Enhancing mass vaccination programs with queueing theory and spatial optimization

Background: Mass vaccination is a cornerstone of public health emergency preparedness and response. However, injudicious placement of vaccination sites can lead to the formation of long waiting lines or queues, which discourages individuals from waiting to be vaccinated and may thus jeopardize the achievement of public health targets. Queueing theory offers a framework for modeling queue formation at vaccination sites and its effect on vaccine uptake. Methods: We developed an algorithm that integrates queueing theory within a spatial optimization framework to optimize the placement of mass vaccination sites. The algorithm was built and tested using data from a mass dog rabies vaccination campaign in Arequipa, Peru. We compared expected vaccination coverage and losses from queueing (i.e., attrition) for sites optimized with our queue-conscious algorithm to those used in a previous vaccination campaign, as well as to sites obtained from a queue-naïve version of the same algorithm. Results: Sites placed by the queue-conscious algorithm resulted in 9–32% less attrition and 11–12% higher vaccination coverage compared to previously used sites and 9–19% less attrition and 1–2% higher vaccination coverage compared to sites placed by the queue-naïve algorithm. Compared to the queue-naïve algorithm, the queue-conscious algorithm placed more sites in densely populated areas to offset high arrival volumes, thereby reducing losses due to excessive queueing. These results were not sensitive to misspecification of queueing parameters or relaxation of the constant arrival rate assumption. Conclusion: One should consider losses from queueing to optimally place mass vaccination sites, even when empirically derived queueing parameters are not available. Due to the negative impacts of excessive wait times on participant satisfaction, reducing queueing attrition is also expected to yield downstream benefits and improve vaccination coverage in subsequent mass vaccination campaigns.