Tumor volume follows a saturating (Gompertzian) growth law: cells divide fast while small, then growth slows as the mass outstrips its blood/nutrient supply. Treatment and the immune system act as competing loss terms on the same population.
dN/dt = a·N·(1 − N/K) − k(t)·N
k(t) = immune_kill·(1 − evasion) + drug_kill(mode, dose, mutation_burden)
- Proliferation rate (a) — how fast cells self-sufficiently drive their own division signals (Hallmark: sustained proliferative signaling).
- Genomic instability — the mutation-supply hallmark that unlocks the other hallmarks over time (colors cells orange→red) and drives immune evasion.
- Immune surveillance — baseline rate at which the immune system culls cells at the tumor margin; reduced by evasion.
- Drug dose + mode — Chemo kills any proliferating cell non-selectively; Targeted (TKI) only kills cells carrying the driver mutation it was designed against (needs a high mutation burden to have many targets); Immunotherapy works by restoring immune recognition (cutting the evasion penalty), not by killing cells directly.
Real-world relevance: this is exactly why oncologists sequence a tumor biopsy before prescribing an EGFR/ALK/BRAF inhibitor — a targeted drug only works on the subset of cells that actually express its target mutation.