Differential Equation Models in Pediatric Growth and Development: An Algebraic and Topological Approach
Keywords:
Pediatric Growth, Differential Equations, Algebraic Structures, Topological Methods, Growth Models, Developmental Dynamics, Nonlinear Systems, Stability Analysis, Mathematical Biology, Healthcare ModelingAbstract
Pediatric growth and development are complex biological processes influenced by genetics, environment, nutrition, and disease. Mathematical modeling offers a structured framework to study these factors. This paper explores differential equation models that capture the dynamics of pediatric growth and development using algebraic and topological tools. Ordinary and partial differential equations are employed to model linear and nonlinear growth patterns, hormonal changes, and the impact of disease. Algebraic structures help in simplifying and solving these models, while topological concepts such as stability, continuity, and fixed-point theorems provide insights into long-term growth behavior and developmental milestones. This interdisciplinary approach aims to enhance prediction accuracy, identify critical developmental thresholds, and support personalized pediatric healthcare.
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