Optimal vaccination at high reproductive numbers: sharp transitions and counter-intuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g., when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation for minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. Furthermore, we show that this phenomenon occurs at a range of basic reproduction numbers relevant for the currently circulating strains of SARS-CoV-19. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a simple two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.