Fractional-order modelling of cancer cell population dynamics affected by radiation

We present a fractional model for cell cycle progression using the Caputo fractional-order derivative. An in-depth analysis of the existence, uniqueness, non-negativity, and boundedness of the solution has been carried out. Finally, the model has been applied to two cell lines: MCF-7 (Breast cancer) and A549 (Lung cancer). By combining the suggested mathematical model with experimental findings, Markov Chain Monte Carlo (MCMC) sampling was used to estimate model parameters within a Bayesian framework. The MCF-7 and A549 cell lines show almost the same values for the transition from the G₂M phase to the G₁ phase, with rates of 0.2h^-0.9 and 0.189h^-0.9, respectively, according to the calculated transition rates. On the other hand, MCF-7 cells undergo a faster transition from the G₁ phase to the S phase, with a rate of 0.159h^-0.9 as opposed to 0.095h^-0.9 in A549 cells. To assess how well MCMC investigated the posterior and generated reliable parameter values, trace plots have been used as a diagnostic tool.