Optimal scheme for vaccine allocation in multi-community networks

The spread of infectious diseases on complex networks has been a hot topic of research in recent years. In this work, we constructed multi-community networks based on the varying frequencies of social interactions between individuals in different regions, in which the frequencies of social interactions are described by the intra-community average degree. We investigated the impact of vaccine allocation in different communities on the overall spreading range of the entire network. The simulation and analysis show that to achieve the optimal control performance, all communities should be ranked from the smallest to the largest in terms of the threshold vaccine number first, and the lower the threshold vaccine number, the easier the community is to be suppressed. Secondly, we compared the total number of vaccines with the threshold number of vaccines required for each community, and if the number of vaccines is sufficient to suppress l communities, then the vaccines should be allocated among the l+1 communities that are most likely to be suppressed. Finally, we sequentially assigned the threshold number of vaccines for each community until they are allocated to the l+1 communities. Our findings provide theoretical support for addressing the challenge of vaccine allocation in resource-limited settings.