Analysis of a Cells Repair Regulations Model of Nasopharyngeal Carcinoma Fajar Adi Kusumo(a*) , Ario Wiraya(b*)
a) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Indonesia.
b)Mathematics Education Study Program, Faculty of Teacher Training and Education, Universitas Sebelas Maret, Surakarta, Indonesia
Abstract
Nasopharyngeal Carcinoma (NPC) is a malignant cancer which is caused by the activation of Epstein-Barr
Virus (EBV) via some external factors. It grows on nasopharyngeal epithelial cells. In the cells repair regulations, the p53 gene mutation can be used as the early indication of the NPC growth. Usually, the NPC growth is due to the DNA damage accumulation caused by the EBV infection. The base model of the cells repair regulations model to characterize
the NPC growth is a 15 dimensional of first order ODE system and consists the proteins and enzymes reactions. However, there are some proteins that play important roles in the regulation of cell repair for metastatic NPC, i.e., ATM, p53, MDM2, and DSB. Therefore, we are able to construct a four-dimensional system of first-order ODE that has a 16-dimensional parameter space to study behaviours of the system and the appearance of attracting patterns of the solutions near the steady-state conditions. In this case, we use the codimension 1 and codimension 2 bifurcations analysis to study the role of several important parameters for the metastasis of NPC and study the possibilities of the system to have chaotic solutions. The appearance of a chaotic solution shows the irregularity of the system due to the changes of the initial conditions. It is important to understand the metastasis behavior NPC and to determine the treatment strategies.
