Mathematical Model Analysis of bifurcation of Cervical Cancer Cell Interactions, effector cells, and IL-2 compounds with Immunotherapy
ABSTRACT: In this research, we discuss about the bifurcation analysis of a mathematical model describing the interaction between three populations, i.e., cervical cancer cells, effector cells, and IL-2 compounds. Cervical cancer is a malignant tumor that is caused by Human Papillomavirus (HPV). Protein E6 and E7 of HPV then respectively inactivate p53 and pRb genes that play a role in regulating normal cell division and apoptosis. As a result, infected cells undergo uncontrolled divisions. Whereas, the immune system in the human body is designed to detect the presence of antigens, i.e. a non-self protein in the body, and efector cells will destroy the HPV-infected cells with stimulation by IL-2. Immunotherapy is a treatment by using part of tumor tissue to enhance the immune response by in-vitro fertilization so that cervical cancer can be cured. In this research, it is assumed that the interaction between the three populations, follow the biochemical reactions that are modelled with the function of Michaelis-Menten kinetics. The analysis is focused on the bifurcation that occurs at the free state cancer equilibrium and infected HPV equilibrium.
