# Revealing endogenous conditions for Peto’s paradox via an ordinary differential equation model

## TL;DR

This paper uses a mathematical model to explain why cancer rates are similar across species despite differences in cell count and lifespan.

## Contribution

The study introduces a novel ODE-based approach to reveal endogenous conditions for Peto’s paradox.

## Key findings

- The study identifies sufficient conditions for the lack of correlation in cancer incidence across species.
- It draws an analogy between cell population dynamics and species cell cycles to explain Peto’s paradox.

## Abstract

Cancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto’s paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto’s paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.

The online version contains supplementary material available at 10.1007/s00285-024-02123-7.