Mathematical SEIR Model of the Lumpy Skin Disease Using Caputo-Fabrizio Fractional-Order

UN SD Goal-3 focuses on good health and well-being, while the 15th goal focuses on life on land. This research aims to study an integral model of Lumpy Skin Disease to establish better knowledge of this condition. In this study, a Caputo-Fabrizio fractional-order model for the dynamics of Lumpy Skin Disease (LSD) is analysed. Using the Picard-Lindelöf theorem in the Banach space C([0, 1], R) with the supremum norm ∥ϕ∥ = max_s∈[0,1] |ϕ(s)|, we prove existence and uniqueness of solutions via fixed-point theory. The positivity, boundedness, and Ulam-Hyers stability of the model are established. Disease-free and endemic equilibria are derived, the basic reproduction number R₀ is computed, and sensitivity analysis is conducted to identify critical transmission parameters. A novel Newton interpolation-based numerical scheme is developed and compared with finite difference method, with superior convergence rates being demonstrated. How non-integer operators enhance LSD progression modeling compared to classical approaches is revealed by fractional-order simulations. Actionable insights for disease control are provided by our results while the efficacy of Caputo-Fabrizio derivatives in epidemiological modeling is demonstrated which will help in framing policies to have a healthy society, SDG-3 and other related goals of UN.