On the effect of remyelination in a mathematical model of multiple sclerosis

Abstract

In the present work, we consider a mathematical model of multiple sclerosis, extending a model, known in the literature, so that it can account for the process of remyelination. Our model comprises of a reaction-diffusion-chemotaxis system of partial differential equations with a time delay. As a first approximation, we consider the model under the assumption of radial symmetry, which is consistent, e.g., with Baló's concentric disease. We conduct numerical experiments in order to study the effect of the remyelination strength on the disease progression. Furthermore, we show that the modified model has greatly enriched dynamics, which is capable of describing qualitatively different types of multiple sclerosis (according to classical classifications of the disease progression) as well as giving a better agreement with experimental data.