COMPUTATIONAL STUDY OF FRACTIONAL-ORDER VECTOR BORNE DISEASES MODEL

Abstract

In this paper, we solve a nonlinear fractional-order model for analyzing the dynamical behavior of vector-borne diseases within the frame of Caputo-fractional derivative. The proposed mathematical model advances the existing integer-order model on transmission and cure of vector-borne diseases. The existence and uniqueness of the solutions of the fractional-order model are proved using the Banach contraction principle. We investigate the local asymptomatic stability for the obtained disease-free equilibrium point and global stability for the proposed model in the sense of Ulam–Hyers stability criteria, respectively. Besides that, we obtain a numerical solution for the projected model using the Corrector-Predictor algorithm. Finally, to illustrate the obtained theoretical results, we perform numerical simulations for different values of fractional-order derivative and make a comparison with the results of the integer-order derivative.