From Immune-Cold to Immune-Hot Tumors: A Fractional Immunomodulation Framework with Topological Signatures

Converting immune-cold tumors into immune-hot tumors is a major objective of cancer immunotherapy. Cold tumors typically exhibit limited T-cell infiltration, weak inflammatory activity, strong local immunosuppression, hypoxia or stromal exclusion, and poor therapeutic responsiveness. We propose a fractional-order immunomodulation model that couples tumor burden, effector immune activity, suppressive immune burden, pro-inflammatory signaling, and hypoxia/stromal exclusion through memory-dependent differential equations. The fractional formulation represents persistent inflammation, immune exhaustion, hypoxia, and treatment history. State-space trajectories are additionally analyzed using persistent homology, including persistence diagrams, barcode plots, and sliding-window topological summaries. The framework identifies threshold-like conditions for immune activation, memory-dependent delays in tumor conversion, and structural signatures of successful tumor-microenvironment reprogramming. Numerical experiments indicate that immune activation alone may be insufficient when suppressive and hypoxic barriers remain dominant, whereas coordinated combination therapy can produce a sustained transition toward an immune-hot regime. The results support interpreting cold-to-hot conversion not only as increased immune activity but also as a reorganization of the tumor-immune dynamical system. This integrated fractional and topological framework offers a mechanistic basis for studying immunomodulation and combination antitumor strategies.