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In this paper, we study a modification of the mathematical model describinginflammation and demyelination patterns in the brain caused by MultipleSclerosis proposed in [Lombardo et al. (2017), Journal of Mathematical Biology,75, 373--417]. In particular, we hypothesize a minimal amount of macrophages tobe able to start and sustain the inflammatory response. Thus, the modelfunction for macrophage activation includes an Allee effect. We investigate theemergence of Turing patterns by combining linearised and weakly nonlinearanalysis, bifurcation diagrams and numerical simulations, focusing on thecomparison with the previous model.

A chemotaxis reaction-diffusion model for Multiple Sclerosis with Allee effect