Bifurcation Analysis in a Model of the Interaction between Cervical Cancer Cells, Effector Cells, and IL-2 Compound with Immunotherapy

Authors

  • Fajar Adi Kusumo* Department of Mathematics, Universitas Gadjah Mada
  • Rara Sandhy Winanda

DOI:

https://doi.org/10.11145/402

Abstract

We consider the bifurcation analysis of a mathematical model describing the interaction between 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 В respectively inactivate p53 and pRb genes that play a role in regulating normal cell division and apoptosis. As a result, the infected cells undergo uncontrolled divisions. Whereas, the immune system in the human body is designed to detect the presence of antigens, i.e. a foreign 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. We assume that the interaction between the three populations В follow the biochemical reactions modeled with the Michaelis-Menten kinetics function. The analysis in this paper is a sequel work of Krischner (1998). In this paper we do some analytical computation to the similar system with the one in Krischner (1998). Moreover we add a perturbation term on the system which shows the fluctuation of the interaction between two type of cells, and study the dynamics and the bifurcation numerically.

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Published

2015-03-09

Issue

Vol. 2 No. 1 (2015)

Section

Conference Contributions

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