Multiscale Dynamics of MMC Chemotherapy in Bladder Cancer: The SPVF Approach

Mitomycin-C (MMC) is the leading chemotherapeutic agent for the treatment of non-muscle invasive bladder cancer (NMIBC), but recurrence rates remain high due to poorly understood interactions between the tumor, immune system, and drugs. We present a five-equation mathematical model that explicitly tracks MMC, tumor cells, dendritic cells (DCs), effector T cells, and regulatory T cells (Tregs). The model incorporates clinically realistic treatment regimens (6-week induction followed by maintenance therapy), including DCs activation by tumor debris, dual DC activation of effector and Treg cells, and reversal of MMC-induced immunosuppression. The resulting nonlinear system exhibits hidden multiscale dynamics. We apply the singular perturbed vector field (SPVF) method to identify fast–slow hierarchies, decompose the system, and conduct stability analysis. Our results reveal stable equilibria corresponding to either tumor eradication or persistence, with a critical dependence on the initial tumor size and growth rate. Modeling shows that increased DC production paradoxically contributes to treatment failure by enhancing Treg activity—a non-monotonic immune response that challenges conventional wisdom. These results shed light on the mechanisms of NMIBC evolution and highlight the importance of balanced immunomodulation in the development of therapeutic strategies.