DOI: 10.5061/dryad.mcvdnck6d
title: Data from: A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease

description: We introduce and study a new model for the progression of Alzheimer's
 disease incorporating the interactions of Aβ-monomers, oligomers,
 microglial cells and interleukins with neurons through different
 mechanisms such as protein polymerization, inflammation processes and
 neural stress reactions. In order to understand the complete interactions
 between these elements, we study a spatially-homogeneous simplified model
 that allows to determine the effect of key parameters such as degradation
 rates in the asymptotic behavior of the system and the stability of
 equilibriums. We observe that inflammation appears to be a crucial factor
 in the initiation and progression of Alzheimer's disease through a
 phenomenon of hysteresis, which means that there exists a critical
 threshold of initial concentration of interleukins that determines if the
 disease persists or not in the long term. These results give perspectives
 on possible anti-inflammatory treatments that could be applied to mitigate
 the progression of Alzheimer's disease. We also present numerical
 simulations that allow to observe the effect of initial inflammation and
 concentration of monomers in our model.
description: Numerical generations are obtained through Matlab Software by
 using the solver ode45.
description: # A qualitative analysis of an Aβ-monomer model with inflammation
 processes for Alzheimer’s disease Access this dataset on Dryad:
 [https://doi.org/10.5061/dryad.mcvdnck6d](https://doi.org/10.5061/dryad.mcvdnck6d) This data set contains the table of parameters and the codes of the numerical methods applied to solve the bi-monomeric ODE system. The parameter values were chosen just to test the structural variables of our system such as the degradation rate of mononers and the initial concentration of interleukins. ## Description of the data and file structure Parameters.xlsx : Table with test parameter values of the system used in the simulations. We focused on the order of magnitude. The scripts to produce the figures are the following: Bifurcation_d.m : Script to generate the bifurcation diagram for degradation of monomers (Figure 2). This script solves a system of equations to compute the steady states of the systems for different values of the degradation rate of monomers through the fzero method of MATLAB. Critical_I_d.m : Script to generate the critical curve for the initial value of inflammation (Figure 3). This script calculates the critical value by computing the solution of the system with different initial conditions for the inflammation and saving the value when the asymptotic behavior changes from converging to the disease-free equilibrium to a positive steady states where the disease persists. Critical_I_m.m: Script to generate the critical curve for the initial value of monomer concentration (Figure 9). This scripts is the same as the previous ones, but computes the solution with different initial conditions for the monomer concentration to compute the respective critical value. The numerical simulations obtained from this parameters include: -Figure 1: Schematic representation of the model. -Figure 2: Bifurcation diagram of the inflammation at equilibrium in terms of degradation rate of monomers. -Figure 3: Region of asymptotic behavior in terms of degradation rate of monomers and initial value of inflammation. -Figures 4-8: Numerical simulations for the analysis of the effect of inflammation. -Figure 9: Region of asymptotic behavior in terms of degradation rate of monomers and initial value of monomer concentration. -Figures 10-11: Numerical simulations for the analysis of the effect of monomer concentration. ## Sharing/Access information Figures available at: [https://hal.archives-ouvertes.fr/hal-03877951](https://hal.archives-ouvertes.fr/hal-03877951) ## Code/Software Numerical simulations were solved in MatLab R2022a with a classical ode45 solver. We include the codes for generating the bifurcation diagram and the critical curve of inflammation. ## Changelog Version October-2024: Updated the MatLab scripts "Critical_I_d.m" and "Critical_I_m.m" to correctly display asymptotic behavior diagrams.