Optimal vaccine allocation for the control of sexually transmitted infections

Abstract

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

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

“…An objective of the form (8) has as a main goal minimization of the disease burden but also the use of control. We remark that alternative formulations can also be found in the literature, for instance, using an isoperimetric constraint to model a specific health budget or minimum-time control problems [1,20,37] but these examples are relatively uncommon, and the majority of OC studies in epidemiology use an objective within the general form (8).…”

“…The optimal control theory (OCT) is an essential tool frequently used to solve a wide range of optimization problems for dynamical systems including vaccine allocation problems in public health [1,4,7,9,15,17,22,27,30,35,37,41,42,44]. Probably one of the most relevant issues when solving optimization problems via OCT is the choice of the performance criterion, that is the objective functional to be minimized or maximized [11,20,16,26,43].…”