Keywords : 

Biomathematical models in microbial ecology, modeling, numerical analysis, dynamic systems, data analysis

Scientific background :

Microbial communities in the human body, including bacteria, phages, viruses, and fungi, form the human microbiota. These microorganisms are present in organs and tissues, creating various ecosystems, such as digestive, cutaneous, pulmonary, and vaginal microbiota. As a result, the human body is an ecological unit consisting of different ecosystems of microorganisms and human cells. Human health and physiology rely on the constant and mutual interactions between the host cells and microbiota. For instance, digestion and protection against pathogens are carried out by both human cells, such as epithelial and immune cells, and the intestinal microbiota. The gut microbiota, mainly consisting of more than 500 different bacterial species, live in a community whose relative abundance can change constantly due to diet. 
The intestinal mucosa, composed of immune and epithelial cells, is the first layer of cells that separate the microbiota from the inner environment. Mucus, a gel-like substance composed of complex glycoproteins, lines the epithelium, preventing direct contact between cells and bacteria. Dysbiosis, a state of imbalance between human cells and microbiota, is linked to pathologies such as inflammatory diseases. Understanding host-microbiota interactions, including the composition, diversity, and metabolic activity of the microbiota and the physiology of the host, is crucial for human and animal health, in order to design effective treatment for these diseases. 
For several years, in silico models of the dynamics of the intestinal microbiota and the digestive physiology of the host have been developed, integrating the knowledge available in the literature and data. Some of these models propose large-scale modeling of the microbiota within the colon including a more or less detailed description of the host, while others propose microscale modeling of the dialogue between epithelial cells and bacterial metabolites. Very macroscopic models at the host scale have also been published. 
The thesis project aims to interface several models and lay the foundations of a computational framework, also known as digital twin to describe the host-microbiota interaction at different scales. We recall that a digital twin can be broadly defined as a combination of data and a digital model designed to reflect, as closely as possible, a real object - or system - (state, characteristics, behaviour), in order to help decision-making about it. At the microscopic scale, these new developments will involve coupling a distributed spatial fluid mechanics model of the colon with a crypt model, simulating the interactions between the host and the microbiota. In this way, the effects generated at the microscopic scale will influence the behavior of the host’s digestive and cardiovascular systems at the macroscopic scale. The modeling of these macroscopic systems is crucial in order to be able to integrate individual-specific data (personalized models) such as inputs describing the diet or treatments (prebiotics, probiotics, drugs) or biological measurements - analysis of blood samples - which will be compared with the model simulation results.

Candidate background and skills :

The candidate should have a Master’s degree in Applied Mathematics or equivalent.
A strong background in modeling, numerical analysis and deterministic (ODE/PDE) dynamical systems is required. As well, proficiency in scientific programming (e.g. Matlab, R, Python or C++) is recommended. Previous experiences with data analysis, especially at the interface with biology, are very welcome.