Modelling cancer cell dormancy in mice: heavy-tailed distributions and the role of cancer cell death in reactivation times

In predicting metastatic potential and improving treatment outcomes in cancer research, it is crucial that we understand the dynamics of cancer cell dormancy and reactivation. In this paper we propose, study, and evaluate a cancer growth model that incorporates cell death, dormancy, reactivation, and proliferation in the secondary sites. Using experimental data from murine models, we test various statistical distributions and identify models that represent the asymmetry and variability observed in dormancy durations. Notably, the estimated cancer cell death rate remained consistent across all tested distributions, supporting its biological relevance as a robust parameter for modelling dormancy survival dynamics. When post-reactivation cell death is present, the most suitable among the distributions we studied exhibit heavy-tails and asymmetric skewness; this aligns with the prolonged and rare dormancy periods expected of cancer cells. In contrast, analysis of complementary data in which no cancer cell death is observed indicates that dormancy can be equally well represented by distributions with finite variance and comparatively light tails. Our findings highlight a close interplay between reactivation/dormancy-time and cancer cell death mechanisms. Furthermore, they stress the importance of selecting appropriate statistical models for dormancy, both in predicting cancer cell reactivation, and in informing therapeutic strategies that focus on dormancy-driven metastasis.