Examination of Gyllenberg and Webb cancer model and exploring the impact of different transition rates

Abstract

Despite considerable advancement in biomedical science, the entire planet is facing a significant deadly illness, “Cancer”. Cancer might also be one of the greatest and most hated diseases. In 2018, cancer is blamed for the deaths of almost 10 million individuals worldwide. It is the second largest cause of death according to WHO.  Over the recent several decades, the incidence of cancer has been steadily on the increase. It is never necessary to assign the origin of any cancer to one particular element. . Furthermore, the inability to find a suitable approach for treating Cancer is that Cancer is not only a particular illness, but a series of several diseases that share an extreme dysregulation of development. We have made an effort in the present research to create a sample of numerous mathematical models produced by various biologists and mathematicians. We developed a comprehensive set of ordinary differential equations, keeping Gyllenberg and Webb model as a reference, at the end of the paper to analyze the various transition rates affecting human tumor cell density. As per the authors’ knowledge, there has been no work done on studying the impact of transition rate from quiescent to proliferating states and also on the rate of death of quiescent state cells.

Keywords: Avascular tumor, proliferation, quiescent, tumor spheroid, transition rate.