Gompertzian tumor cell growth using a discrete dynamic model

Abstract

Some benign tumors (made up of non-cancer cells) can become malignant (made up of cancer cells) over time, such as in our skin or colon. The dynamic interaction between cancer and non-cancer cells in tumors becomes interesting to analyze to predict tumor growth. This paper uses a predator-prey model to interpret the dynamic tumor growth, which uses cancer cells as a predator and non-cancer cells as prey. A Gompertzian growth function completes the model to describe natural tumor growth and add a treatment parameter. First, we investigate the stability criteria of each model equilibrium using an analytical approach. The eigenvalues ​​obtained in the stability analysis are used to construct a discrete dynamic model using the Non-Standard Finite Difference (NSFD) scheme. This scheme is implemented numerically in Python and is highly accurate since the maximum difference with the 4th Runge Kutta scheme is 0.42%. Finally, sensitivity parameter analysis shows that intensive treatment mostly affects the dynamic of the tumor cell population. The related party can use the simulation and analysis results to plan the proper and effective treatment to minimize tumor growth.