An Analysis of a Fractional-Order Model of Colorectal Cancer and the Chemo-Immunotherapeutic Treatments with Monoclonal Antibody

Ali Alhajraf, Ali Yousef () and Fatma Bozkurt
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Ali Alhajraf: College of Nursing, Public Authority of Applied Education and Training, Safat 13092, Kuwait
Ali Yousef: Department of Natural Sciences and Mathematics, College of Engineering, International University of Science and Technology in Kuwait, Ardiya 92400, Kuwait
Fatma Bozkurt: Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey

Mathematics, 2023, vol. 11, issue 10, 1-29

Abstract: The growth of colorectal cancer tumors and their reactions to chemo-immunotherapeutic treatment with monoclonal antibodies (mAb) are discussed in this paper using a system of fractional order differential equations (FDEs). mAb medications are still at the research stage; however, this research takes into account the mAbs that are already in use. The major goal is to demonstrate the effectiveness of the mAb medication Cetuximab and the significance of IL-2 levels in immune system support. The created model is broken down into four sub-systems: cell populations, irinotecan (CPT11) concentration for treatment, IL-2 concentration for immune system support, and monoclonal antibody Cetuximab. We show the existence and uniqueness of the initial value problem (IVP). After that, we analyze the stability of the equilibrium points (disease-free and co-existing) using the Routh–Hurwitz criteria. In addition, in applying the discretization process, we demonstrate the global stability of the constructed system around the equilibrium points based on specific conditions. In the end, simulation results were carried out to support the theory of the manuscript.

Keywords: stability; existence and uniqueness; colorectal cancer; fractional-order differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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