The Impact of Fractional Differentiation in Terms of Fitting for a Prostate Cancer Model Under Intermittent Androgen Suppression Therapy

Abstract

Actually, the main motivation for the contents of this chapter is to introduce fractional calculus as a prospective mathematical tool for cancer dynamics, in particular prostate cancer modeling. In this context, firstly, our main problem on the controversial role of androgens for prostate cancer development is handled, and according to our hypothesis a new mathematical model consisting of conventional logistic growth phenomena is constructed versus another prospective model based on ecological phenomena, cell quota. Then, we compare these two models demonstrating the mean squared error (MSE) values for androgen and prostate-specific antigen (PSA) for the first 1.5 cycles of intermittent androgen suppression (IAS) therapy administered to 62 selected patients from Vancouver Prostate Center (Vancouver, BC, Canada). To reduce MSE values, we also generate the fractional version of the model and verify that fractional differentiation provides nearly better data fitting for mathematical modeling. Moreover, with a discussion part, which hints for future works should be taken into account are pointed out.