Qualitative Properties and Stability Analysis of Autonomous and Non-Autonomous Longitudinal T2DM Models

Abstract

In this paper, we investigate the qualitative properties, long-term dynamic behavior, and stability of a longitudinal mathematical model describing the progression of Type 2 Diabetes Mellitus (T2DM). We significantly extend and refine the mathematical analysis of the model recently proposed by De Gaetano et al. (Journal of Theoretical Biology, 2024). Specifically, we analyze both the autonomous system with a fixed age parameter and the non-autonomous system incorporating explicit time-dependent aging dynamics under generalized conditions, providing rigorous proofs for global existence, uniqueness, positivity, asymptotic bounds, and stability properties.