The Role of HPV on Cervical Cancer with Several Functional Response: a Control Based Comparative Study

Abstract

The development of cervical cancer cells from normal cells is caused by the human papilloma virus (HPV), and the progression can be described using a population model of the cells and free virus. We develop a mathematical model consisting of five compartments to describe the interactions between the human papilloma virus and four classes of epithelial and basal cells (susceptible, infected, precancerous, and cancerous) of cervix. In our mathematical model, we consider that the disease transmission rate from precancerous to cancerous cells is governed by a response function f(P) according to the risk and our cell immunity power which is dependent on the antibody genes p53 and pRb. So we have considered f(P) as three types of functions linear, Holling type II, and Holling type III. We analyze the local stability of the equilibrium points of each of the types in a comparative way and investigate analytically and numerically the parameters that play an important role in the progression towards the cervical cancer. Furthermore, we have taken some control strategies on the Holling type III functional response based on two types of drugs to eradicate the infected and cancer cell populations.