Optimal vaccination strategies for a community of households

The effectiveness of a vaccination program depends on how the vaccinations are spread over the households of the community. Here we formulate the optimal allocation of vaccinations as a linear programming problem, when the objective is to prevent epidemics with the minimum vaccination coverage. A vaccine efficacy of less than 100%, as is usual in practice, is allowed for. Optimal vaccine allocations attempt to leave the same number of susceptibles in every household if the disease has a very high transmission rate within households. This means that proportionately more individuals need to be vaccinated in larger households if the vaccine efficacy is less than 100%. The linear programming formulation can accommodate heterogeneity among individuals of the proportionate mixing form and can also minimize the initial reproduction number for a given achievable vaccination coverage.