Mathematical model of the lumpy skin disease using Caputo fractional-order derivative via invariant point technique
Gunaseelan Mani, Arul Joseph Gnanaprakasam, Sakthi Ramalingam, Abdoalrahman S.A. Omer, Ilyas Khan
Abstract
The aim of this paper is to study the fractional model of Lumpy Skin Disease, aiming to enhance our understanding of this disease. Specifically, we employ the recently introduced Caputo-Fabrizio fractional (CFF) derivative to analyze the Lumpy Skin Disease model in detail. To comprehensively study the model's solutions, we utilize the Picard-Lindelof approach to assess their existence and uniqueness. Furthermore, we employ numerical techniques, specifically the CFF derivative combined with the fundamental theorem of fractional calculus and fixed point theorem, to obtain the solutions of Lumpy Skin Disease in near form using fractional order. This innovative approach offers novel insights into the dynamics of the disease model that were previously unexplored. In addition, numerical simulations are conducted to explore the change in effects of control parameters on specific compartments within the model. The geometric representation of the model provides valuable insights into its complexity and reliability. By simulating each model compartment at various fractional orders and comparing them with integer-order simulations, we highlight the effectiveness of modern derivatives. Overall, our fractional analysis emphasizes the enhanced accuracy of non-integer order derivatives in capturing the dynamics of the Lumpy Skin Disease model. These findings contribute to advancing our understanding of the disease and may have implications for its control and management strategies.