Abstract
This research studies the over-dispersion on breast cancer patient data resulting from the presence of a latent variable and varying fluctuations around the mean. Both Fractional Poisson distribution and Standard Poisson distribution can be applied to estimate the number of positive axillary lymph nodes in the cases of the presence and absence of cancer stem cells at different time intervals for the size of the tumor. Additionally, The Relaxed Cure Rate model and the Standard Cure Rate model can be applied to estimate the survival probability and time of breast cancer patients when undergoing radiation therapy and when not undergoing radiation therapy in the presence or absence of cancer stem cells. Furthermore, survival rate models can be applied at different intervals for the number of positive axillary lymph nodes when radiation therapy was applied versus when it was not applied.