TITLE:
Mathematical Models and Numerical Simulation for Dynamic Evolutions of Cancer and Immune Cells
AUTHORS:
Benjamin Oyediran Oyelami
KEYWORDS:
Model, Cancer, Numeric Simulation, Pollution, Carcinogenic
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.6,
June
6,
2018
ABSTRACT: Cancer is a major public health problem worldwide and finding a total cure or
eradication of the disease has been the expectations of medical researchers
and medical practitioners in the recent times. In this paper, invasion of normal
cells by carcinogens is considered. The purpose of the research is to study
the dynamic evolutions of cancer and immune cells with the view finding
most effective strategic way to control or eradicate cancer growth in human
beings. We proposed five growths and mitigate models for benign and malignant
cancer which are coupled ordinary differential equations and partial differential
equations and Numerical simulations are made for the models. Analytic
and Numerical solutions and sensitivity analysis of the models to parameters
are obtained. It is found that the benign and malignant cancer cells
displayed out of control growth and hence unstable in nature and the immune
cells depreciated to the point of immune collapse. By the use of energy function
it is established that staving of cancer cells of oxygen or use of drugs are
strategic ways of combating cancer disease. Moreover, if the cancer cells are
starved of basic nutrients or some basic enzymes inhibited it is expected that
similar effect can also be achieved. The starvation of cancer cells should focus
on oxygen, nutrients and vital enzymes. However, it is hoped that drugs developers
and bioengineers will come up with means to achieve the starvation
strategies to combat cancer disease.