A mathematical model for inflammation and demyelination in multiple sclerosis

Multiple sclerosis (MS) is an incurable, life-long disease caused by the demyelination of neurons in the brain and spine. MS is often characterised by relapses in inflammation and demyelination, that are then followed by periods of remittance. Symptoms can be highly debilitating and there are still many open questions about the origin and progression of the disease. Mathematical modelling is well-placed to capture the dynamics of MS and provide insight into disease aetiology. In this work, we present a minimal model for MS disease onset and progression driven by inflammation and demyelination. The model dynamics are capable of describing a typical evolution of the illness, with changes from a healthy state to a diseased scenario captured by certain ranges of parameter values. Our model also describes the non-uniform oscillatory nature of the disease, born from a Hopf bifurcation due to the strength of the inflammatory response. In particular, using experimental data for Contrast Enhancing Lesions (CELs) obtained from MS patients, we are able to reproduce some of the typical relapsing-remitting behaviours of this disease. We hope that the model presented here can serve as a baseline for more complex approaches and as a tool to predict possible evolutions of the disease.