Optimal prophylactic vaccination in segregated populations: When can we improve on the equalising strategy?

• Allocating prophylactic vaccination in a segregated population is a key issue.
• The equalising strategy (ES) has been proposed as an optimal means of vaccination.
• However, the ES only holds for density-dependent transmission,
• We consider more realistic types of transmission and show the ES can be improved.
• This highlights the possibility of more targeted vaccination strategies.

One of the fundamental problems in public health is how to allocate a limited set of resources to have the greatest benefit on the health of the population. This often leads to difficult value judgements about budget allocations. However, one scenario that is directly amenable to mathematical analysis is the optimal allocation of a finite stockpile of vaccine when the population is partitioned into many relatively small cliques, often conceptualised as households. For the case of SIR (susceptible–infectious–recovered) dynamics, analysis and numerics have supported the conjecture that an equalising strategy (which leaves equal numbers of susceptible individuals in each household) is optimal under certain conditions. However, there exists evidence that some of these conditions may be invalid or unsuitable in many situations. Here we consider how well the equalising strategy performs in a range of other scenarios that deviate from the idealised household model. We find that in general the equalising strategy often performs optimally, even far from the idealised case. However, when considering large subpopulation sizes, frequency-dependent transmission and intermediate levels of vaccination, optimality is often achieved through more heterogeneous vaccination strategies.