A New Mathematical Model for Eye Vision Disability Dynamics: Investigation of Visual Acuity, Lens Power, Pupil Diameter, and Environmental Factors

This study presents a mathematical model to understand the dynamics of eye vision disability, incorporating key physiological and environmental variables such as visual acuity, lens power, pupil diameter, and environmental influence. The novel model developed in this work consists of four state variables that describe their interactions, aiming to simulate changes in visual acuity and the progression of vision disability under different circumstances. Various mathematical aspects including positivity and equilibrium points along with local and global stability are demonstrated. In addition, the sensitivity analysis is also presented to examine the impact of variations in parameters on the model’s outcomes, highlighting the factors that significantly influence visual acuity and pupil adjustments. Furthermore, the phase portraits explore the dynamic interactions between variables, revealing different insights into the stability of the system and adaptive responses. These results provide a thorough understanding of factors influencing eye vision, offering new insights into vision disability dynamics through an integrated, non-autonomous model and practical applications in developing corrective strategies.