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

Abstract

IntroductionCOVID-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.MethodsThis 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.ResultsQueueing 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.ConclusionsQueueing 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.

Enhancing Mass Vaccination Programs with Queueing Theory and Spatial Optimization

“…[4][5][6] Moreover, excessive queueing during pandemic emergencies also pose health risks, as long wait times may increase exposure to infectious pathogens. 7 Queueing theory is a branch of applied mathematics that offers a valuable framework for studying the behaviors and effects of waiting lines or queues. 8 In brief, queueing models aim to capture how a customer population moves through a queueing system via a series of processes dictated by probabilistic rates: arriving at a service site, receiving service, waiting in a queue if the server is busy, or leaving the queue before service is rendered when waiting times exceed a customer's willingness to wait.…”

“…Queueing theory is foundational to operations research and has been applied to many facets of healthcare operations, including the triage process in emergency care departments, 9 staffing needs in operating rooms, 10 hospital bed management, 11,12 and outpatient scheduling. 13 Additionally, it has been applied to COVID-19 vaccine distribution and capacity planning, 7,[14][15][16][17][18] as well as the containment of disease outbreaks, bioterrorist attacks, and other public health emergencies. [19][20][21][22] Mass dog vaccination campaigns (MDVCs) are held annually in Arequipa, Peru to address the re-emergence of canine rabies in the region; 23 they have important parallels with early pandemic vaccination and testing programs in that success depends, in part, on strategically placing and optimally allocating resources across a discrete number of fixed-location facility sites.…”

“…4–6 Moreover, excessive queueing during pandemic emergencies also pose health risks, as long wait times may increase exposure to infectious pathogens. 7…”

“…Queueing theory is foundational to operations research and has been applied to many facets of healthcare operations, including the triage process in emergency care departments, 9 staffing needs in operating rooms, 10 hospital bed management, 11,12 and outpatient scheduling. 13 Additionally, it has been applied to COVID-19 vaccine distribution and capacity planning, 7,14–18 as well as the containment of disease outbreaks, bioterrorist attacks, and other public health emergencies. 19–22…”