MATHEMATICAL MODEL OF GUILLAIN-BARRE SYNDROME WITH HOLLING TYPE II FUNCTIONAL RESPONSE

LISA RISFANA SARI1, PUJI ANDAYANI1;∗, AGUS SURYANTO2, ISNANI DARTI2
1Universitas Internasional Semen Indonesia, Gresik City 61122, Indonesia
2Department of Mathematics, Brawijaya University, Malang City 65145, Indonesia

This paper studies the dynamics of the Guillain-Barre syndrome model (GB’s) with Holling type II functional responses. Autoimmune disorders occur when the immune system is damaged where the immune system attacks tissues and organs. It was reported that a viral infection can be related to GB’s. A mathematical model about the mechanism of autoimmunity in GB’s was studied. The immune response used is assumed to follow the Holling Type II functional response. The dynamics of the model are analyzed to see system behavior. The
GB’s model has three equilibrium points in its conditions. The equilibrium represents health, autoimmune disease, and complications. The local stability for each equilibrium point is analyzed with certain stability conditions. Numerical simulations are also performed to observe the dynamic behavior of the model. The results of the model analysis show the factors that determine the outcome of the disease.

Keywords: dynamical behavior; functional response; Guillain-Barre syndrome; Holling tipe II; stability.

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