In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in Lombardo et al. (J Math Biol 75:373-417, 2017). In particular, we hypothesize a minimal amount of macrophages to be able to start and sustain the inflammatory response. Thus, the model function for macrophage activation includes an Allee effect. We investigate the emergence of Turing patterns by combining linearised and weakly nonlinear analysis, bifurcation diagrams and numerical simulations, focusing on the comparison with the previous model.

A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect / Bisi, Marzia; Groppi, Maria; Martalò, Giorgio; Soresina, Cinzia. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 2023, 73:(2024), pp. 29-46. [10.1007/s11587-023-00806-9]

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

Soresina, Cinzia
2024-01-01

Abstract

In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in Lombardo et al. (J Math Biol 75:373-417, 2017). In particular, we hypothesize a minimal amount of macrophages to be able to start and sustain the inflammatory response. Thus, the model function for macrophage activation includes an Allee effect. We investigate the emergence of Turing patterns by combining linearised and weakly nonlinear analysis, bifurcation diagrams and numerical simulations, focusing on the comparison with the previous model.
2024
Bisi, Marzia; Groppi, Maria; Martalò, Giorgio; Soresina, Cinzia
A chemotaxis reaction–diffusion model for Multiple Sclerosis with Allee effect / Bisi, Marzia; Groppi, Maria; Martalò, Giorgio; Soresina, Cinzia. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 2023, 73:(2024), pp. 29-46. [10.1007/s11587-023-00806-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/402245
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