Fair and effective vaccine allocation during a pandemic.

This paper presents a novel model for the Vaccine Allocation Problem (VAP), which aims to allocate the available vaccines to population locations over multiple periods during a pandemic. We model the disease progression and the impact of vaccination on the spread of the disease and mortality to minimise total expected mortality and location inequity in terms of mortality ratios under total vaccine supply and hospital and vaccination centre capacity limitations at the locations. The spread of the disease is modelled through an extension of the well-established Susceptible–Infected–Recovered (SIR) epidemiological model that accounts for multiple vaccine doses. The VAP is modelled as a nonlinear mixed-integer programming model and solved to optimality using the Gurobi solver. A set of scenarios with parameters regarding the COVID-19 pandemic in the UK over 12 weeks are constructed using a hypercube experimental design on varying disease spread, vaccine availability, hospital capacity, and vaccination capacity factors. The results indicate the statistical significance of vaccine availability and the parameters regarding the spread of the disease. • The problem of allocating vaccines to a set of locations to minimise total mortality and inequity among locations is studied. • A mathematical programming model combining epidemiological disease spread and resource allocation under capacity limitations is provided. • The model is nonlinear and nonconvex but can be solved to optimality by an off-the-shelf solver. • The model is applied to the COVID-19 case in the UK by generating numerous scenarios. • The results demonstrate a strong correlation between the model's outcomes and real-world data, and underscore the statistical significance of vaccine availability. [ABSTRACT FROM AUTHOR]