Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

• Photoreceptor interaction in degenerative disease is modeled.
• Bifurcation analysis found additional stable modes.
• Sufficient nutrients are critical to have stable modes.
• Model suggests alternative approaches for physiologists.

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.