Stability Analysis Using Nonstandard Finite Difference Method and Model Simulation for Multi-Mutation and Drug Resistance with Immune-Suppression

Abstract

We introduced recently a model that takes into account multi-mutation and drug resistance of tumor cells in a case of simple immune system and immune-suppression caused by the resistant tumor cells. The present study is to apply the Nonstandard finite difference method to that model we recently developed in analyzing the stability of non-tumor states to identify under which conditions tumor can be eliminated in the presence of both immunotherapy and chemotherapy. Numerical simulations of the model in the presence of both immunotherapy and chemotherapy are performed with the aid of MATLAB software using ode45 function and under different treatment strategies to analyze the behavior of both the tumor and immune system cells. The findings of this study indicate that tumor cells can be only eliminated under certain conditions, when a second specific chemotherapy drug that is only toxic to resistant tumor cells is introduced. Moreover, it gives an insight into how tumor and immune system cells evolve when the dynamical system conveys both inherent and drug-induced resistance with immune-suppression, in the presence of both immunotherapy and chemotherapy. Treatment strategies effective are proposed in this case.

Keywords: Cancer modeling, Drug resistance, Mutation, Immune system, Immunotherapy, Immune-Suppression, Chemotherapy, Nonstandard finite difference method / scheme.

AMS Subject Classifications: 37C75; 65L12; 92C37; 68U20.