Optimal Control Strategies for Mitigating Cardiovascular and Type 2 Diabetes Risks in Psoriasis and Psoriatic Arthritis : A Mathematical Model and Numerical Simulations

Resumen

In this study, we investigate a novel mathematical model that describes the dynamics of psoriasis and psoriatic arthritis. The goal of this paper is to mitigate the risks associated with psoriasis and psoriatic arthritis on cardiovascular health and type 2 diabetes through control strategies involving three variables: awareness programs for patients with psoriasis or psoriatic arthritis, medical follow-up, and promoting a healthy and regular lifestyle. We demonstrate the existence of optimal controls and describe them using states and adjoint functions, primarily based on Pontryagin's maximum principle. Numerical simulations for various scenarios validate the effectiveness of the optimization approach.