Mathematical Modelling of Disability Progression in Patients with Multiple Sclerosis

Abstract

The tools of mathematical modelling offer promising possibilities in our attempts to deepen our knowledge of insufficiently well-understood diseases such as multiple sclerosis. In this article we formulate a mathematical model, mainly based on differential equations, while gradually incorporating the needed modifications to the model with the aim of more accurately simulating the typical qualitative behaviours of the different types of MS. The agents active in the disease process are grouped in two main categories—beneficial cells and harmful cells, based on their influence on the nervous system. In this text a deterministic as well as a stochastic model are proposed, with the goal of the stochastic model being a better representation of the observed irregularities in the occurrence of relapses and remissions in MS. The dynamics of the cell types’ concentrations are modelled through the utilization of appropriate periodic functions. The analytical properties of the models are studied and the connection between parameter values, initial conditions and end results is utilized to produce models capable of simulating disease courses with quantitative characteristics in accordance with real-world clinical data.