Multi-type age-dependent branching processes as models of metastasis evolution.

Metastasis, the spread of cancer cells from a primary tumor to secondary location(s) in the human organism, is the ultimate cause of death for the majority of cancer patients. Although studied for more than 180 years, increasing efforts in recent years have significantly contributed to a better understanding of this aspect of tumor development. Adding to this understanding, our current paper proposes a multi-type branching process model, through which various topics, such as extinction of cancer cell clones, occurrence of successful mutants, and immediate risk of escaping extinction, are investigated. More specifically, the relationship between the lifespan distribution of cancer cells with subcritical reproduction and the waiting time until the occurrence of a mutant (having supercritical reproduction) cancer cell, escaping extinction, is highlighted. The theoretical studies formulated in this paper may allow our model to be tailored to real data available for particular kinds of cancer and chemotherapy. [ABSTRACT FROM AUTHOR]