The cell-to-cell transmission of Guillain-Barre syndromes: modeling and analysis

Abstract

Guillain-Barre Syndrome (GBs) is an autoimmune disease that interchangeability of functions immune cells so the immune cells do not work properly. In people with GBs, immune cells destroy healthy cells, thereby reducing the growth rate of healthy cells. One of the causes of GBs is Zika virus infections. GBs in Indonesia has been around since 1859, but this incident is still rarely identified because the symptoms of leg pain and rheumatism have been complained about by many people with various causes. The epidemiological mathematical model for GBs has been modified, with a focus on cell-to-cell interactions, to study the behavior of the GBs transmission by involving healthy cells, infected cells, and immune cells. The mathematical model has considered the role of immune cells in every healthy cell interaction so it can inhibit the interaction of infected cells with healthy cells. The model created is a system of non-linear differential equations with saturated incidence rates. The mathematical model obtained will be analyzed using a dynamical analysis. The stability analysis around the equilibrium point is studied by analyzing the eigenvalues of the Jacobian matrix at the equilibrium point. In the end, the numerical simulation is analyzed to ensure the analytical result. Then the conclusion from the analysis results is described as a solution to the problem.