MUSCLEES is the evolution of the MAMBA Inria project-team, headed by Marie Doumic (now head of the Inria project-team MERGE in Saclay) during 9 years (2014-2022); which was in turn a continuation of the BANG Inria project-team, headed by Benoît Perthame during 11 years (2003-2013). Just as its scientific ascendants, this new project-team aims at developing, analyzing, controlling, observing, identifying and simulating models involving dynamics of phenomena encountered in various biological systems.

Overview

The nature of the populations involved in different biological systems is very diverse, as well as the nature of the interactions between their members. They may contain chemical species, cells, molecules, neurons, bacteria, (human or animal) individuals. We are interested for example in cell motion, (physiological or tumor) cell development, binding/unbinding of macro-molecules, bacteria micro-colony growth, tissue development, repair and ageing, epidemic spread, vector control, together with methodological questions related to these questions.
In accordance with the context, we develop stochastic or deterministic models, systems of ordinary (possibly defined on graphs) or partial differential equations, and agent-based approaches. Another part of the team activity is devoted to the link between models of different types, exploring the behavior across different scales and developing tools from control theory to treat issues of (optimal or non-optimal) control, state observation or parametric identification.

The MUSCLEES project-team gathers researchers with complementary skills and interests in applied math-
ematics (partial differential equations, stochastic processes, control theory). Our goal is to incorporate the
different knowledges present in the team as well as expertise obtained from first hand collaborators specialists of the considered applications, in order to provide firm mathematical ground to the representation, understanding, numerical assessment and control of the biological systems of interest. As a peculiarity, we also intend to locate these questions in the larger framework of analysis methods. We will always attempt to unify as much as possible the specific application domains within a common formalism, with scales ranging from individual decision to collective behaviour. Altogether, the team ambitions to provide a deep Mathematical Understanding across Scales of Complex Living Ecosystems with Emerging Structures, whence the acronym: MUSCLEES.

Research directions

• Multiscale study of interacting particle systems
• Stochastic models for biological systems
• Theoretical analysis of nonlinear partial differential equations (PDE) modelling various structured population dynamics
• Mathematical epidemiology
• Development and analysis of mathematical models for biological tissues confronted to experimental
  data