Optimal vaccination strategies for imperfect vaccines and variable host susceptibility

I present a method to allocate a given number of vaccines to members of a population who differ in their susceptibility to the disease so that the final size of the epidemic is minimised. I consider an arbitrary distribution of protection that the vaccine confers, including the extreme cases of leaky and all-or-none vaccines. The optimal vaccination policy depends on the distribution of protection. While for low values of the basic reproduction number R0 the optimal policy prioritises the most susceptible hosts, I show that for almost any distribution the order of priority reverses and the least susceptible hosts should be vaccinated when R0 is high. The exception where this does not happen is the all-or-none vaccine. However, even a small deviation from the ideal all-or-none distribution can imply that the limited number of vaccines should be given to less susceptible hosts already at realistic values of R0.