD8 T cells drastically decreases and the whole process
generates "memory" cells. These latter will be able to react faster and
more efficiently when the pathogen is presented again.
This work is performed through the PhD thesis of Emmanuelle Terry,
co-supervised by Olivier Gandrillon and myself.
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