Cancer model with moving extinction threshold reproduces real cancer data.

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 response to cancer, which leads to the emergence of an extinction threshold. We first identify the limitations of commonly used extinction threshold models from population biology 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 model the different immune response at different phases of the menstrual cycle and menopausal treatment and show that this leads to a moving extinction threshold. This approach provides new insights into the effects of hormone replacement therapy and menstrual cycle length on breast cancer in women. More generally, it can be applied to a variety of other cancer scenarios where the immune response or other important factors vary over time.