Fibonacci Wavelet Operational Matrix Method for a Fractional Dengue Transmission Model with Human–Mosquito Dynamics
This study considers a fractional-order dengue transmission model incorporating hu man and mosquito populations. The human population is classified into susceptible, exposed, infected, and recovered compartments, while mosquitoes are divided into susceptible and infected classes. The model is formulated using Caputo fractional derivatives to account for memory effects inherent in epidemic processes.To compute approximate solutions, a Fibonacci wavelet operational matrix method is employed. The state variables are expanded in terms of Fibonacci wavelets, and the system is reduced to a set of nonlinear algebraic equations, which are solved numerically. Numerical simulations for varying fractional orders are conducted to examine the influence of memory on disease dynamics. The basic reproduction number is also derived to de termine the threshold for disease persistence. The results indicate that the fractional framework enhances modeling flexibility, while the proposed numerical scheme provides an efficient solution.