Queueing Theory and COVID-19 Prevention: Model Proposal to Maximize Safety and Performance of Vaccination Sites

COVID-19 (Coronavirus Disease 19) has rapidly spread all around the world. Vaccination represents one of the most promising counter-pandemic measures. There is still little specific evidence in literature on how to safely and effectively program access and flow through specific healthcare settings to avoid overcrowding in order to prevent SARS-CoV-2 transmission. Literature regarding appointment scheduling in healthcare is vast. Unpunctuality however, especially when targeting healthcare workers during working hours, is always possible. Therefore, when determining how many subjects to book, using a linear method assuming perfect adhesion to scheduled time could lead to organizational problems.

This study proposes a "Queuing theory" based approach. A COVID-19 vaccination site targeting healthcare workers based in a teaching hospital in Rome was studied to determine real-life arrival rate variability. Three simulations using Queueing theory were performed.

Queueing theory application reduced subjects queueing over maximum safety requirements by 112 in a real-life based vaccination setting, by 483 in a double-sized setting and by 750 in a mass vaccination model compared with a linear approach. In the 3 settings, respectively, the percentage of station's time utilization was 98.6, 99.4 and 99.8%, while the average waiting time was 27.2, 33.84, and 33.84 min.

Queueing theory has already been applied in healthcare. This study, in line with recent literature developments, proposes the adoption of a Queueing theory base approach to vaccination sites modeling, during the COVID-19 pandemic, as this tool enables to quantify ahead of time the outcome of organizational choices on both safety and performance of vaccination sites.