Modeling for the body defense mechanisms in stage I melanoma patient and sensitivity analysis by using Partial Rank Correlation Coefficient (PRCC) method

The scientific modeling of cellular growth and proliferation can significantly help to physicians to offer an appropriate treatment. In this paper the modeling of the body's immune system function for a patient with melanoma cancer has been studied. The main advantage of this model is considering more variables to describe dynamics of the melanoma patient’s body, which will make our model more realistic. For estimating the coefficients of the mathematical model, a multi-objective optimization method, "Non-Dominated Sorting Genetic Algorithm", is used. One of the major advantages of such method is considering multiple objectives and simultaneously constraining them. Simulation results reveal that our mathematical model can successfully simulate the function of the body defense system of the melanoma patient. In order to analyze the sensitivity and determine the correlation of the mathematical model output to changing in some parameters, Partial Rank Correlation Coefficient (PRCC) method is employed. Finally, it is demonstrated that Interleukin-2 (IL-2) generation rate change has the highest PRCC value and changing this parameter will have a high impact on the model outputs.