Fractal–fractional dynamical system of Typhoid disease including protection from infection

Abstract

The current paper analyzed a fractal–fractional mathematical model of typhoid to study the dynamics of fever disease incorporating protection against infection. The considered model is investigated into fractional-order and fractal dimension in sense of Caputo derivative. The existence theory of the considered model is determined and the uniqueness of the solution by the approach of fixed point theorem. Furthermore, the Ulam–Hyres stability is derived for the considered system by perturbing the problem with a small factor. The non-integer order model is evaluated numerically by fractional Adams–Bashforth iterative techniques and compares the results of fractional order and fractal dimension with integer order. © 2023 Elsevier B.V., All rights reserved.