Sensitivity parameter for a discrete-time logistic melanoma cell growth under virotherapy

Abstract

Melanoma is a rare type of skin cancer but the most serious compared to other types of skin cancer. The study of melanoma growth is interesting to analyze so that related parties can determine how quickly this cancer spreads and determine the proper and efficient treatment method. This paper uses the mathematical modeling of tumor growth to describe melanoma growth in the presence of virotherapy. The model shows the interaction between melanoma and uninfected tumor cells, completed by a Logistic law as a classical fraction for population growth to represent the natural melanoma growth function. Then, this model is discretized by the Non-Standard Finite Difference Method, then solved numerically, and completed by the 4th Runge Kutta method for validation. Moreover, this study gave a sensitivity analysis of several parameters to see how much melanoma growth changes over these parameters. Finally, it can be shown that the melanoma cell growth rate and virotherapy rate have the most significant effect on the number of melanoma cells.