Modeling bistable dynamics arising from macrophage–tumor interactions in the tumor microenvironment

Macrophages in the tumor microenvironment (TME), known as tumor-associated macrophages (TAMs), originate primarily from circulating monocytes that differentiate under the influence of tumor-derived signals. Within the TME, naïve macrophages can adopt either a pro-inflammatory, anti-tumor (M1-like) or anti-inflammatory, pro-tumor (M2-like) phenotype. These phenotypic shifts significantly affect tumor progression, making TAMs attractive targets for therapeutic intervention aimed at blocking recruitment, promoting anti-tumor polarization, or disrupting tumor–macrophage interactions. In this study, we develop a mathematical model capturing the temporal dynamics of tumor volume alongside populations of naïve, M1-like, M2-like, and mixed (M1/M2) phenotype TAMs. The model incorporates the bidirectional influence between tumor development and macrophage polarization. Through numerical simulations with different parameter sets, our tumor–macrophage population model exhibits the emergence of bistability, demonstrating the system becomes more controllable, responsive to perturbations, and sensitive to immunotherapy. We conduct the bifurcation as well as global sensitivity analyses to identify regions of bistability for tumor dynamics in the parameter space and the impact of sensitive parameters on TME. These results are then linked to treatment strategies that may effectively induce transitions from high to low tumor burden.