Stability analysis of a mathematical model for methimazole dosing in graves' hyperthyroidism: A dynamic approach

Jasmine D and Lavanya G *

Department of Mathematics, Bishop Heber College, (Affiliated to Bharadhidasan University), Trichy,Tamil Nadu, India.
 
Review
Journal of Science and Research Archive, 2024, 12(01), 3025–3040.
Article DOI: 10.30574/ijsra.2024.12.1.1099
 
Publication history: 
Received on 05 May 2024; revised on 25 June 2024; accepted on 28 June 2024
 
Abstract: 
This study explores a novel mathematical model for analyzing methimazole (MMI) therapy in patients with Graves' disease, a common autoimmune cause of hyperthyroidism. The model leverages a system of ordinary differential equations to capture the interplay between key factors: methimazole concentration, thyroid-stimulating hormone (TSH), free thyroxine (FT4) concentration, thyroid-stimulating hormone receptor antibody (TRAb) concentration, and functional thyroid gland size (V). Thirteen parameters account for the underlying physiological processes. Stability analysis were employedby Lyapunov stability theory and LaSalle's principle, to demonstrate the model's asymptotic stability. This implies the system converges towards a steady state under defined conditions. Additionally, a clinically relevant chart is constructed based on FT4 levels and treatment duration.For model validation, patient data is utilized within SimBiology simulations implemented in MATLAB. These simulations offer valuable insights into the dynamic response of hyperthyroidism to MMI treatment. This approach holds promise for future applications in optimizing treatment strategies and facilitating personalized medicine approaches.
 
Keywords: 
Hyperthyroidism; Methimazole; Graves’ disease; Ordinary Differential Equations; Stability
 
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