Abstract: Cancer resistance is shaped by clonal competition and treatment-driven selection. This study develops a coupled evolutionary game model for therapy-sensitive and therapy-resistant tumor cells. Frequency-dependent selection is combined with one-way phenotypic switching and resource-limited tumor growth. The full triangular dynamical system is analyzed. Biological admissibility, equilibrium structure, local stability, and long-term tumor-burden behavior are established. Explicit treatment thresholds classify sensitive dominance, resistant dominance, stable coexistence, and bistability. In the switching-free case, the threshold crossings form boundary transcritical bifurcations. Increasing treatment pressure promotes resistance, whereas a larger resistance cost shifts the transition toward higher treatment levels. Phenotypic switching removes the sensitive-only equilibrium and shifts the resistant-state stability boundary toward lower treatment pressure. Numerical simulations confirm the analytical equilibria for representative parameter regimes, with equilibrium errors below 6 10 .  A finite-time parameter sweep is also consistent with the derived threshold structure. The model provides a qualitative mathematical framework for understanding how treatment pressure, resistance cost, clonal competition, and phenotypic switching shape cancer resistance.

Keywords: Evolutionary game theory, cancer resistance, clonal competition, replicator dynamics, treatment thresholds, phenotypic switching

Pages: 357-369