Tumor expansion and immune regulation in a mathematical model of cancer under variations in tumor cell proliferation rate and innate immune stimulation

In this article, we proposed a simplified mathematical model of primary tumor growth that involves four cell populations: Two types of cancer cells with different levels of immunogenicity, and the immune response in its two components, innate and adaptive. By varying the proliferation rate of non-immunogenic cancer cells and the innate immune stimulation parameter, and applying biparametric numerical continuation techniques, we identified distinct stability regions that revealed scenarios of tumor escape and latency. A closed curve of supercritical Hopf bifurcation points was also detected, delineating the parameter region in which limit cycles emerged. By examining the population maxima of each cell type at steady state, we identified parameter values at which both immunogenic and non-immunogenic tumor cell populations remain in stable equilibrium at modest levels, sustained by an immune response that does not escalate to intensities associated with immunological damage.