A Novel Mathematical Model for Hearing Disability: Dynamics, Equilibrium Analysis, and Stability

Disability or impairment of any part of the human being is very painful, which not only affects physical shape, comfort, and normal routine but also affects financial situation of one being as well. The proper diagnosis and treatment of impairment prior to the damage of a certain body part are very crucial. This work introduces a new mathematical model to analyze the hearing impairment by combining key rehabilitative factors. The proposed model is comprised of four classes: hearing ability, ear damage, neurological signal transmission efficiency, and rehabilitation efforts. The aforementioned variables are modeled through system of differential equations. The equilibrium points including disease free and endemic equilibrium are also derived and analyzed. Local and global asymptotically stability analyses of the model based on equilibrium points are demosntrated. The numerical simulations are carried out via RK4 method to show the dynamics of the proposed model. The numerically simulated results show that when R 0 < 1, the system tends toward recovery and a healthy state. Conversely, if R 0 > 1, hearing impairment persists despite rehabilitation efforts. The proposed model provides theoretical framework to understand the interplay of biological and external factors affecting hearing health.