A mathematical model with piecewise constant arguments of colorectal cancer with chemo-immunotherapy

Bozkurt F., Yousef A., BİLGİL H., Baleanu D.

Chaos, Solitons and Fractals, vol.168, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 168
  • Publication Date: 2023
  • Doi Number: 10.1016/j.chaos.2023.113207
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Keywords: Colorectal cancer, Period-doubling, stationary and Neimark-Sacker bifurcations, Piecewise constant arguments, Stability
  • Kayseri University Affiliated: No


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.