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

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. •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