Modeling Multi-Mutation And Drug Resistance: A Case of Immune- Suppression, Global Journal of Pure and Applied Mathematics

Abstract

A model that takes into account multi-mutation and drug resistance in a case of sim- ple immune system and immune-suppression caused by drug resistant tumor cells is proposed. Since methods for revising therapeutic approaches (immunotherapy and chemotherapy) during cancer treatment are still being explored, we analyzed mathematically and simulated numerically with the aid of MATLAB software the corresponding tumor-immunotherapy model to determine the effectiveness of the immunotherapy. Through the mathematical analysis, the existence, the uniqueness and the boundedness of solutions are shown. The non-tumor states are stable, un- der conditions only in the presence of the immunotherapy drug and in the absence of the drug resistant tumor cells. The numerical results show the behavior of the tumor cells and immune system cells in the absence and in the presence of the immunotherapy drug. This study provides an efficient treatment strategie to cancer in the absence and in the presence of the drug resistant tumor cells.