Modeling and sensitivity analysis of reaction diffusion brain disease with control rate under neurological disorder

Abstract

The central nervous system (CNS) is frequently affected by multiple sclerosis, a common neurological condition that can result in lesions that progress over time and space. Our work provides a mathematical model that demonstrate the course of the illness and its probability of return. A fractional order model is obtained by applying the fractal–fractional operator to a mathematical model that is designed with the notion of enhancing immune system development. To identify its stable location, a recently created system HI$I_v$TR is analyzed statistically and qualitatively. The study guarantees trustworthy bounded conclusions by examining the system’s well-posedness and local and global stability, which are critical characteristics of epidemic models. The Lipschitz condition is used with a fixed point theory tool to satisfy uniqueness and existence constraints. Additionally, the reproductive number is ascertained using a sensitivity study of factors including chaos control. Lyapunov first derivative functions are used to analyze the system for local and global stability in order to assess the overall impact of these measurements. By using power-law kernel at fractional orders, a dependable solution is derived by the use of the fractal–fractional operator. Furthermore, we confirm our theoretical results using numerical simulations. Our results are shown in graphs that illustrate the model’s different reactions for different values of the parameters.