A Study Of Mathematical Modeling Of Cancer Cell Growth Using Generalized Logistic Model

Abstract

Mathematical Modelling Provides An Effective Framework For Understanding The Growth Dynamics Of Cancer Cells. In This Study, Generalized Logistic Models (GLM) Is Used To Analyse Cancer Cell Growth And To Unify Several Classical Growth Models. The Exponential, Logistic, VonBertalanffy And Richards’s Models Are Discussed And Shown To Arise From Generalized Growth Assumptions Under Suitable Parameter Choices. The Formulation Of Each Model Is Presented Along With The Procedure For Obtaining Their Analytical Solutions. Using The Derived Solutions, Growth Values Are Computed At Selected Time Intervals By Solving Numerical Problems. To Ensure A Fair Comparison, The Same Initial Data Is Used For All Models. Furthermore, Pythonprogramming Is Employed To Perform Numerical Evaluations Of The Analytical Solutions, Allowing Efficient Computation And Comparison Of Growth Behaviour Across Different Models. The Results Reveal That The Exponential Growth Model Exhibits The Maximum Spreading Nature Due To The Absence Of Growth Restrictions, Making It Suitable Only For Early-stage Cancer Growth Analysis. In Contrast, GLM And Richards Models Incorporate Growth-limiting Factors And Provide More Realistic And Controlled Descriptions Of Long-term Cancer Cell Growth. This Study Highlights The Importance Of Combining Mathematical Theory With Computational Tools For Realistic Modelling And Analysis Of Cancer Cell Growth.

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