This thesis presents a comprehensive mathematical study of the transmission dynamics of the Nipah virus by constructing and analyzing a fractional-order differential model. The model incorporates five interacting compartments representing susceptible individuals, two types of infected individuals, recovered cases, and deceased or severely affected individuals. To approximate the solution of the nonlinear system, the Sumudu-Adomian Decomposition Method (SADM) is employed, offering an efficient approach for solving complex fractional differential equations.

A modified version of the model is proposed to ensure the mathematical robustness of the system, particularly focusing on the positivity and boundedness of solutions. The study thoroughly investigates the stability of equilibrium points and explores the bifurcation behavior near the disease-free state.

Numerical simulations using MATLAB are conducted to validate the theoretical findings and illustrate the impact of fractional orders on disease progression.
We demonstrate that fractional-order models provide more flexibility and accuracy in describing the memory-dependent nature of real-world infectious disease dynamics. This research contributes to the mathematical modeling literature by enhancing understanding of fractional systems and offering a framework applicable to other infectious diseases with similar complexity.

Very good