A mathematical model with piecewise constant arguments of colorectal cancer with chemo-immunotherapy. (March 2023)

• Record Type: Journal Article
• Authors: Bozkurt, Fatma; Yousef, Ali; Bilgil, Halis; Baleanu, Dumitru
• Is Part Of: Chaos, solitons and fractals. Volume 168(2023)
• Publication Date: 2023-03
• Subjects: Stability -- Period-doubling, stationary and Neimark-Sacker bifurcations -- Colorectal cancer -- Piecewise constant arguments; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2023.113207
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We propose a new mathematical model with piecewise constant arguments of a system of ODEs to investigate the growth of colorectal cancer and its response to chemo-immunotherapy. Our main target in this paper is to analyze and represent the I.S.'s (immune system) efficiency during the chemotherapeutic process. Therefore, we proved and illustrated the necessity of IL-2 that supports the immune system, especially in early-detected cases of tumor density. Thus, the constructed model has been divided into sub-systems: the cell populations, the effects of the medications doxorubicin, and IL-2 concentration. Firstly, we analyze the stability of the equilibrium points (disease-free and co-existing) using the Routh-Hurwitz criteria. In addition, our study has shown that the system undergoes period-doubling, stationary and Neimark-Sacker bifurcations based on specific conditions. In the end, we illustrate some simulations to assist the theory of the manuscript. Highlights: Modeling colorectal cancer as a system of differential equations with piecewise constant arguments Stability analysis of a chemotherapeutic treatment and immune response Considering the effect of IL-2 concentration in early detection and significant tumor density. Investigating the therapeutic stages because of the toxicity of the medications