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Asymptotic approach to spatial and dynamical organizations

Periodic Reporting for period 2 - ADORA (Asymptotic approach to spatial and dynamical organizations)

Reporting period: 2019-03-01 to 2020-08-31

Despite the immense progresses made over the last decades in mathematical biology, the multifaceted nature of biological processes still represents an enormous challenge for mathematical modeling.
Technological advances lead to many new experimental observations, which can then be used to improve the accuracy of modeling. As a result, sophisticated mathematical methods have become crucial for addressing the key questions and paradigms in diverse biological systems, for making predictions of the effects of system perturbations and for their control. Examples are numerous and Adora focusses on population of bacteria (as the famous E. coli of medical interest), the mathematical modeling of tissue growth and tumor development, networks of neurones.

Adora focusses on those systems because spatial, social and dynamical organization of large numbers of agents plays an important role for their understanding and control. More precisely, we aim to develop mathematical models, under the form of Partial Differential Equations, able to explain the experimental observations, the qualitative behavior of solutions and to quantify their properties.

The recent COVID-19 pandemic has motivated new research directions in the area of mathematical epidemiology.
A core of mathematical modeling for biological questions has been developed which address many areas of biology, namely
- Darwinian evolution and evolution of dispersal
- Bacterial colonies self-organization and movement by run and tumble
- Mechanical models of living tissues
- Models for neural assemblies based voltage distribution or age distribution

These questions have been developed in an international context and have motivated several teams around the worlds.

They place biology as one of the main front for applied mathematics nowadays.
At this stage, the most remarkable outcomes are
- the development of a new class of kinetic model for processing (chemical) information in bacterial movement
- a successful collaboration with biologist on cell movement and initiation of metatstses
- a new type of estimates for the porous medium equation