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

Abstract

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.

Keywords

• Tumor microenvironment
• Cold-to-hot transition
• Fractional dynamics
• Persistent homology
• Topological signatures
• Cancer immunotherapy

References

1. Diethelm, K., N. J. Ford, and A. D. Freed, 2002 A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 29: 3–22.
2. Diethelm, K., N. J. Ford, and A. D. Freed, 2004 Detailed error analysis for a fractional adams method. Numerical Algorithms 36: 31–52.
3. Gündogdu, H. and H. Joshi, 2025 Numerical analysis of timefractional cancer models with different types of net killing rate. Mathematics 13: 536.
4. Hu, M. M., Y. Zhao, N. Zhang, F. Y. Gong, W. Zhang, et al., 2025 Tumor microenvironment: Obstacles and opportunities for t cellbased tumor immunotherapies. Molecular Cancer Research 23: 277–287.
5. Joshi, H. and M. Yavuz, 2026 A novel fractional-order model and analysis of cancer-immune system interaction in an avascular environment with an efficient control mechanism. Journal of Computational and Applied Mathematics 473: 116888.
6. Kong, X., S. Ou, Z. Wei, J. Li, Y. Wang, et al., 2025 Transforming the “cold” tumors to “hot” tumors: Strategies for immune activation. Biochemical Pharmacology 236: 117216.
7. Liu, L., D. Wu, Z. Qian, J. Wang, Y. Chen, et al., 2025a Empowering hypoxia to convert cold tumors into hot tumors for breast cancer immunotherapy. Cell Death Discovery 11: 381.
8. Liu, Y. T., Y. L.Wang, S.Wang, J. J. Li,W. He, et al., 2025b Turning cold tumors into hot tumors to ignite immunotherapy. Molecular Cancer 24: 254.

9. Park, J. H., S. Lee, H. Kim, et al., 2026 Targeting cytokine/ chemokine signaling to convert cold tumors into hot tumors. Trends in Pharmacological Sciences .
10. Qayyum, M., H. Ahmad, A. Alsaedi, et al., 2025 Analysis of timefractional cancer-tumor immunotherapy model using modified he-laplace algorithm. Scientific Reports 15: 1655.
11. Vipond, O., J. A. Bull, et al., 2021 Multiparameter persistent homology landscapes identify immune cell spatial patterns in tumors. Proceedings of the National Academy of Sciences 118: e2102166118.
12. Wu, Y., Y.Wu, Z. Gao, et al., 2026 Revitalizing t cells: Breakthroughs and challenges in overcoming t cell exhaustion. Signal Transduction and Targeted Therapy 11: 1.
13. Xie, Z., Y. Fang, Y. Zhang, Y. Liu, X. Chen, et al., 2025 The emerging role of dendritic cells in the tumor microenvironment: From antigen presentation to targeted immunotherapy. Cell Death and Disease 16: 900.
14. Yang, J., H. Fang, J. Dhesi, I. H. R. Yoon, J. A. Bull, et al., 2025 Topological classification of tumour-immune interactions and dynamics. Journal of Mathematical Biology 91: 25.