The Prisoner's dilemma as a cancer model

TL;DR

This paper models tumor development as an evolutionary game using the Prisoner's Dilemma, demonstrating how simple stochastic models can replicate complex tumor growth behaviors and treatment responses.

Contribution

It introduces a minimal mathematical model of cancer evolution based on the Prisoner's Dilemma game, capturing key tumor growth and treatment dynamics.

Findings

Reproduces Gompertzian tumor growth patterns

Derives the log-kill law relating treatment dose to survival

Models tumor regression consistent with Norton-Simon hypothesis

Abstract

Tumor development is an evolutionary process in which a heterogeneous population of cells with differential growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner's Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated "cancer-like" features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.