Stability Analysis in a Mathematical Model for Allergic Reactions

Stability Analysis in a Mathematical Model for Allergic Reactions

We present a mathematical model that captures the dynamics of the immune system during allergic reactions. Using delay differential equations, we depict the evolution of T cells, APCs, and IL6, considering cell migration between various body compartments. The biological discussions and interpretatio...

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Veröffentlicht in:Axioms 2024-01, Vol.13 (2), p.102
Hauptverfasser: Abdullah, Rawan, Badralexi, Irina, Halanay, Andrei
Format: Artikel
Sprache:eng
Schlagworte:
Allergens
Allergic reaction
Allergic reactions
Allergies
Allergy
Analysis
Antibodies
Antigens
APCs
Blood
Chemotherapy
Cytokines
delay differential equations
Dendritic cells
Desensitization
Differential equations
Fatalities
Immune system
immune system dynamics
Immunology
Leukocytes
Lymphocytes
Mathematical analysis
mathematical model
Mathematical models
Partial stability
Stability
Stability analysis
T cells
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Beschreibung
Zusammenfassung:We present a mathematical model that captures the dynamics of the immune system during allergic reactions. Using delay differential equations, we depict the evolution of T cells, APCs, and IL6, considering cell migration between various body compartments. The biological discussions and interpretations within the article revolve around drug desensitization, highlighting one potential application of the model. We conduct stability analysis on certain equilibrium points, demonstrating stability in some cases and only partial stability in others. Numerical simulations validate the theoretical findings.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13020102