MATHEMATICAL STUDY OF THE SPREAD AND BLOCKING IN INFLAMMATORY BOWEL DISEASE
Résumé
Ulcerative colitis (UC) and Crohn's disease (CD) are chronic inflammatory diseases that affect the digestive tract, causing daily discomfort. Although symptoms are similar, the modes of disease propagation are different. CD spreads discontinuously and excavating along the digestive tract, while UC spreads continuously and superficially, affecting a uniform area from the rectum to different parts of the colon. In our research work, we are interested in studying a mathematical model of inflammation caused by Inflammatory Bowel Disease that has been developed by Nadin and al. in the Journal of Mathematical Biology in 2021 with modifications. It is a reaction-diffusion system governing the dynamics of a pathogen in interaction with immune cells. The first study focuses on the existence of propagation waves for such a system in a homogeneous medium, the second study focuses on blocking these waves in a heterogeneous medium. We will use numerical simulations to highlight these theoretical results.
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