Aggregation, Spatio-Temporal Structures and Well-Posedness in Chemotaxis Models of Inflammatory Diseases

Inflammation is the body's immune response to outside threats and traumas, aiming to prevent the insurgence of diseases. Although it is a protective mechanism, a derangement of the inflammatory response can lead to severe and debilitating diseases, such as Multiple Sclerosis. For this reason, understanding the mechanisms driving an inflammatory response has become one of the biggest challenge in immunology. The subject of this Thesis is the study of mathematical models aiming to explore the mechanisms of the inflammatory response and the resulting clinical patterns. Our aim to prove that the proposed models, within biologically relevant ranges of the parameter values, are able to reproduce different pathological scenarios observed in patients.