Section: New Results

Growth, evolution and regeneration in populations and tissues

Amyloid disease

With Wei-Feng Xue in Canterbury, we continued to investigate the intrinsic variability among identical experiments of nucleation  [78], [90], with recent results in [13].

Making use of data assimilation and statistical methods  [52], we proposed new models and mechanisms and most recently we predicted the existence of several coexisting species of protein fibrils [2].

Dengue fever

The release of Wolbachia-infected mosquitoes in Dengue infested zones and the study of their propagation may be represented by spatial reaction-diffusion models. When implementing such a method, an important issue concerns the spatial propagation of the mosquitoes: on releasing infected mosquitoes in a given domain (which can be part of a city), the hope is to invade the whole area. The study of this propagation phenomena falls into the study of existence of travelling waves. We proposed in  [125] a mathematical model to study such phenomena and have simplified it to recover a well-known simple bistable system for which existence of traveling wave is known. The study of the probability of success of spatial invasiveness has been performed in  [126], and [41] is devoted to the blocking of the propagation in heterogeneous environment presenting strong enough population gradient. In the previous works, the invasion is installed by large enough impulsive deliveries. Another approach, consisting in igniting the propagation by feedback control, has been studied in  [63], [6].

Toxicity extrapolation from in vitro to in vivo

The investigation of this field has been continued by Géraldine Cellière, leading to her PhD defense in June 2017  [71].