Determine Vaccination Priority in a Population of Partially Overlapping Groups

Abstract

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.

Keywords

Vaccination priority / overlap matrix / basic reproduction number / multi-group epidemic model