WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 21, 2026
Stability Analysis of an Impulsive Differential Equation Model for Bone Metabolism under Estrogen Treatment during COVID-19 Infection
Authors: ,
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Abstract: COVID-19-associated inflammation, immobilization, and altered endocrine signaling can disrupt bone remodeling. We formulate a reduced impulsive differential-equation model for the interactions among parathyroid hormone, active osteoclasts, and active osteoblasts under periodic estrogen intervention. After a quasi-steady reduction of the fast parathyroid-hormone variable, we establish positivity and dissipativity, derive the unique osteoclast-free periodic solution, and obtain its exact transverse Floquet multiplier, which is shown to be exact for the unreduced three-dimensional model as well. Sufficient conditions for global attraction and uniform persistence are proved, and a simple-eigenvalue bifurcation of positive periodic solutions is characterized through the Poincaré map. Analytical sensitivity and constrained pulse-design formulas are confirmed by numerical calculations.
Keywords:
Impulsive mathematical model, bone, COVID-19-associated effects, parathyroid hormone, estrogen treatment, persistence, sensitivity analysis
Pages: 226-237
DOI: 10.37394/23203.2026.21.21