Impulsive simulation model for the analysis of allergy dynamics

Abstract

This work approach the analysis of the problems caused by the incidence of allergic diseases, using an impulsive simulation model as a methodological approach, in this, the dynamics of the model is governed by two time scales, one discrete and the other continuous which represents the interaction dynamics among pollen allergens, immune system and intestinal microbiota, evidencing the variable regulation of the Thymus by sending mature T lymphocytes into the bloodstream as a pulse. Due to the complexity of the interacting systems, scientific computing is used to represents a model at the microscopic level where the particles obey a simplified dynamic. To carry out the simulations, the values of parameters used are taken from secondary sources. The scenarios described in the simulations show the behavior of helper T cells, these being an indicator of allergic reactions. The model shows that the intestinal microbiota helps Treg cells in the inhibition of the immune response, also showing that if there is a high concentration of bacteria produced by the ingestion of functional foods, it is possible to control the allergic symptoms.

Simulation Model for Hashimoto Autoimmune Thyroiditis Disease

“…The mathematical model construction assumed a dynamic interaction between thyrocytes, the immune system, and the gut microbiota, which are represented in a system of 4 differential equations that describe the autoimmune dynamics of HT. This system is based on the hypothetical-deductive nature of mathematical modeling ( 42 ). The variables and parameters that compose this model describe the dynamics interactions of the cellular immune response and the development of this autoimmune disease.…”

Impulsive simulation model for the dynamics of allergen immunotherapy

“…This study presents a mathematical model that describes allergen immunotherapy treatment in people with pollen allergies. The methodology based on a hypothetical-deductive structure typical of mathematical modeling [16,17] where the selection of variables, parameters and the conjecture of the relationships in the interaction dynamics between lymphocytes T h 0 , T reg and T h 2 . This allows the construction, simulation and interpretation of a model based on impulsive differential equations that describe said treatment.…”