Mathematical Modeling and Analysis of Multi-Mutation and Drug Resistance

Abstract

A model that takes into account multi-mutation and drug resistance in a case of simple immune system and immune-suppression caused by drug resistant tumor cells is proposed. Since the methods for revising therapeutic approaches (immunotherapy and chemotherapy) during cancer treatment are still being explored, we have analysed mathematically the corresponding tumor-immunotherapy model and its non tumor states using nonstandard finite difference method to identify under which conditions tumor can be eliminated. Numerical simulations of the tumor-immunotherapy model is done with the aid of MATLAB software using ode45 function, in order to determine the effectiveness of the immunotherapy. Through the mathematical analysis, the existence, the uniqueness and the boundedness of solutions are shown. This study indicates that tumor can be eliminated under certain conditions in the presence of the immunotherapy drug and in the absence of the drug resistant tumor cells. Moreover, it provides an understanding of the evolution of tumor cells and immune system cells for all types of mutations, in the absence and in the presence of the immunotherapy drug. Effective treatment strategies are proposed when the drug resistant tumor cells are absent and when they are present.