Numerical Bifurcations and Sensitivity Analysis of an SIVPC Cervical Cancer Model

We consider a mathematical model of cervical cancer based on the Natural History of Cervical Cancer. The model is a five dimensional system of the first order of ordinary differential equations that represents the interaction between the free Human Papilloma Virus (HPV) population and four cells sub-populations, i.e., the normal cells, infected cells by HPV, precancerous cells, and cancer cells. We focus our analysis to determine the existence conditions of the nontrivial equilibrium point, the bifurcations, and the sensitivity of the parameters that play important roles in metastasis. Based on the basic reproduction ratio of the system, we found that the infection rate, the new viruses production rate, the free viruses death rate, the infected cells growth rate, and the precancerous cells progression rate play important roles for the cancer spreads in the cellular level. By applying sensitivity and numerical bifurcation analysis, we found that there are some important bifurcations that trigger some irregular behaviours of the system, i.e., fold, Hopf, cusp and Bogdanov-Takens.