Optimal Control on a Model for Cervical Cancer

Cervical cancer is caused by the human Papillomavirus (HPV) that attacks the cervix. Cervical cancer globally ranks third as the most frequent cancer among women. In this research, a model of HPV infection in cervical cancer consists of five sub categories of cells, namely susceptible cells, infected cells, pre-cancer cells, cancer cells, and viruses. The study was conducted by forming a model of HPV infection with the addition of treatment controls on pre-cancerous cells. The aim is to minimize the number of pre-cancerous cells while minimizing cost. The HPV infection model with control was solved using Pontryagin’s maximum principle in order to obtain optimal control. Numerical simulations are performed on the differential equations for the cell densities using the fourth order Runge-Kutta method. The simulation results indicate that a smart administration of treatment can be tailored such that the number of pre-cancer cells is minimized at minimal cost. This configuration with a minimal number of pre-cancer cells is favourable since it inhibits the development of cancer cells. © 2021, Springer Nature Switzerland AG.