Computational optimization of fractional-order influenza SIR epidemic modeling using two effective techniques

Abstract

In this study, we employ two efficient approaches, the q-homotopy analysis transform method and the Predictor-Corrector method to find and analyze the solution for the fractional order influenza SIR epidemic model. In recent times, numerous innovative definitions of fractional derivatives have been proposed and employed to construct mathematical models for an extensive array of complex problems, including nonlocal effects, memory, and history. We implement the Caputo fractional derivative for the considered SIR epidemic model of influenza which is characterized by ordinary differential equations of nonlinear form. The q-homotopy analysis method and the Laplace transform are combined to form the basis of q-homotopy analysis transform method. The outcomes of the methods under consideration can be found as a quickly convergent solutions. To illustrate the accuracy, speed, and high order of convergence of the q-homotopy analysis transform method, its solution is compared to that produced by the Residual power series method and fourth-order Runge-Kutta method. The 3D plots, graphs and numerical results express the physical representation of the considered model. It exhibits that the Predictor-Corrector approach and the q-homotopy analysis transform method are meticulous, reliable, and effective to examine the suggested influenza SIR epidemic model and a few other fractional order differential equations in epidemiology. The details of the solution behavior are provided by this analysis, which ensures accurate epidemic predictions. In addition to improving epidemic modeling, this new approach is a more precise tool for forecasting and planning public health. The paper establishes an evaluation for fractional epidemic models and demonstrates the utility of the methods in the context of disease transmission.