Optimal control against the human papillomavirus: protection versus eradication of the infection. (English) Zbl 1474.92122

Saldaña, Fernando; Korobeinikov, Andrei; Barradas, Ignacio

Abstr. Appl. Anal. 2019, Article ID 4567825, 13 p. (2019).

Summary: 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.

MSC:

92D30	Epidemiology
92C60	Medical epidemiology
49J15	Existence theories for optimal control problems involving ordinary differential equations
49K15	Optimality conditions for problems involving ordinary differential equations
49N90	Applications of optimal control and differential games

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