The dynamics of relapses during treatment switch in relapsing-remitting multiple sclerosis

Based on reported trends in relapse incidence among patients with relapsing-remitting multiple sclerosis, an original model for the response to disease modifying therapies is proposed. With a population approach and separate states for patients accounting for their risk of relapses, a system of nonlinear equations is formulated, similarly to established epidemiological models. Different parameters describe the effect of drugs and treatment switch in reducing the frequency of relapses. The model allows for a good fit to previously published data for experiments where different drugs are used. It also shows that different treatments maintain a high degree of similarity, with analogous dynamical features: a pre-treatment increment in relapse frequency leading to a distinct peak, a rapid drop after treatment switch and a plateau corresponding to a new base relapse activity, which seems dependant on the treatment chosen. A sensitivity analysis shows that the uncertainty in the initial proportions of different populations and the frequency of relapses can modify the overall dynamics of the response to treatment. Drugs are observed to induce effects that depend on patient sample's intrinsic characteristics, producing two clearly distinct and independent dynamics of relapse response. This confirms the clinical observation that certain drugs may be overall more successful in lowering the rate of relapses more significantly than others, notwithstanding the fact that patients behave differently across experiments.