Optimal control efforts to reduce the transmission of HPV in a fractional-order mathematical model
A. El-Mesady, Tareq M. Al-shami, Hegagi Mohamed Ali
Abstract
Human papillomavirus (HPV) is a sexually transmitted virus that causes cervical cancer in women and leads to death. In this research paper, we prepare a fractional mathematical model that contains a system of four fractional differential equations (FDEs) based on the Caputo operator to describe the most significant epidemiological features of HPV infection and how this infection is transmitted. To check this model’s well-posedness, we investigate solutions existence, positivity, uniqueness and boundedness. Additionally, we identify the disease-free and endemic equilibrium points (EPs) to introduce their local stability, and also bifurcation analysis is presented. To find out whether the infection is spreading among the population or not, we calculated the basic reproduction number ( $R_{0}$ ) and accordingly we conducted a sensitivity analysis to determine the main epidemiological parameters controlling the proposed model. Further, the fractional optimal control problem (FOCP) is implemented for the proposed problem by utilizing Pontryagin’s maximum principle (PMP) with three time-dependent control variables, which are the efforts to promote safe sexual habits such as using a condom or monogamy, vaccination for HPV, and preventive measures for cervical cancer such as early screening and using drugs that prevent cells from turning cancerous. The necessary optimality conditions (NOCs) for this FOCP are established. Numerical simulations are carried out and presented in graphical representation to display the impact of combining different intervention optimal control strategies on the transmission dynamics of HPV. From the presented results, we confirm that all the proposed control measures help limit the spread of the disease to some extent, but the most effective strategy to eliminate the disease is to combine all control efforts.