Age and Generation-Based Model of Metastatic Cancer

Metastasis is a hallmark of cancer, yet current mathematical models often rely solely on tumor size to forecast metastatic burden. In the current work, we propose a novel generationbased mathe matical approach that approximates the metastatic process in terms of tumor age rather than size. Building on the seminal work of Iwata Kawasaki and Shigesada (IKS), we introduce a recursive integral approach that captures the hierarchical metastatic nature through successive generations, bypassing the need to solve complex partial differential equations as in the IKS model. We de rive closedform solutions for the distribution of first generation of metastatic tumors, compute numerically higherorder generations across generations and validate our method against numer ical solutions of the IKS transport equation. Our findings reveal that younger generations of metastases eventually dominate the overall tumor burden due to cumulative emissions, while older generations primarily contribute to the largesize tail of the distribution. From the clini cal perspective the current approach provide a foundation for precise and personalized treatment strategies that can target distinct metastatic generations.