Cancer model with moving extinction threshold reproduces real cancer data

TL;DR

This paper introduces a dynamic cancer model incorporating a moving extinction threshold to account for immune response variability, successfully reproducing diverse real-world cancer data and providing insights into hormonal influences on cancer risk.

Contribution

A novel cancer progression model that includes a time-varying immune extinction threshold, improving the reproduction of real cancer data and understanding hormonal effects.

Findings

Model accurately reproduces age-specific cancer risk data.

Incorporates immune response variability over time.

Provides insights into hormone therapy and menstrual cycle effects.

Abstract

We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee effect in population biology. We first identify the limitations of commonly used Allee effect models in reproducing typical cancer progression. We then address these limitations by deriving a new model that incorporates: (i) random mutations of stem cells at a rate that increases with age and (ii) immune response whose strength may also vary over time. Our model accurately reproduces a wide range of real-world cancer data: the typical age-specific cumulative risk of most human cancers, the progression of breast cancer in mice, and the unusual age-specific cumulative risk of breast cancer in women. In the last case, we use a moving extinction threshold to reflect the different immune response at different phases of the menstrual cycle and menopausal treatment. This provides new insights into the effects of hormone replacement therapy and menstrual cycle length. This moving threshold approach can be applied to a variety of other cancer scenarios where the immune response or other important factors may vary over time.