Optimal vaccination at high reproductive numbers: sharp transitions and counterintuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g. when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation minimizing the number of infections prioritizes the vaccination of those who are
least
likely to be infected. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

Methods
The MATLAB source code, including all data and parameters used to produce the graphs presented in this work, is available on GitHub at https://github.com/NGavish/HighR0 or Zenodo at https://doi.org/10.5281/zenodo.6962689.

The contact matrices used in the code were obtained from [Citation 28; PLOS Computational Biology, e1009098]. There are provided as .mat files under the subdirectory /CountryData and under the names xxx_data.mat where xxx is the country code.

Pre-computed data files are provided as .mat files under the subdirectory /data.  By default, the graphs are produced from pre-computed simulation output. See Usage Notes for instructions on producing the graphs without relying on these pre-computed data files.