CSIAM Trans. Life Sci., 1 (2025), pp. 506-521.
Published online: 2025-10
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Personal diverse interests and many group interactions naturally create partially overlapping groups within a population. Those who belong to multiple groups play a crucial role in spreading of infectious diseases across the whole population. We develop an algorithm to decompose the microscopic overlap structure of groups with representing a population of partially overlapping groups as a hypergraph of partially overlapping hyperedges, and characterize it using a newly defined overlap matrix. We formulate a specific multi-group SIR epidemic model, and address a one-time preventive vaccine allocation problem aimed at effectively reducing the basic reproduction number. By leveraging perturbation theory, we derive a principled ranking index to measure the vaccination priority of different groups, and establish a ranking vaccination strategy, which usually outperforms random vaccination strategies as verified by a series of numerical examples. These results offer a theoretical foundation for public health decision-making to develop effective vaccination allocation plans.
}, issn = {3006-2721}, doi = {https://doi.org/10.4208/csiam-ls.SO-2025-0011}, url = {http://global-sci.org/intro/article_detail/csiam-ls/24513.html} }Personal diverse interests and many group interactions naturally create partially overlapping groups within a population. Those who belong to multiple groups play a crucial role in spreading of infectious diseases across the whole population. We develop an algorithm to decompose the microscopic overlap structure of groups with representing a population of partially overlapping groups as a hypergraph of partially overlapping hyperedges, and characterize it using a newly defined overlap matrix. We formulate a specific multi-group SIR epidemic model, and address a one-time preventive vaccine allocation problem aimed at effectively reducing the basic reproduction number. By leveraging perturbation theory, we derive a principled ranking index to measure the vaccination priority of different groups, and establish a ranking vaccination strategy, which usually outperforms random vaccination strategies as verified by a series of numerical examples. These results offer a theoretical foundation for public health decision-making to develop effective vaccination allocation plans.