A simple mathematical model for Guillain–Barré syndrome

Autor:	Mohammed Fathy Elettreby, Elsayed Ahmed, Muntaser Safan
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Guillain–Barré syndrome Steady states Stability analysis Tolerance Flare-up Dormancy Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-18 (2019)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-019-2146-9
Popis:	Abstract In this paper, four different forms of a model to describe the dynamics of autoimmune diseases (with emphasis on Guillain–Barré syndrome) are proposed. In the first two cases, the immune response is supposed to be linear, while in the other two cases it is supposed to be in the Holling type III form. In case of linear immune response, the model has a basic reproduction number and shows forward bifurcation. However, in the nonlinear Holling type III immune response cases, the model does not have a basic reproduction number and two positive equilibria do exist for a range of the parameters. The stability analysis of the model’s steady states has been established. Our analytical results have been illustrated by numerical simulations.
Databáze:	Directory of Open Access Journals
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