CHAOS, SOLITONS AND FRACTALS, vol.168, no.2023, pp.1-16, 2023 (SCI-Expanded)
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.