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

Mathematical Theory and Modeling, Vol 8, No.7, 2018

20 Pages Posted: 7 Dec 2018

See all articles by Houénafa Alain Togbenon

Houénafa Alain Togbenon

Jomo Kenyatta University of Agriculture and Technology; Pan African University, Institute for Basic Sciences, Technology and Innovations (PAUISTI)

Guy Aymard Degla

Université d'Abomey-Calavi (UAC) - Institute of Mathematics and Physical Sciences

Mark Eric Kimathi

Machakos University

Date Written: November 2, 2018

Abstract

We introduced recently a model that takes into account mutation and drug resistance of tumor cells in a case of simple immune system and immune-suppression caused by the resistant 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 indicates 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

JEL Classification: 37C75, 65L12, 92C37, 68U20

Suggested Citation

Togbenon, Houénafa Alain and Degla, Guy Aymard and Kimathi, Mark Eric, Stability Analysis Using Nonstandard Finite Difference Method and Model Simulation for Multi-Mutation and Drug Resistance With Immune-Suppression (November 2, 2018). Mathematical Theory and Modeling, Vol 8, No.7, 2018, Available at SSRN: https://ssrn.com/abstract=3283341

Houénafa Alain Togbenon (Contact Author)

Jomo Kenyatta University of Agriculture and Technology ( email )

P.O. Box 62000
Nairobi, Nairobi
Kenya
+254796517224 (Phone)

Pan African University, Institute for Basic Sciences, Technology and Innovations (PAUISTI) ( email )

P.O. Box 62000-00200
Nairobi-Kenya, 62000
Kenya

Guy Aymard Degla

Université d'Abomey-Calavi (UAC) - Institute of Mathematics and Physical Sciences ( email )

Benin

Mark Eric Kimathi

Machakos University ( email )

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
58
Abstract Views
411
Rank
653,722
PlumX Metrics