Section: New Results

Analysis and control for population dynamics

Time asymptotics for nucleation, growth and division equations

We revisited the well-known Lifshitz-Slyozov model, which takes into account only polymerisation and depolymerisation, and progressively enriched the model. Taking into account depolymerisation and fragmentation reaction term may surprisingly stabilisde the system, since a steady size-distribution of polymers may then emerge, so that “Ostwald ripening” does not happen [33].

Cell population dynamics and its control

The question of optimal control of the population dynamics, that naturally arises when dealing with anticancer drug delivery optimisation, has been specifically the object of [24], work led in common with E. Trélat (LJLL and Inria team CAGE) and published in the J. Maths. Pures Appl.

The asymptotic behaviour of interacting populations in a nonlocal Lotka-Volterra way is also, independently of any control, studied for two populations in this article, and for many in [49].

Mathematical models of infectious diseases

First results in this subject (which is new for the team) have been obtained for elementary models including a model of vector-borne disease [31], [29].