An Ordinary Differential Equation Model for Hearing Threshold Dynamics Under Aging and Noise Exposure
Year: 2026
Type: article
Abstract: Background: Hearing loss is a major and growing public-health challenge, driven by an aging population and by noise exposure that is, in principle, preventable. Longitudinal audiometric studies show that hearing thresholds deteriorate progressively across adulthood, at rates that depend on age, frequency, sex, and exposure history. Methods: We develop a continuous-time ordinary differential equation (ODE) framework for hearing-threshold progression that incorporates age-related degeneration, dynamic noise exposure, exposure clearance, threshold saturation, and protective intervention, with hearing threshold H(t), effective noise burden N(t), and chronological age a(t) as state variables. A closed-form solution is derived for a simplified linear regime, and the full coupled system is integrated numerically using fourth-order Runge–Kutta (RK4) over a 30-year horizon. Five exposure/intervention scenarios are evaluated, followed by stability, sensitivity, and parameter-estimation analyses. Results: During revision, independent recomputation uncovered and corrected inconsistencies between the originally reported hearing-threshold values and the stated differential equation; the corrected values are used throughout. Under the specified parameters, the 30-year threshold reaches 27.98 dB HL for low exposure and 51.43 dB HL for sustained high exposure, whereas 50% protection introduced at year 10 limits the year-30 threshold to 42.74 dB HL. The RK4 solution agrees with the matching analytical solution to within a maximum absolute error of roughly 1.03 × 10⁻¹⁰ dB HL.Conclusion: We present the framework as a transparent tool for hypothesis generation, trajectory simulation, and future calibration against longitudinal audiometric datasets, rather than as a clinically validated predictive tool pending external validation.
Authors: Amgad Bobaker, Emad Awadh
Institution: Tobruk University
Language: English
Subfield: Sensory Systems
Field: Neuroscience
Domain: Life Sciences
Open Access status: diamond
OpenAlex ID: W7213935751