Modélisation mathématique de l'inflammation

Inflammation is a fundamental defense mechanism of the human body in response to various external stimuli. It plays an important role in the development and progression of numerous diseases, including cardiovascular disorders, and neurodegenerative diseases. Although each type of inflammatory disease has its own characteristic stimuli, the inflammatory response mechanism is generic. It begins with the recognition of harmful agents by pattern recognition receptors on cell surfaces, followed by the activation of inflammatory signaling pathways. This leads to the release of inflammatory mediators and the subsequent recruitment of immune cells to the region of inflammation. This thesis focuses on the mathematical modeling of the inflammatory process. In particular, it aims to develop a generalized models that capture the key phases of inflammation, namely initiation, development, and resolution, using a system of reaction-diffusion and integro-differential equations. We also demonstrate its applicability to a range of diseases, such as atherosclerosis, Alzheimer's disease, skin diseases, and auto-immune diseases.