A Comparison Between the Stability Properties in a DDE Model for Leukemia and the Modified Fractional Counterpart

TL;DR

This paper compares the stability properties of a leukemia model using delay differential equations and a modified fractional-order system, highlighting differences and implications for disease dynamics.

Contribution

It introduces a leukemia model with DDEs and compares its stability with a fractional-order version, providing new insights into their dynamical differences.

Findings

Stability properties differ between DDE and fractional models.

Numerical results illustrate distinct dynamical behaviors.

Medical implications are discussed based on simulation outcomes.

Abstract

In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model takes into account three types of division that a stem-like cell can undergo and cell competition between healthy and leukemia cell populations. The action of the immune system on the leukemic cell populations is also considered. The stability properties of the equilibrium points are established through numerical results and the differences between the two types of approaches are discussed. Medical conclusions are drawn in view of the obtained numerical simulations.