Optimal Control against the Human Papillomavirus: Protection versus Eradication of the Infection

Fernando Saldaña,Ignacio Barradas,Andrei Korobeinikov

doi:10.1155/2019/4567825

Abstract

We investigate the optimal vaccination and screening strategies to minimize human papillomavirus (HPV) associated morbidity and the interventions cost. We propose a two-sex compartmental model of HPV-infection with time-dependent controls (vaccination of adolescents, adults, and screening) which can act simultaneously. We formulate optimal control problems complementing our model with two different objective functionals. The first functional corresponds to the protection of the vulnerable group and the control problem consists of minimizing the cumulative level of infected females over a fixed time interval. The second functional aims to eliminate the infection, and, thus, the control problem consists of minimizing the total prevalence at the end of the time interval. We prove the existence of solutions for the control problems, characterize the optimal controls, and carry out numerical simulations using various initial conditions. The results and properties and drawbacks of the model are discussed.

Highlights

Human papillomavirus (HPV) is the leading etiological factor for the development of cervical cancer
Gardasil-9 protects against HPV types 6, 11, 16, and 18 and against the five most common oncogenic viral types, namely, HPV 31, 33, 45, 52, and 58
We propose and study a compartmental model for the transmission dynamics of the HPV types targeted by the nonavalent vaccine Gardasil-9

Summary

Introduction

Human papillomavirus (HPV) is the leading etiological factor for the development of cervical cancer. To examine the dynamics of HPV spread and control, numerous mathematical models have been proposed [5,6,7,8,9,10,11,12,13,14,15] While these and other recent studies analyzed different strategies for HPV control and brought important insight into the problem, the majority of them did not take into account the optimality of these interventions. The aim is to use optimal control theory to gain insight into the best combination of vaccination and screening to reduce the spread of HPV infection, as well as the cost of the intervention strategy To address this issue, we construct a mathematical model that allows vaccination prior to and after sexual initiation in both males and females. The last section contains the conclusions and a discussion of the obtained results

Model Formulation and Analysis

The Optimal Control Problems

The Pontryagin Maximum Principle

Results

Discussion and Conclusion