Modeling the progression of Primary Open Angle Glaucoma through an Ordinary Differential Equation Framework

Abstract

Primary open-angle glaucoma is a progressive eye disease and a leading cause of irreversible vision loss. The disease is largely categorized by elevated intraocular pressure. Current treatment reduces intraocular pressure and slows disease progression; however, treatment cannot restore vision that has already been lost. Consequently, understanding disease progression is essential for developing more effective treatment strategies. This mathematical model comprises four coupled equations describing the interactions among intraocular pressure, medication concentration, optic stress, and optic nerve health. These coupled dynamics capture how treatment influences pressure regulation and how elevated pressure contributes to progressive vision loss. The model was analyzed through numerical simulations using the classic fourth-order Runge-Kutta method under varying parameter values and initial conditions to investigate disease progression and treatment response. Simulation results demonstrate that maintaining intraocular pressure below the critical threshold sustainably reduces optic stress and preserves optic nerve health, while inconsistent treatment accelerates disease progression. This work also contributes to United Nations Sustainable Development Goal #3: “Good Health and Well-Being”.