Nonlinear Dynamics of Sensitive-Resistant Tumor Populations under Therapy-Induced Clonal Competition

This study develops and analyzes a nonlinear mathematical model for therapy-sensitive and therapy-resistant tumor populations under therapy-induced clonal competition. The model incorporates logistic growth, asymmetric interclonal competition, conversion from sensitivity to resistance, and a constant treatment pressure acting directly on sensitive cells. We establish well-posedness of the model by proving positivity, boundedness, global existence, and the existence of an absorbing region in the biologically feasible domain. Equilibrium points and threshold quantities are derived to characterize sensitive-cell persistence, resistant dominance, coexistence, and resistant-cell invasion in the mutation-free case. Local stability and bifurcation-related conditions are analyzed using the Jacobian matrix and threshold functions. The results show that increasing treatment intensity can suppress sensitive cells while reducing their competitive pressure on resistant cells. This mechanism promotes resistant dominance through therapy-induced competitive release. Numerical simulations support the analytical findings. Weak treatment may lead to coexistence, whereas strong treatment can produce an initial decline in tumor burden followed by resistant regrowth. Bifurcation-style and heat-map simulations further show how treatment intensity and clonal competition shape long-term tumor composition. These findings provide a threshold-based framework for understanding therapy-induced resistance and adaptive treatment design.