Modeling the transmission dynamics and vaccination strategies for human papillomavirus infection: An optimal control approach

Saldaña, Fernando; Camacho-Gutíerrez, José Ariel; Villavicencio-Pulido, Geiser; Hernández, Juan González

doi:10.1016/j.apm.2022.08.017

Cited by 10 publications

(12 citation statements)

References 59 publications

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“…As shown in Saldaña et al. ( 2022 ), a vaccination rate u can be approximated by where is the fraction of vaccinated individuals at time t , that is, the vaccination coverage. Considering a very optimistic case in which health authorities achieve a vaccination coverage of the population in year, we obtain that the constant vaccination rate per year.…”

Section: Optimal Vaccine Allocationmentioning

confidence: 99%

Optimal vaccine allocation for the control of sexually transmitted infections

et al. 2023

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The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases. Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes. Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack–McKendrick-type model, where the control variables are the daily vaccination rates for females and males. One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin’s Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward–backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ( – vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection.

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Section: Optimal Vaccine Allocationmentioning

confidence: 99%

Optimal vaccine allocation for the control of sexually transmitted infections

et al. 2023

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“…daily vaccination rate. As shown in (Saldaña et al, 2022), a vaccination rate u can be approximated by u = − ln(1 − Vc(t))/t (15) where Vc(t) is the fraction of vaccinated individuals at time t, that is, the vaccination coverage. Considering a very optimistic case in which health authorities achieve a vaccination coverage Vc(t) = 80% of the population in t = 1 year, we obtain that the constant vaccination rate u ≈ 1.60 per year.…”

Section: Optimal Vaccine Allocationmentioning

confidence: 99%

Optimal vaccine allocation for the control of sexually transmitted infections

Saldaña

Steindorf

Srivas

et al. 2023

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The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases.Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes.Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack-McKendrick-type model, where the control variables are the daily vaccination rates for females and males.One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin's Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward-backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ($20%-30%$ vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least $40%$ coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection. MSC Classi cation: 92B05 , 49N90 , 34A34

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“…Baseline parameter values for system (4) are summarized in Table 1. Mean values for some of the model parameters are obtained using sexual behavior data from [28] and estimations from previous studies of STIs (see [13,18,35] and the references therein). Instead of focusing on a single disease, we consider a set of scenarios of interest that are feasible for the most frequent STIs.…”

Section: A Multigroup Sir-type Model With Time-dependent Vaccinationmentioning

confidence: 99%

“…daily vaccination rate. As shown in [35], a vaccination rate u can be approximated by u = − ln(1 − C(τ ))/τ where C(τ ) is the immunization coverage at time τ . We consider a case in which health authorities can achieve a vaccination coverage C(τ ) = 80% of the population in one year (τ = 365 days), then the vaccination rate is equal to u ≈ 1.60/365 per day.…”

Section: A Multigroup Sir-type Model With Time-dependent Vaccinationmentioning

confidence: 99%

“…One important attribute of the L 2 −formulation is that it is amenable to mathematical analysis in the sense that the optimal control problem (OCP) can be reduced to a two-point boundary value problem which can be easily solved by standard numerical methods [22]. This mathematical convenience is probably the main reason that the L 2 −formulation is so widespread in the literature [4,3,5,7,15,16,20,23,26,30,35,36,44,47]. Yet, for biomedical and epidemiological applications, the use of L 2 −objective functionals is frequently difficult to validate.…”

Section: Introductionmentioning

confidence: 99%

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Optimal vaccination strategies for a heterogenous population using multiple objectives: The case of L1− and L2−formulations

Saldaña

Kebir

Camacho-Gutíerrez³

et al. 2023

Preprint

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The choice of the objective functional in optimization problems coming from biomedical and epidemiological applications plays a key role in optimal control outcomes. In this study, we investigate the role of the objective functional on the structure of the optimal control solution for an epidemic model that includes a core group with higher sexual activity levels than the rest of the population. An optimal control problem is formulated to find a targeted vaccination program able to control the spread of the infection with minimum vaccine deployment. Both $L_{1}-$ and $L_{2}-$objectives are considered as an attempt to explore the trade-offs between control dynamics and the functional form characterizing optimality. Our results show that the optimal vaccination policy for both the $L_{1}-$ and the $L_{2}-$formulation share one important qualitative property, that is, immunization of the core group should be prioritized by policymakers to achieve a fast reduction of the epidemic. Nevertheless, quantitative aspects of this result can be significantly affected depending on the objective weightings. Overall, our results suggest that the optimal control profiles are reasonably robust with respect to the $L_{1}-$ or $L_{2}-$formulation when the monetary cost of the vaccination policy is substantially lower than the cost associated with the disease burden but if this is not the case the optimal control profiles can be radically different for each formulation.

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Modeling the transmission dynamics and vaccination strategies for human papillomavirus infection: An optimal control approach

Cited by 10 publications

References 59 publications

Optimal vaccine allocation for the control of sexually transmitted infections

Optimal vaccine allocation for the control of sexually transmitted infections

Optimal vaccine allocation for the control of sexually transmitted infections

Optimal vaccination strategies for a heterogenous population using multiple objectives: The case of L1− and L2−formulations

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