Modeling Tumor Cell Proliferation and Therapeutic Treatment Simulation

K. W.  Bunonyo; Odinga  T.; C. G.  Ikimi

K. W. Bunonyo Department of Mathematics and Statistics, Federal University Otuoke, Nigeria
Odinga T. Department of Biochemistry, Rivers State University, Nigeria
C. G. Ikimi Department of Biochemistry, Federal University Otuoke, Nigeria

Keywords: Modeling, simulation, chemo-immunotherapy, Tumour growth, cell proliferation, carcinogenic, therapeutic treatment

Abstract

Background and Objectives: Tumor growth and cell proliferation have been global health concerns over the years. This research involves the formulation of mathematical models to investigate tumor cell proliferation and the application of treatments to control and reduce cell proliferation. Materials and Methods: The study is divided into two parts: first, the model depicts the tumor spreading through the cell proliferation caused by a carcinogenic substance (agent), which causes the tumor to grow exponentially, thereby putting lives at risk and facilitating death. Secondly, chemo-immunotherapeutic models were formulated and used to modify the tumor spread, and cell proliferation models were developed to control and reduce the proliferation rate. The formulated models were solved analytically. Graphical and tabular results were generated from the simulation using Wolfram Mathematica software, where we studied cases of a steady supply of chemo-immunotherapeutic drugs, the fading rate of chemo-immunotherapeutic drugs, the increase in carcinogenic substances, and the variation of growth rates on cell proliferation. Results: The study showed that cell proliferation increased, indicating the fast spread of the tumor as the carcinogenic substance exposure rate increased. However, it is seen that the steady supply of chemo-immunotherapeutic drugs helps in reducing and controlling cell proliferation. In addition, the fading rate of chemo-immunotherapeutic drugs, independently and combined, also decreases cell proliferation in the presence of a quantified carcinogenic substance. The study concludes that carcinogenic substances and the use of chemo-immunotherapeutic drugs in controlling and reducing cell proliferation can cause tumor spread.

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