Numerical simulation for the fractional prey-predator model with infection by fractional variational iteration method

Purpose This study aims to investigate the dynamical properties of a fractional-order prey-predator infection model and to assess the performance of the Fractional Variational Iteration Method (FVIM) in solving and reconstructing the model, regarding the aspects of memory effects, parameter identification, convergence and accuracy. Design/methodology/approach The fractional-order prey-predator infection model is analysed using the FVIM. The least-square-based parameter identification algorithm is applied to identify the model parameters and analyse its dynamics. Simulations are conducted at different orders of fractional derivatives to observe the memory effects on the dynamics of the model. Also, threshold analysis is applied to determine the effect of the changes in parameters on the model dynamics. Convergence criteria and numerical accuracy are determined by iteration errors and variable-wise discrete errors, respectively. Findings From the obtained numerical results, it can be concluded that the FVIM provides accurate approximations for the fractional-order prey-predator infection model since the estimated solutions show a high degree of similarity with the observed data. The least-square-based parameter identification procedure is capable of reconstructing the dynamics of the fractional-order prey-predator infection model adequately. Different fractional orders highlight the importance of the memory effect on the population dynamics. Originality/value This research paper is unique because it uses the FVIM, along with the least-squares method for parameters, to examine a fractional-order prey-predator infection system. The numerical analysis conducted on memory effects through different values of fractional order will help gain deeper insight into fractional ecological systems.