A Mechanistic, Stochastic Model Helps Understand Multiple Sclerosis Course and Pathogenesis
Figure 7
Solutions of the mechanistic, stochastic model. The solutions of (4) as a function of time are shown for (a) the symmetric (β = 0) and (b) asymmetric (β = 0.08) double-well potential. In both cases, the control parameter is set to = 1, and a stochastic perturbation of the same variance is applied ( = 0.13). Under the effect of the random perturbation, the state variable (i.e., the health state of a patient in our metaphor) jumps erratically from −1 to +1 and vice versa (a). When a small asymmetry is introduced in the potential , the variable still changes erratically its state but spends more time around −1 than around +1 (b). The latter case appears suitable for describing the random occurrences of relapses in MS as observed in clinical data.
