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 $R_0$ 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 $R_0$ 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 $R_0$.