A Qualitative Analysis of Leukemia Fractional Order SICW Model

Kalyan Das, G. Ranjith Kumar, K. Ramesh, Md. Haider Ali Biswas

Abstract


Using a series of fundamental differential equations, including the Caputo derivative, which makes it easier to specify the initial conditions of the differential equations, we present a fractional order concept of leukemia in this study. The universality, positivity, and boundedness of solutions are first established. The local stability properties of the equilibrium are studied using the fractional Routh-Hurwitz stability criteria. The differential equation system has been solved using unconventional finite difference techniques. The Leukemia Fractional Order SICW model introduces several innovative elements compared to traditional epidemiological and disease models. This stands out due to its integration of fractional-order differential equations, inclusion of leukemic cells and immune cells compartments, simulation of treatment strategies, consideration of waning immunity, and its application to leukemia-specific scenarios. These elements collectively make it a valuable tool for studying leukemia dynamics, exploring treatment options, and improving our understanding of how the immune system interacts with cancer cells in leukemia patients. Numerical simulations of the model are shown at the conclusion to interpret our theoretical outcomes in support of various fractional orders of derivative   options. From there, we can observe how the evolution of the system components is impacted by the fractional derivative .


Keywords


Segment Model; Leukemia; Caputo Fractional Derivative; Stability Analysis; Nonstandard Finite Difference; Numerical Simulations

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DOI: https://doi.org/10.37905/jjbm.v5i1.24961

Copyright (c) 2024 Kalyan Das, G. Ranjith Kumar, K. Ramesh, Md. Haider Ali Biswas

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