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

Abstract

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.