Dynamical Analysis Of Cervical Cancer Disease Model With Treatment

Abstract

This study proposes a model of cervical cancer due to infection with the Human Papilloma Virus (HPV). Various new assumptions are considered to get the model as ideal as possible. Among them, the transmission process depends on interactions with individuals infected with HPV, and the chance of cure is quite high with treatment. In this case, treatment can be in the form of radiotherapy, chemoradiation, chemotherapy, and palliative care. Five subpopulations were constructed, namely the subpopulation of susceptible individuals (S), the subpopulation of vaccinated individuals (V), the subpopulation of individuals infected with HPV (H), the subpopulation of individuals with cervical cancer (K), and the subpopulation of cured individuals (R). The model is formed into a five-dimensional nonlinear differential equation system. Dynamic analysis is carried out by determining the model’s equilibrium point and the conditions for the existence and local stability of the equilibrium point. The results of the analysis show that the system has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The disease-free equilibrium point exists unconditionally and is shown to be stable under certain conditions. The endemic equilibrium point exists fR_0>1 and is unstable because it has positive eigenvalues. Thus, based on the model that has been formed, the spread of cervical cancer can be controlled with treatment and the number of individuals being vaccinated is increasing.