A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease

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 progr..., Numerical generations are obtained through Matlab Software by using the solver ode45., , # A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease

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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 cu...