BioMaths Colloquium Series – 2023/24
1 November 2023 – 1pm
Online only (register here for Zoom link)
Application to Multiple Sclerosis of a reaction-diffusion system with chemotaxis derived from kinetic models
We present the latest results in studies modeling anomalous immune responses, which extend the work proposed in the literature . These models provide a description of the dynamics over time of a large number of interacting cells within an autoimmune framework, utilizing the tools of the kinetic theory of active particles. We describe a spatio-temporal model, considering the motion of immune cells stimulated by cytokines  and applying it to a specific case of autoimmune disease, Multiple Sclerosis . We derive macroscopic reactiondiffusion equations for the number densities of the constituents with a chemotaxis term. A natural progression is to study the system, exploring the formation of spatial patterns through a Turing instability analysis of the problem, and basing the discussion on microscopic parameters of the model. In particular, we observe spatial patterns that reproduce the brain lesions characteristic of the pathology during its different stages.
 R. Della Marca, M. P. D. Machado Ramos, C. Ribeiro, A. J. Soares, Mathematical modelling of oscillating patterns for chronic autoimmune diseases. Math.l Meth. Appl. Sci., 45(11), 7144-7161 (2022)
 J. Oliveira, A. J. Soares, R. Travaglini, Kinetic models leading to pattern formation in the response of the immune system. Special Issue of Rivista di Matematica dell’Universita di Parma in memory of Giampiero Spiga. (Accepted for publication)
 J. M. S. Oliveira, R. Travaglini, Reaction-diffusion systems derived from kinetic models for Multiple Sclerosis. arXiv preprint arXiv:2309.05119