key: cord-1034204-tclvkl5c
authors: Cabanilla, K. I. M.; Enriquez, E. A. T.; Mendoza, R.; Mendoza, V. M. P.
title: Optimal Selection of COVID-19 Vaccination Sites at the Municipal Level
date: 2021-06-24
journal: nan
DOI: 10.1101/2021.06.20.21259194
sha: 4ac4c61f66096d8d92025217caf5c3b9122eebc6
doc_id: 1034204
cord_uid: tclvkl5c

In this work, we present an approach to determine the optimal location of coronavirus disease (COVID-19) vaccination sites at the municipal level. We assume that each municipality or town is subdivided into smaller administrative units, which we refer to as villages or barangays. The proposed method solves a minimization problem arising from a facility location problem, which is formulated based on the proximity of the vaccination sites to the villages, number of COVID-19 cases, and population densities of the villages. We present a numerical scheme to solve the optimization problem and give a detailed description of the algorithm, which is coded in Python. To make the results reproducible, the codes used in this study are uploaded to a public repository, which also contains complete instructions on how to use them. As an illustration, we apply our method in determining the optimal location of vaccination sites in San Juan, a town in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic plans for the COVID-19 vaccine rollout.

The coronavirus disease , which was first reported in Wuhan, China, has spread across the globe and was declared a pandemic by the WHO on March 11, 2020 [1,2] . It has been shown that the COVID-19 vaccines are effective against severe disease and initial findings suggest that they can protect the population against infection [3] [4] [5] . An effective vaccination campaign can reduce the probability of disease resurgence and alleviate the economic burden of the pandemic [6] . It is estimated that 60-70% of the population must be fully vaccinated to achieve herd immunity, a threshold that provides indirect protection to uninfected individuals from getting COVID-19 from infected hosts [7] [8] [9] . To achieve the target immunity, the community's hesitancy over the COVID-19 vaccines must be addressed by the policymakers [10] . In a survey conducted in January 2021 by the Pulse Asia, almost half of the Filipino respondents said that they are not willing to get vaccinated against COVID-19 because of safety concerns. Hence, a collaborative effort among several stakeholders and sectors is needed to address this issue [11] . Unfortunately, COVID-19 vaccination in the Philippines is progressing at a very slow rate due to the inadequacy of the policymakers' long-term strategic plan [12] . We hope that this study may guide the Philippine local government units in coming up with strategic plans for vaccine rollout. We propose a way to select optimal vaccination sites from already existing facilities to make the vaccines more accessible to the public and achieve herd immunity at the soonest possible time.

Our proposed approach solves a facility location program, which is a problem that minimizes the cost of satisfying a set of demands with respect to some set of constraints [13] . Facility location problem has a variety of applications in determining optimal locations of solar power plant sites [14] , hydrogen production sites [15] , tsunami sensors [16, 17] , infrastructure maintenance depot [18] , tower sites for early-warning wildfire detection systems [19] , and high-speed train stations [20], among others. Facility location has also been used in several COVID-19-related studies. In [21] , an optimal allocation of COVID-19 testing kits among accredited testing centers has been proposed. The optimal location of pharmacies for COVID-19 testing to ensure access has been studied in [22] .

Identification of locations of COVID-19 emergency logistic centers has been proposed in [23] . In [24] , optimal COVID-19 testing facility sites in Nigeria have been studied.

Based on our review of related literature, very few studies have been conducted on the applications of facility location problems in COVID-19 vaccination distribution strategies. In [25] , an approach to optimize vaccine . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 24, 2021. ; https://doi.org/10.1101/2021.06.20.21259194 doi: medRxiv preprint *Corresponding Author: rmendoza@math.upd.edu.ph ORCID ID 0000-0003-3507-0327 distribution strategies has been proposed by selecting locations that will minimize the death toll. The method relies on an epidemiological model to capture the effects of vaccinations and mortality caused by COVID-19. In [26] , a mathematical framework in finding the optimal locations of distribution centers for test kits and vaccines has been developed. In [27] , a linear programming model was used for COVID-19 vaccine allocation in the Philippines at the national level. Because of the scale of these studies, constraints must be considered (e.g., shipping cost, production capacity, operating cost, etc.). In this study, we consider a local-scale vaccination strategy. By doing so, we can remove the logistic constraints associated with the delivery of the vaccines. Thus, we can focus on finding the optimal location of vaccination sites that will make the vaccines more accessible to the population of the town or city. Our work can be used in conjunction with vaccine allocation methods at the national level [25] [26] [27] . Once the vaccines are allocated to a town, our method can be applied to identify the sites where the vaccines will be distributed.

In the next section, we formulate the mathematical optimization model to address the vaccination site location problem. Then, we present the numerical method that solves the minimization problem and the open-source software that we developed. The open-source software is designed to be user-friendly and easy to implement. We illustrate how our proposed method works by applying the program in identifying optimal vaccination sites in San Juan, Batangas, Philippines. Finally, we present our conclusions and recommendations for future research.

Our goal is to determine the optimal location of vaccination sites in a town from a list of possible vaccination sites. We consider existing facilities such as public schools and hospitals as possible vaccination sites.

Furthermore, suppose that the town is divided into administrative units, which we refer to as villages. These are usually the country's basic units of government. In the Philippines, all towns are composed of several administrative units called barangays. Let { ∶ = 1,2, … , } be the set containing the locations of the possible vaccination sites. Each is represented by a two-dimensional vector whose components are the latitude and longitude of the th vaccination site. Define { ∶ = 1,2, … . } as the set containing the location of the administrative units. We can set as the location of the village/barangay hall or the community center, which is usually situated at the center of the village. Similarly, each is a two-dimensional vector whose components are the latitude and longitude of the th village or barangay. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Eq. 4

In the next section, we discuss how the minimization problem above is solved numerically.

For the overall numerical computation and some of the data extraction, we utilized the ease of use and availability of advanced open-source packages of the Python programming language. To compute the driving or road distance between two points, we leverage Open Street Maps (OSM) and its corresponding Python package OSMNX. OSM is a dynamic repository of detailed map data such as road level data, buildings, and even natural geographic objects such as rivers and mountains. OSM is built and continues to be actively updated by contributors from diverse backgrounds such as hobbyist mappers, disaster risk experts, and GIS professionals. OSM is open source, which means anyone can access and use the full breadth of its data. OSMX uses OSM data in conjunction with network graphs for a wide range of applications, such as all kinds of urban traffic and planning, all in a network graph analysis framework.

To solve the optimization problem for a given town, the user must input two files: the village centers contains the location of the all the possible vaccination sites. This is a CSV file with the schema shown in Table   2 . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. We found that it is possible to automate the extraction of the latitude and longitude data for the vaccination centers table using OSM to a considerable extent. However, the OSM automation could not differentiate between public and private schools, thus necessitating some manual review. OSM automation can be used to generate an initial version of the vaccination centers table on which the end-users can then build on by adding or removing vaccination centers to be considered. Even though the automation is only partial, it will still significantly reduce the manual processing needed to obtain a sufficiently good vaccination centers table. On the other hand, OSM could not identify the village halls, so manual extraction of this data using Google Maps is needed. Careful extraction must be done, e.g., via Google Street View, as there are some discrepancies in Google Maps on the location of the village halls.

The cost function is computed directly as shown in Eq. (4), where the road distance ( , ) between the th vaccination site and the th village hall, is computed via OSMX in Python. For both the single center and thesite optimization, we iterate through every possible combination of all the vaccination sites and villages so that the resulting optimum is the global optimum.

The Python program we developed takes in the two tables previously mentioned and outputs a ranked list of the vaccination centers and their respective costs. Since it is already ordered by cost, the optimum would be the first row.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 24, 2021. ; https://doi.org/10.1101/2021.06.20.21259194 doi: medRxiv preprint *Corresponding Author: rmendoza@math.upd.edu.ph ORCID ID 0000-0003-3507-0327

The code and a tutorial for the implementation of the numerical optimization method are found in the following GitHub repository: https://github.com/kurtizak/Covid-Site-Optimization. Sample xlsx files of the inputs can also be downloaded from this repository. The users can simply modify the Microsoft Excel files for easier implementation.

To illustrate how our proposed method works, we find the optimal placement of vaccination centers in San Juan, table and the vaccination centers table, respectively, which are the required inputs from the user.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 24, 2021. ; https://doi.org/10.1101/2021.06.20.21259194 doi: medRxiv preprint *Corresponding Author: rmendoza@math.upd.edu.ph ORCID ID 0000-0003-3507-0327

The code has two outputs. First, the geographic map of the area with the locations of the vaccination sites and barangay halls. Second, a data frame showing the vaccination site assignments of each barangay, as well as the distance between them. These results can be easily exported as a csv, excel, or any other format the user prefers. Figures 3 and 4 show the geographic distribution of the optimal vaccination sites in San Juan, Batangas along with their corresponding assigned barangays for = 1 and 2 sites, and = 3 and 4 sites, respectively. The stars represent the optimal vaccination sites while the circular nodes are the barangay halls. All barangays assigned to a particular vaccination site have the same color. We observed that for = 1, the optimal site location is close to the most populous area, which is in the northern part of the town. For = 2, one optimal site is in the north (yellow star) and the other optimal site is in the south (purple star). The barangays assigned to the vaccination site in the north are represented by yellow dots, while the barangays assigned to the vaccination site in the south are represented by purple dots. As expected, the vaccination sites become more spaced out as the number of sites increases. In all cases, the optimal locations obtained are all situated in the national highway. This is also expected because the problem is formulated to minimize the driving distance from the barangay halls to the centers. Notice that for = 4 sites, the two vaccination sites from the three sites did not change. The site in the northern part of the town was replaced by two sites. This is expected because the northern part of the town is the most populated and has the greatest number of confirmed COVID-19 cases (see the supplementary file). Figure 5 illustrates a sample data frame output of the vaccination centers for ten barangays in San Juan assuming that there are only 2 vaccination sites. For instance, barangay 'Abung' is assigned to the vaccination site named 'San Juan Rural Health Unit 1'. The distance between the barangay and the assigned vaccination center is 6692.14 meters. Similarly, barangay 'Barualte' is assigned to the vaccination site 'Paaralang Elementarya ng Bataan' and the distance between them is 2693.79 meters. Observe that the distance between barangay 'Bataan' and its assigned vaccination site is 0 meters. This is because the barangay hall of Barualte and the elementary school of Bataan are in the same compound. Figure 6 shows the average distance (in kilometers) of the barangays in San Juan, Batangas to the assigned optimal vaccination site, for = 1, 2, 3, 4 sites. On average, the difference between the road distance for one and two sites is approximately 3 kilometers while the difference between three and four sites is 600 meters. The trend shows that as more vaccination sites are opened, accessibility to the vaccines, in terms of distance, is improved.

However, opening more sites has associated operational costs. Results in Figure 6 can provide information for the policymaker on finding a balance between accessibility and cost-effectiveness related to the number of vaccination sites to open.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Figure 7 shows the number of weeks it takes to vaccinate 70% of the population of San Juan for = 1, 2, 3, 4 sites. If there is only 1 vaccination site, it takes around 62 weeks to inoculate 70% of the population in San Juan, while increasing the number of sites to 2 shortens the number of weeks to 44. Observe that the difference in time between three and four sites is only 7 weeks. If the local government has the capacity to hold vaccinations at three sites only and wishes to achieve the target of vaccinating 70% of the population in 21 weeks (same length of time as in four sites), then they can ramp up the vaccination rate at the three sites by 34.5% or by vaccinating additional 69 people per day in the three sites.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 24, 2021. ; https://doi.org/10.1101/2021.06.20.21259194 doi: medRxiv preprint *Corresponding Author: rmendoza@math.upd.edu.ph ORCID ID 0000-0003-3507-0327 

Building vaccination sites uses up resources and delays the goal of achieving herd immunity. Hence, it is reasonable to set up vaccination sites from already existing facilities. In this study, we proposed an approach to strategically select COVID-19 vaccination sites at the municipal level to bring the vaccines closer to the people who need them. In finding the optimal location of the COVID-19 vaccination sites, the method considers the location of the sites, the population density of the town, and the number of COVID-19 cases per village or

barangay. An open-access software has been created to make the results reproducible. The code only requires two files, one for the data on the list of possible vaccination sites and the other for the data on the villages or barangay.

Our numerical simulations show strategic placements of vaccination sites to make the vaccines more accessible . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 24, 2021. ; https://doi.org/10.1101/2021.06.20.21259194 doi: medRxiv preprint *Corresponding Author: rmendoza@math.upd.edu.ph ORCID ID 0000-0003-3507-0327 to the people and urge them to get vaccinated as soon as possible. The method can be beneficial to underdeveloped rural towns in developing countries, where public transportation is not reliable (or in some cases, not available).

In the illustration, we considered at most 4 vaccination sites, but the software can be easily extended to more accommodate more sites. However, this would require more computational time. Since our method is enumerative, parallel computing can be used to address the computational cost in case one wants to use our method to determine optimal locations of vaccination sites in big cities or at the provincial level. If a computing facility is not available, one can use other optimization algorithms (like meta-heuristic algorithms). Exploring other algorithms that can solve the optimization problem is a research direction that can be pursued. One can also extend the results of this study to find optimal locations of new vaccination sites. This can be tricky because the optimization problem will become continuous and hence, other numerical techniques must be employed.

Although the method is intended for COVID-19 vaccinations, the method is general enough that it can be applied to formulating vaccination strategies of other diseases. For example, if the vaccination is only for school-age children, (this is applicable for diseases like soil-transmitted helminths and schistosomiasis), then the locations can be restricted to just the elementary schools.

We hope that this study can help stakeholders in planning strategies to end the COVID-19 pandemic, which has crippled the world economy and has affected the lives of millions of people worldwide.

Funding. The authors do not have funding to declare.

Availability of data and material. The data used in the numerical method section can be found in the Supplementary File.

Code availability. The code and the tutorial for the optimization implementation can be found in the following GitHub repository: https://github.com/kurtizak/Covid-Site-Optimization . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The population data were collected from the website of the Philippine Department of Health (https://doh.gov.ph/publications). The number of COVID-19 confirmed cases per barangay in San Juan, Batangas was obtained from the Facebook page of the San Juan local government unit (https://www.facebook.com/lgusanjuanbatangas).

The list of hospitals and schools was manually generated from the directories of the Philippine Department of Health (https://nhfr.doh.gov.ph/rfacilities2list.php?pageno=1&t=rfacilities2&recperpage=ALL), Philippine Commission on Higher Education (https://ched.gov.ph/list-higher-education-institutions/), and the Philippine Department of Education (https://www.deped.gov.ph/k-to-12/senior-high-school/list-of-senior-high-schools/). The coordinates of the barangay halls and vaccination sites were collected with the help of the OSM package in Python and Google maps 

*Corresponding Author: rmendoza@math.upd.edu.ph ORCID

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