Allegheny County, Pennsylvania, where the city of Pittsburgh is located, served as the study area for this research. Although this study focuses on one jurisdiction, the methods employed can be applied to any geographic area. The Allegheny County Health Department has preselected 50 places in the county that could serve as mass immunization locations. Each site is an existing public high school in the county. High schools are recommended for several reasons,^{5(Annex 3, p14)} the primary one being their capacity to handle large crowds because of the gymnasiums, auditoriums, and ample parking they have on-site. To determine the best number of locations to open in Allegheny County for travel time and distance minimization, a function in GIS known as Location-Allocation, was used. In a general GIS context, “Location” describes the process involved in finding the optimal locations for facilities (mass immunization locations) given a set of demand points. “Allocation” is the process of allocating demand points (households) to service areas that contain the facilities providing goods or services that satisfy the demand. In this type of analysis, the best facilities are located in such a way that the sum of all weighted costs between demand points and solution facilities is minimized.

The Location-Allocation uses heuristic methods that involve minimizing the distances from all facilities and each demand point.^2(p265) Heuristic techniques are designed for solving a problem more quickly when classic methods are too slow, or for finding an approximate solution when traditional methods fail to find any exact solution. The procedure begins by finding the shortest-path allocation of demand points to solution facilities. An iterative process subsequently occurs to create an improved facility-demand point allocation. The method continues refining until the optimal location-allocation results are obtained. The algorithm uses the street network to allocate each demand point (household) to a facility (mass immunization location), taking into account several factors including the total number of facilities available, their geographic locations, and their distances to the demand points. The households used in the analysis were supplied from a synthetic population developed by Wheaton⁶ for agent-based modeling with GIS. Synthetic households are placed across the landscape to match high-resolution population distribution data from the US Census Public Use Microdata Sample and are assigned to the closest road segment for use in the Location-Allocation process. The synthetic households accurately reflect the composition and distribution of real households.

The location-allocation analyses were processed at 5-site increments beginning with 30 (n=30, n=35 … n= 50) to obtain the most favorable sites that minimize time and distance for residents. The output generated from the process included a count of the demand points (total persons based on the synthetic population) allocated at each site. The first step in calculating throughput was to obtain the number needed to achieve a herd immunity threshold that would abate an epidemic, based on the R₀ of the epidemic. This threshold is equivalent to⁷

Herd immunity threshold = 1 − R₀/R₀.

Therefore, to tabulate the vaccination requirements, the population allocated at each site was multiplied by the proportion of the population needed to achieve herd immunity (33.3% for an epidemic with R₀ = 1.5 (corresponding to an influenza epidemic); 50% for an epidemic with R₀ = 2; 66.7% for an epidemic with R₀ = 3; 75% for an epidemic with R₀ = 4 (corresponding to an SARS epidemic); 80% for an epidemic with R₀ = 5; 83.3% for an epidemic with R₀ = 6; and 85.7% for an epidemic with R₀ =7 (corresponding to a smallpox epidemic). We also assumed that the county would have no more than a week (or 5 working days) to get its population protected. Thus, to get the daily throughput required to complete the immunizations within 5 days for each of these R₀s, the number needed to achieve the herd immunity threshold is divided by 5. The 5900 persons per day vaccination delivery estimate found in the CDC’s Smallpox Response Plan & Guidelines^{5(Annex 3, p8)} was used as a basis for determining which sites would exceed the throughput recommendation. (We used the smallpox throughput capacity as an example because none were readily available for other types of infectious epidemics). Any site with a throughput value exceeding this estimate was identified as a mass immunization location that would be over capacity.

The Location-Allocation assigned each household in Allegheny County to one of the high school mass immunization locations. Residents assigned to selected facilities in and around the city of Pittsburgh are relatively close (1 or 2 miles) to their destination sites. Low-density areas, such as those outside the city, generally require longer travel times and distances, and thus, selected locations in those areas have people coming to them from longer distances. Figure 2 illustrates an example of the results obtained from selecting the best 30 sites from the complete set of 50. The large, white circles represent the 30 sites ideal for travel time and distance minimization. The smaller circles are the sites that did not get selected during the Location-Allocation analysis. The lines on the map, which illustrate the path between each household and its assigned immunization location, are symbolized in the legends to indicate the time in minutes and distance in miles that it would take for each household to travel to its associated site. For the vast majority of households, the travel distance is 5miles or less, and the travel time would be 5 minutes or less under normal traffic conditions. The large circles with the star indicate sites that would not meet the daily throughput required to complete immunizations for smallpox in 5 days.

The numbers of people assigned to each of the selected locations in each scenario were then analyzed to determine which of those selected sites were not able to meet the smallpox throughput recommendation of 5900 people per day. The Table contains a few records from the spreadsheet, including a location that was not selected (BRENTWOOD Senior High School) and one that was allocated but does not have sufficient throughput to meet allocated demand for R₀ ≥ 5 (NORTH HILLS Senior High School). At an R₀ of 1.5, the population allocated at each location was sufficient for achieving herd immunity in each of the scenarios explored. The number of locations that exceeded the capacity needed for herd immunity increased with rising R₀s. When the top 30 sites of 50 were selected for travel time and travel distance minimization, there were 18 to 19 sites where demand exceeded capacity at the highest R₀s. As the number of selected sites increased, the number of sites that could meet this throughput increased. Even when all 50 sites were in operation, however, multiple locations were inadequate in meeting the demand to achieve herd immunity, beginning with an R₀ equal to 2 for travel time minimization and an R₀ of 3 for travel distance minimization. For these cases, health department officials could consider adding secondary immunization locations, such as nearby elementary or middle schools, or shifting residents to sites that were not initially selected for travel time or distance minimization. This could be viewed as a limitation of the model because the reallocation of residents from overloaded sites must be done as a secondary step.

The geospatial techniques employed in this study were used to identify the prime n mass immunization sites (from a previously determined set of sites) for travel time and travel distance minimization for residents in Allegheny County, Pennsylvania. When resources are limited, public health departments can use the Location-Allocation to select a subset of their locations such that the set of sites chosen minimizes travel time and travel distance. Although the function of the model was to allocate the universe of residents in the study area without instituting a “cap” at each site, health department officials are able to assess which locations would exceed capacity after the allocation is complete and then add resources to alleviate overburdened service areas.

The Location-Allocation is a heuristic and, as such, provides a useful tool for locating POD sites. Nevertheless, this method is subject to several limitations. First, it does not take into account qualitative variables, such as human behavior. Second, its results are static—meaning that any issues that arise during a dispensing process are not factored in. Third, although the methods are applicable to jurisdictions other than Allegheny County, potential issues with scalability in larger or smaller jurisdictions could exist.

Further research will involve the development of a Web-enabled tool that will aid in the decision-making process for selecting the most ideal sites for mass vaccination as well as for other POD site location needs—such as pharmaceutical dispensing. When implemented, the methods described in this study can be used to enhance a public health department’s preparedness and demonstrate its progress toward meeting government standards and performance measures for medical countermeasure delivery during a disease outbreak or public health emergency.