In stem cell research, extending the stem cell phenotype which is undifferentiated, is among the most challenging aspects. The accuracy of the mathematical models often used to depict the stem cells growth is not as optimal as desired. The Deasy model is used to compare experimental results on polio stem cells with embryonic stem cells, with the aid of hyperbolastic growth model H3. Here, we offer multiple models that are applicable to the study of stem cell populations in general and are particularly useful for modeling cell proliferation in the real world. We talked about structured cell population models and contrasted various methodologies used in cell proliferation mathematical modeling. The findings of this study advance our scientific and mathematical knowledge of stem cell dynamics. The models are also expected to be useful in standardizing cell culture conditions and scalable systems, as well as in the development of clinical procedures for stem cell treatments. Moreover, it may be used to conduct a more accurate examination of preexisting data. Certain experiments' outcomes can be predicted. In this manuscript, all data analysis is shown in Figures 1-15.