Efficacy versus coverage: population-level impacts of vaccination schemes

The effectiveness of vaccination campaigns depends on vaccine efficacy, vaccination coverage, and vaccine allocation. A fundamental yet often overlooked question is whether higher vaccine efficacy or higher coverage should be prioritised. Here, within a leaky vaccine framework, we provide a theoretical analysis of their relative impact on reducing the epidemic final size in both homogeneous and heterogeneous populations, under proportional and optimal vaccine allocations. We prove that, when vaccine efficacy (in reducing susceptibility) and coverage are traded off so that their product $P$ remains fixed but below the herd immunity threshold, the epidemic final size decreases as efficacy increases and increases as coverage increases, implying that efficacy should be prioritised. Mechanistically, under a fixed efficacy-coverage product, increasing efficacy amplifies population heterogeneity in susceptibility, which in turn reduces the final size. The difference between prioritising efficacy and prioritising coverage can be substantial, particularly when $R_0$ is large. For example, when the basic reproduction number $R_0=5.0$ and the product $P=0.6$ , the final size under prioritising coverage can be 250% as large as that under prioritising efficacy, and up to 400% in heterogeneous populations. These results highlight the critical importance of vaccine efficacy and could provide useful guidance for vaccination policy and epidemic control.