Mathematical Modeling and Optimal Control of HPV Infection of Epithelial Cells and Cervical Cancer
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Abstract
In this paper, a within-host model of human papillomavirus (HPV) infection and cervical cancer is proposed. The model consists of seven compartments including susceptible, exposed, infected, early-stage cervical cancer cells, end-stage cervical cancer cells, HPV, and recovered cervical cells. The existence, positivity and boundary of solutions are proved and the basic reproduction number is calculated. We obtain that when the basic reproduction number is less than one, an infection-free equilibrium point is both locally and globally stable, whereas when it is greater than one an infected steady state exists and is globally stable. Further, the optimal control problem is applied in this study by using Pontryagin’s Minimum Principle with three control variables which are preventive vaccine, treatment effort for infected cervical cells and treatment effort for early-stage cervical cancer cells. Numerical simulations of optimal control model demonstrate that each individual control could reduce an HPV infection and cervical cancer to some certain extent, however, a combination of all three controls gives the best scenario in controlling HPV infection and cervical cancer.
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