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

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

CHAOS, SOLITONS AND FRACTALS, cilt.168, sa.2023, ss.1-16, 2023 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 168 Sayı: 2023
  • Basım Tarihi: 2023
  • Dergi Adı: CHAOS, SOLITONS AND FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Sayfa Sayıları: ss.1-16
  • Erciyes Üniversitesi Adresli: Evet

Özet

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.