Branching Process Model

The model omits several in vivo factors such as spatial effects, immune effects, and microenvironmental heterogeneity. Under bounded rates, the expectation semigroup has a unique bounded-in-time solution to an integral evolution equation. The main model uses two cell classes: cancer stem cells and non-stem cancer cells. The model defines the cancer stem cell growth parameter E as p2 minus p0. Non-stem cancer cells divide for a finite number of generations before becoming senescent. Active cells can divide, become non-active, or be removed. Non-active cells cannot divide and can only be removed. The model predicts that the asymptotic senescent-cell fraction is independent of the number of non-stem cancer-cell generations. The model links molecular telomere replication mechanics to population-scale cell dynamics.