A Mathematical Model for the Treatment of Melanoma with the BRAF/MEK Inhibitor and Anti-PD-1

Skin cancer treatment is a combination of BRAF and MEK kinase inhibitors administered as tablets, along with immunotherapy treatment (treatment into the vein) with a group of drugs that inhibit the activity of the immune barrier proteins PD-1 and PDL1. Here, we propose a new approach to the therapy for melanoma with the BRAF/MEK inhibitor and anti-PD-1. With the help of explicit analytical functions, we were able to model this combined treatment and present the treatment in a mathematical model described by a system of differential equations including variables, such as Treg, IL12, Il10, TGF-$\beta$, and cytokine, which are significant variables that are all critical factors which determine the effectiveness of therapies. The most significant advantage of a treatment described by a mathematical model with explicit analytical functions is the control of parameters, such as time and dose, which are variable critical parameters in the treatment, that is, these parameters can be adapted to the patient’s personalized treatment. In the current study, we showed that by simultaneously changing and combining these two parameters, we could decrease the tumor volume. To validate the numerical results, we computed the relative error between the results obtained from the mathematical model and clinical data.