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Optimal selection of COVID-19
vaccination sites in the Philippines at the
municipal level
Kurt Izak Cabanilla*, Erika Antonette T. Enriquez*,
Arrianne Crystal Velasco, Victoria May P. Mendoza and
Renier Mendoza
Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines
*These authors contributed equally to this work.
ABSTRACT
In this work, we present an approach to determine the optimal location of
coronavirus disease 2019 (COVID-19) vaccination sites at the municipal level.
We assume that each municipality is subdivided into smaller administrative units,
which we refer to as 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 barangays, the number of COVID-19 cases, and the
population densities of the barangays. These objectives are formulated as a single
optimization problem. As an alternative decision support tool, we develop a
bi-objective optimization problem that considers distance and population coverage.
Lastly, we propose a dynamic optimization approach that recalculates the optimal
vaccination sites to account for the changes in the population of the barangays that
have completed their vaccination program. A numerical scheme that solves the
optimization problems is presented and the detailed description of the algorithms,
which are coded in Python and MATLAB, are uploaded to a public repository. As an
illustration, we apply our method to determine the optimal location of vaccination
sites in San Juan, a municipality in the province of Batangas, in the Philippines.
We hope that this study may guide the local government units in coming up with
strategic and accessible plans for vaccine administration.
Subjects Mathematical Biology, Health Policy, Public Health, Computational Science, COVID-19
Keywords COVID-19, Dynamic programming, Facility location, Genetic algorithm, Multi-
objective optimization, Open street maps, Philippines, Vaccination
INTRODUCTION
The coronavirus disease 2019 (COVID-19), which was first reported in Wuhan, China, has
spread across the globe and was declared a pandemic by the World Health Organization
(WHO) on March 11, 2020 (Xu et al., 2020;Cao, 2020). Initial findings suggest that
vaccination can protect the population against infection (Amit et al., 2021;Levine-
Tiefenbrun et al., 2021;Thompson et al., 2021) and may reduce onward transmission (Eyre
et al., 2022). COVID-19 vaccines have been shown to be safe and can protect against severe
disease, hospitalization, and death (WHO, 2022a). An effective vaccination campaign
can lessen the probability of disease resurgence and alleviate the economic burden of the
How to cite this article Cabanilla KI, Enriquez EAT, Velasco AC, Mendoza VMP, Mendoza R. 2022. Optimal selection of COVID-19
vaccination sites in the Philippines at the municipal level. PeerJ 10:e14151 DOI 10.7717/peerj.14151
Submitted 21 June 2022
Accepted 7 September 2022
Published 30 September 2022
Corresponding authors
Victoria May P. Mendoza,
vmpaguio@math.upd.edu.ph
Renier Mendoza,
rmendoza@math.upd.edu.ph
Academic editor
Hidayat Arifin
Additional Information and
Declarations can be found on
page 18
DOI 10.7717/peerj.14151
Copyright
2022 Cabanilla et al.
Distributed under
Creative Commons CC-BY 4.0
pandemic (Ella & Mohan, 2020). With the constant emergence of new variants of the virus
and the waning of immunity provided by vaccines or infection, a herd immunity threshold
for COVID-19 seems impossible to identify (Aschwanden, 2021;Morens, Folkers & Fauci,
2022). Classical herd immunity threshold is described as the proportion of the population
with immunity, induced by vaccine or infection, against a disease wherein above this
threshold, transmission is considerably prevented (John & Samuel, 2000;Fine, Eames &
Heymann, 2011;Jones & Helmreich, 2020;Randolph & Barreiro, 2020;Morens, Folkers &
Fauci, 2022). Nevertheless, both non-pharmaceutical interventions and vaccination of
as many people as possible are necessary for optimal control of COVID-19 (Kadkhoda,
2021;Morens, Folkers & Fauci, 2022).
Besides the global shortage of vaccine supply during the early vaccination phase, safety
concerns, vaccine brand hesitancy, and misinformation were among the challenges that
delayed vaccination in the Philippines (Huh & Dubey, 2021;Amit et al., 2022). The online
survey done before the vaccine rollout in the Philippines revealed that around 70% of
the respondents would only get vaccines after many other people or politicians have been
vaccinated, and about 97% were worried about fake vaccines (Caple et al., 2022). Proper
handling and storage, and fast distribution of COVID-19 vaccines posed logistics
challenges, particularly the preparedness of cold chain infrastructure at the national and
local levels (Park et al., 2021;Reyes, Dee & Ho, 2021). Shortage of healthcare workers
who can administer vaccines also hindered the expansion of the rollout (Sales et al., 2022).
As of 9 May 2022, around 68% of the Philippine population aged 5 years or older have
been vaccinated with the primary doses. However, vaccine coverage among different age
groups and regions greatly varies (WHO, 2022b). Most people who have not received a
single vaccine dose include those in geographically isolated and disadvantaged areas, as
well as around 2.4 million of the elderly population, who do not have affordable and
practical resources to go to vaccination sites. Strategies such as house-to-house campaigns
to reach these vulnerable groups and encourage getting vaccinated are being done in a
few provinces (WHO, 2022c). A collaborative effort among several stakeholders and
sectors is therefore needed to address these issues to protect and save more lives (Corpuz,
2021;WHO, 2022c). We hope that this study may guide the Philippine local government
units in coming up with more strategic plans for vaccine administration. We present a
way to select optimal vaccination sites from already existing facilities to make the vaccines
more accessible to the public and accelerate recovery of the nation from this pandemic.
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
(Facility Location, 2009). Facility location problem has a variety of applications including
determining optimal locations of solar power plant sites (Wang et al., 2020), hydrogen
production sites (Yee et al., 2020), tsunami sensors (Ferrolino, Lope & Mendoza, 2020;
Ferrolino et al., 2020), infrastructure maintenance depot (Kim & Kim, 2021), tower sites for
early-warning wildfire detection systems (Heyns et al., 2020), and high-speed train stations
(Chanta & Sangsawang, 2020), among others. Facility location has also been used in
several COVID-19-related studies. In Buhat et al. (2020), an optimal allocation of
COVID-19 testing kits among accredited testing centers has been proposed. The optimal
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 2/23
location of pharmacies for COVID-19 testing to ensure access has been studied in Risanger
et al. (2021). Identification of locations of COVID-19 emergency logistic centers has been
proposed in Wang & Ma (2021).InTaiwo (2020), optimal COVID-19 testing facility sites
in Nigeria have been studied.
Several studies have been conducted on the applications of facility location problems in
COVID-19 vaccination distribution strategies. In Bertsimas et al. (2021), an approach to
optimize vaccine 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 vaccination against, and mortality caused by COVID-19. In Basciftci, Yu &
Shen (2021), a mathematical framework for finding the optimal locations of distribution
centers for test kits and vaccines has been developed. In Buhat et al. (2021), a linear
programming model was used for COVID-19 vaccine allocation in the Philippines at the
national level. The scale of these studies necessitates the consideration of logistic
constraints (e.g., shipping cost, production capacity, operating cost, etc.). In this study, we
consider a local-scale vaccination strategy. By doing so, we can focus on finding the
optimal location of vaccination sites that will make the vaccines more accessible to the
population of a municipality. Our work can be used in conjunction with vaccine allocation
methods at the national level (Bertsimas et al., 2021;Basciftci, Yu & Shen, 2021;Buhat
et al., 2021). Once the vaccines are allocated to a municipality, our method can be applied
to identify the sites where the vaccines will be distributed. A vaccine strategy in Germany
(Leithäuser et al., 2021) has been proposed that considers three different objectives,
including minimizing the sum of travel distances. In their study, the user can choose which
objective they intend to prioritize. In our work, a single cost function is proposed to
incorporate all the objectives. Alternatively, we also propose a bi-objective optimization
approach that considers both distance and population coverage so that the policymaker
may choose among multiple optimal solutions a strategy that prioritizes the needs of the
municipality. In Zhang et al. (2022) and Tang et al. (2022), the distance between the
vaccination site to the recipient was one of the objectives to be minimized. However, these
studies use Euclidean distance, which is not realistic in a municipality setting. In this
study, we utilize the Open Street Maps (OSM) and its corresponding Python package
OSMNX, to calculate the actual road distance.
In the next section, we formulate three mathematical optimization models to address
the vaccination site location problem. The first model incorporates the distance to the sites,
COVID-19 cases, and population density in a single-objective function. As an alternative
decision support tool, we also present a multi-objective optimization model. The third
model is a dynamic optimization problem that recalculates the optimal vaccination sites
considering the remaining unvaccinated population of the barangays. Then, we discuss the
numerical methods and open-source software used to solve the minimization problems.
We illustrate how our proposed method works by using the method to identify the
optimal vaccination sites in San Juan, Batangas, Philippines. Finally, we present our
conclusions and recommendations for future research.
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 3/23
OPTIMIZATION PROBLEM
Our goal is to determine the optimal location of Lvaccination sites in a municipality from
a list of Mpossible vaccination sites. We consider existing facilities such as public schools
and hospitals as possible vaccination sites. Furthermore, suppose that the municipality
is divided into Nadministrative units, which we refer to as barangays. These barangays or
villages are usually the country’s basic units of government. Let Vi:i¼1;2;...;M
fg
be the set containing the locations of the Mpossible vaccination sites. Each Viis
represented by a two-dimensional vector whose components are the latitude and longitude
of the ith vaccination site. Define Bj:j¼1;2;...:N
as the set containing the location
of the Nbarangays. We can set Bjas the location of the barangay hall, which is usually
situated at the center of the barangay. Similarly, each Bjis a two-dimensional vector whose
components are the latitude and longitude of the jth barangay.
Define dV
i;Bj
as the distance of the vaccination site Vifrom the barangay hall Bj.
In facility allocation problems, different distance measures are used. For example, the
Euclidean distance was used in Wong et al. (2009). It was argued in Du, Zhang & Xia
(2005) that the l1distance (also known as Manhattan distance) is more accurate in
modeling the driving distance in a city road network. However, in rural municipalities, the
roads may not follow a rectangular grid pattern. Since Viand Bjare accessible via the road
network of a municipality, we utilize OSMNX (Version 1.2.1) to calculate the actual
driving distance from Vito Bj. This approach makes the computation of distance more
realistic.
Now, suppose L¼1;that is, only one vaccination site is assigned to the whole
municipality. Then, one distribution strategy is to choose the vaccination site that lies the
closest to all the Bj0s:That is, we solve
min
1iMX
N
j¼1
dV
i;Bj
:(1)
However, the minimization problem in Eq. (1) does not take into consideration the
population of the barangays. To resolve this, we add more weight on the vaccination sites
that are closer to the more populous areas of the municipality. Define Pjas the population
of the jth barangay and Tpas the total population of the municipality. Then PN
j¼1Pj¼Tp
and the problem becomes
min
1iMX
N
j¼1
Pj
Tp
dV
i;Bj
:(2)
Moreover, we want to place the vaccination sites near barangays with high numbers
of confirmed COVID-19 cases. Define Cjas the number of confirmed COVID-19 cases in
the jth barangay and Tcas the total number of confirmed COVID-19 cases in the
municipality. Then PN
j¼1Cj¼Tc. Similar to how population is incorporated in Eq. (2),we
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 4/23
add weights on the barangays with high number of confirmed COVID-19 cases. Thus, we
solve
min
1iMX
N
j¼1
Pj
Tp
þCj
Tc
dV
i;Bj
:(3)
Next, we consider the case when the number of vaccination sites is more than one, that
is, L2:If there are Lvaccination sites, we want the resident of the jth barangay to
go to the nearest vaccination site. We can generalize the minimization problem in Eq. (3)
as follows:
min
1i1;i2:...;iLMX
N
j¼1
Pj
Tp
þCj
Tc
min dV
i1;Bj
;dV
i2;Bj
;...;dV
iL;Bj
:(4)
The formulation in Eq. (4) successfully accounts for the population density, number of
confirmed COVID-19 cases, and distances of the barangays to the vaccination sites.
To make the optimization problem a more flexible decision support tool, we can also
consider two goals:
1. minimize the total distance from vaccination sites to barangays and
2. maximize the total population that are within a pre-defined radius (e) from the
vaccination sites.
Hence, we can redefine the minimization problem in Eq. (4) as the bi-objective
optimization
min
1i1;i2:...;iLM
F1Vi1;Vi2;...;ViL
ðÞ
F2Vi1;Vi2;...;ViL
ðÞ
(5)
where
F1Vi1;Vi2;...;ViL
ðÞ¼
X
N
j¼1
Cj
Tc
min dV
i1;Bj
;dV
i2;Bj
;...;dV
iL;Bj
;
F2Vi1;Vi2;...;ViL
ðÞ¼
X
L
i¼1X
j2A
Pj;where A¼j:dV
i1;Bj
e
:
Since the bi-objective optimization problem may have multiple solutions, the user can
choose from its corresponding Pareto set a solution depending on whether total distance or
total population coverage is prioritized. If the user prefers a single solution that
incorporates both objectives, then we recommend that the optimization problem in Eq. (4)
is considered.
Note that both optimization problems in Eqs. (4) and (5) assume that same sites are
used throughout the vaccination program. To make the approach more dynamic, we
propose a third optimization problem based on Eq. (4) that moves the vaccination sites
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 5/23
towards the barangays which have yet to complete their vaccination program. Suppose
there are Svaccination schedules. For k¼1:S, we determine the optimal vaccination sites,
denoted by VkðÞ
i1;VkðÞ
i2;...;VkðÞ
iL, during the kth schedule by solving
min
1i1;i2:...;iLMX
N
j¼1
gkðÞ
j
Pj
Tp
þCj
Tc
min dV
i1;Bj
;dV
i2;Bj
;...;dV
iL;Bj
;(6)
where gkðÞ
jis set to zero if the jth barangay has achieved the target percentage of vaccinated
population during the kth schedule. Otherwise, gkðÞ
jis set to one. Note that the formulation
in Eq. (6) is similar to Eq. (4) except for the indicator parameter gkðÞ
j, which is introduced
so that barangays who have completed their vaccination program will have no priority
when choosing the optimal vaccination sites for the next schedule. In this study, we assume
that the vaccination at the jth barangay is finished when 70% of its population has been
vaccinated.
NUMERICAL METHODS
Road distance using open street maps
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 for 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. OSMNX 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.
Single-objective optimization problem
In this subsection, we discuss the numerical algorithms that will be used to solve the
single-objective minimization problems in Eqs. (4) and (6). To solve the optimization
problem for a given municipality, the user must input two files: the village centers table
and the vaccination centers table. The village centers table contains the number of
COVID-19 cases, population, and location of all the barangays in the municipality. It is a
CSV file with the schema given in Table 1. The vaccination centers table contains the
location of all the possible vaccination sites. This is a CSV file with the schema shown in
Table 2.
We found that it is possible to automate the extraction of the latitude and longitude data
for the vaccination centers table using OSMNX to a considerable extent. However, the
OSMNX automation could not differentiate between public and private schools, thus
necessitating some manual review. OSMNX automation can be used to generate an initial
version of the vaccination centers table on which the end-users can then build on by
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 6/23
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, for the village centers table,
OSM could not identify the village centers or barangay halls so manual extraction of this
data using Google Maps was needed. This means that we had to first identify which
building served as the barangay hall and then determine its latitude and longitude via
Google Maps. In some cases, the coordinates of the barangay centers given by Google
Maps were inaccurate. Thus, we used Google Street View to locate the building based on its
address and then use that location’s coordinates for the latitude and longitude data.
Once the barangay hall was identified and its coordinates finalized, we used various
government data repositories to identity the most recent population of the barangay along
with its number of infected cases. This was done manually for every barangay in the
municipality until we completed the village centers table. To summarize, the vaccination
centers table can largely be automated using OSMNX extraction and then manually
tweaked by domain experts or policymakers in that region. Meanwhile, the village centers
table must be constructed by hand using both Google Maps and government statistics
databases. The partial automation of the vaccination centers table is shown in the Github
repository for this article (Cabanilla, 2022) along with the rest of the program.
The cost function is computed directly as shown in Eq. (4), where the road distance
dV
i;Bj
between the ith vaccination site and the jth barangay hall is computed via
OSMNX in Python. For both the single and L-site optimization, we iterate through every
possible combination of all the vaccination sites and barangays so that the resulting
optimum is the global optimum.
The Python program we developed takes in the two tables previously mentioned and
outputs the assignments of each barangay center to its optimal vaccination site as well
as a ranked list of other suboptimal combinations of vaccination centers and their
respective costs. Since it is already ordered by cost, the optimum would be in the first row.
Table 1 The village centers table contains the number of COVID-19 cases, population, latitude, longitude, and names of all the villages or
barangays in a town.
Infected
(data type: integer)
Population
(data type:
integer)
Latitude
(data type: float)
Longitude
(data type: float)
Barangay_name
(data type: string)
Number of COVID-19 cases
in the village/barangay
Population of the
village/barangay
Latitude of the village hall/
community center/barangay hall
Longitude the village hall/
community center/ barangay hall
Name of the village/
barangay
Table 2 The vaccination centers table contains the latitude, longitude, and names of all possible
vaccination sites in a town.
Latitude
(data type: float)
Longitude
(data type: float)
Name
(data type: string)
Latitude of the vaccination center Longitude of the vaccination center Name of the vaccination center
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 7/23
The code and a tutorial for the implementation of the numerical optimization method
are found in Cabanilla (2022). Sample CSV files of the inputs can also be downloaded from
this repository. The users can simply modify the CSV files for easier implementation.
Using the road distance matrix dV
i;Bj
2RMNcalculated via OSMNX in Python, a
MATLAB version of this enumerative technique can be found in Enriquez (2022).
For smaller values of L, the enumerative approach presented above is sufficient so
that the global solution is obtained. For higher values of L, identifying the best solution
from all possible combinations can be computationally expensive. Hence, an efficient
optimization algorithm is needed. Observe that the objective function in Eq. (4) is an
integer nonlinear programming problem. In this study, we use a genetic algorithm (GA)
capable of solving mixed integer optimization problems (Deep et al., 2009) to solve Eq. (4)
for higher values of L. GA has been shown to be effective in solving a wide range of
applications in science and engineering (Khosravian et al., 2021;Zhang, 2019;Yang,
Gomez & Blackburn, 2020;Katoch, Chauhan & Kumar, 2021;Velasco et al., 2020;Caro,
Mendoza & Mendoza, 2021;Jamilla, Mendoza & Mendoza, 2021). For ease of use and open
accessibility, the GA we implement is from the geneticalgorithm Python package, which
has options for integer programming. All the hyperparameter settings are set to default
values except for the number of iterations, population size, and maximum number of
iterations without improvements before stopping. Because GA is probabilistic, the result of
one run may differ from another. Although capable of attaining global minimizers, the
obtained solution can be local in some cases. Hence, we run the genetic algorithm
300 Ltimes and store the best solution among these runs. To account for the
dimensionality of the problem, particularly for L7, we suggest increasing the number of
runs. We set the population size to 20 LLand the maximum number of iterations
to 50, based on experimentation. The code implementing this optimization method
can also be found in the GitHub repository (Cabanilla, 2022). Alternatively, a MATLAB
version of the program can be downloaded in Enriquez (2022).
Multi-objective optimization problem
In this subsection, we discuss the numerical algorithm used to solve the bi-objective
minimization problem given in Eq. (5). The algorithm requires the number of COVID-19
cases per barangay, population of each barangay, and road distances dV
i;Bj
2RMN
between each vaccination center and barangay. The user must also enter L;the desired
number of optimal vaccination sites. The algorithm finds all possible combinations of
sites taken Lat a time and computes for the cost values of each combination based on
the two objective functions given in Eq. (5). We note that in our experiments, we set the
radius (e) in the second objective function to 3,000 m. The cost values are then listed in a 2-
column vector, say C.
To obtain the Pareto optimal set, we apply a bubble sorting method. We first sort
the rows of Cbased on increasing values of the first column of C, that is, increasing values
of F1. This consequently makes the first row of Ca member of the Pareto optimal set.
Then, the algorithm treats the F2-value of this first member as the current-best and goes
through the rest of the values of the second column of C, that is, the values of F2. If the
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 8/23
algorithm finds a lower F2-value than the current-best, its corresponding row will then
become a member of the Pareto optimal set, and the current-best is updated. This is done
until all the rows of Chave been checked. The combinations of Lhaving the function
values in the final Pareto optimal set represent the optimal vaccination sites that solve the
bi-objective minimization problem. MATLAB was used for the implementation of this
algorithm and the codes are available in Enriquez (2022).
RESULTS
To illustrate how our proposed method works, we find the optimal placement of
vaccination sites in San Juan, a municipality in the province of Batangas, Philippines.
San Juan is comprised of 42 barangays. A map detailing the location of the barangays in
San Juan is shown in the Supplemental File. Hence, Bj;j¼1;2;...;42
contains the
locations of the 42 barangay halls in San Juan. The latitudes and longitudes of the barangay
halls were manually obtained from local government directories and Google maps.
Hospitals in San Juan are listed as possible vaccination sites. Since face-to-face classes were
suspended in the Philippines during the COVID-19 pandemic, public schools (elementary,
high school, and college) are also listed as possible vaccination sites (Ranada, 2021).
In January 2021, the Catholic Bishops’Conference of the Philippines offered to transform
churches in the country as COVID-19 vaccination sites (Department of Health Press
Release, 2021). The latitudes and longitudes of the hospitals, schools, and churches are
obtained from the Philippine Department of Health and Department of Education
directories, and Google maps. A total of 65 sites were identified in San Juan, consisting of
five hospitals, 42 elementary schools, 13 junior high schools, two senior high schools, two
universities, and one church. Hence, Vi;i¼1;2;...;65
fg
contains the location of all the
65 possible vaccination sites. In cases when these sites are not available, one can easily
modify the input to include other sites and exclude unavailable sites.
San Juan, Batangas has a projected population of 125, 252 in 2021 (Department of
Health Publications, 2020). Meanwhile, as of May 31, 2021, San Juan recorded a total
number of 579 confirmed COVID-19 cases. We chose May 31, 2021 because during this
time, the vaccination program in San Juan, Batangas had just started. The complete
information on the locations of possible vaccination sites and barangay halls in San Juan,
the number of COVID-19 confirmed cases per barangay, and the population of San Juan
per barangay are found in the Supplemental File.
Two outputs are provided by the codes. First, a 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.
For a sample implementation, we consider selecting one to four vaccination sites among
Vi;i¼1;2;...;65
fg
, that is, L¼1;2;3;or 4. Figures 1 and 2show the geographic
distribution of the optimal vaccination sites in San Juan, Batangas along with their
corresponding assigned barangays for L¼1 and 2 sites, and L¼3 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
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 9/23
color. On the other hand, Fig. 3 illustrates a sample data frame output of the vaccination
centers for ten barangays in San Juan assuming that there are only two 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 site is
6,692.14 m. Similarly, barangay ‘Barualte’is assigned to the vaccination site ‘Paaralang
Elementarya ng Bataan’and the distance between them is 2,693.79 m. Observe that the
distance between barangay ‘Bataan’and its assigned vaccination site is zero because the
barangay hall of Barualte and the elementary school of Bataan are in the same compound.
Figure 4 shows the average distance (in kilometers) of the barangays in San Juan,
Batangas to the assigned optimal vaccination site, for L¼1;2;3;or 4 sites. Figure 5
displays the number of weeks it takes to vaccinate 70% of the population of San Juan for
L¼1;2;3;4;or 5 sites, given different daily vaccination rates (100, 200, or 400 people
per day).
As mentioned earlier, the enumerative approach is used only for smaller values of Ldue
to the limited memory capacity. For higher values of L, the problem was solved using GA.
Table 3 displays the indices of the optimal vaccination sites for L¼1;2;...;7.
We observe that we obtain the same optimal sites for L¼1;2;...;6 using GA and the
enumerative approach. For L¼7, the computer runs out of memory in generating all
Figure 1 The roadmap of San Juan, Batangas showing the optimal locations of one (left) or two
(right) vaccination sites. The dots represent the village/barangay halls while the stars are the com-
puted optimal vaccination sites. The colors depict the vaccination site assignment of each village/bar-
angay in the town. Full-size
DOI: 10.7717/peerj.14151/fig-1
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 10/23
the possible combinations in the enumerative approach and no solution was obtained.
On the other hand, GA was able to generate an optimal solution.
The results of the bi-objective optimization problem in Eq. (5) are presented in Figs. 6
and 7. The cost values of all site combinations for L¼2, along with the corresponding
Pareto optimal set (blue) and the optimal solution from the single-objective enumerative
problem (red star) are illustrated in Fig. 6. All the other possible combinations of the
vaccination sites are shown as green circles. Figure 7 shows the Pareto optimal sets for
L¼2;3;4;and 5.
Figure 8 illustrates a sample result of the dynamic optimization approach in Eq. (6)
assuming L¼2 and a daily vaccination rate of 200. Figures 8A–8F demonstrate the
monthly change in the locations of the optimal vaccination sites as more people were
vaccinated. To simulate the vaccination process, random sampling was done to assign the
barangay where the vaccinated individuals belong to and identify the remaining number of
unvaccinated individuals in a barangay which is needed in the recalculation of the optimal
sites. The sampling assumes that individuals residing in barangays close to the vaccination
sites have higher probability of getting vaccinated. If a barangay has completed its
vaccination program, that is, 70% of the population has been vaccinated, then it is excluded
from the sampling. Figure 8A shows that the vaccination sites in the first month of the
Figure 2 The roadmap of San Juan, Batangas showing the optimal locations of three (left) or four
(right) vaccination sites. The dots represent the village/barangay halls while the stars are the com-
puted optimal vaccination sites. The colors depict the vaccination site assignment of each village/bar-
angay in the town. Full-size
DOI: 10.7717/peerj.14151/fig-2
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 11/23
vaccination program are situated at ‘San Juan Rural Unit I’(located in ‘Poblacion’, which is
San Juan’s central barangay) and ‘Paaralang Elementarya ng Bataan’(located in the
barangay of ‘Bataan’). In Figs. 8A–8E, we observe that one of the vaccination sites did
not change until after 4 months. This may be because this area (‘Poblacion’) contains the
most populous barangays in San Juan and hence, the vaccination program here is expected
to take time. In Fig. 8E, a site moved back to the south at the ‘Laiya Aplaya National
High School’to vaccinate the remaining residents of ‘Laiya Aplaya’.Figure 8F shows that
the two vaccination sites moved to the northern part of the municipality, and the target
population to be vaccinated has been completed.
DISCUSSIONS
For the single-objective optimization problem, we observed that for L= 1, the optimal site
location is close to the most populous area, which is in the northern part of the
municipality. For L= 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 situated along the national highway since the problem is formulated to
minimize the driving distance from the barangay halls to the sites. Notice that for L=4,
two vaccination sites out of the optimal three-site solutions did not change. The site in the
Figure 3 Sample output of the algorithm showing ten barangays in San Juan, Batangas and the
assigned vaccination site based on proximity. The road distance (in meters) between the barangay
and the assigned optimal vaccination site is also shown. Here, we assume that there are only two vac-
cination sites (L=2). Full-size
DOI: 10.7717/peerj.14151/fig-3
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 12/23
northern part of the municipality was replaced by two sites. This is expected because this
region is the most populated and has the greatest number of confirmed COVID-19 cases
(see the Supplemental File).
On average, the difference between the road distance for one and two sites is
approximately three kilometers while the difference between three and four sites is 600 m.
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 Fig. 4 can provide information for the policymaker on finding a
balance between accessibility and cost-effectiveness related to the number of vaccination
sites to open.
Assuming a constant vaccination rate, we can determine the number of weeks it takes
for a municipality to reach a target number of people to be vaccinated, say 70% of the total
population (see Fig. 5). Suppose a site in San Juan can inoculate 200 individuals per
day. This rate is based on the vaccination rate of the University of the Philippines Diliman
gym in Quezon City (Ayalin, 2021). If there is only one vaccination site, it takes around
62 weeks to inoculate 70% of the population in San Juan. Meanwhile, increasing the
number of sites to two shortens the number of weeks to 44. Observe that the difference in
Figure 4 Average road distance (in kilometers) of the barangays in San Juan, Batangas to the
obtained optimal vaccination site for L = 1, 2, 3, or 4 sites.
Full-size
DOI: 10.7717/peerj.14151/fig-4
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 13/23
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 the
vaccination rate at the three sites can be ramped up by 34.5% or by vaccinating additional
69 people per day in the three sites.
Figure 5 The time needed to inoculate the first dose of COVID-19 vaccines to 70% of the population
of San Juan, Batangas for L = 1, 2, 3, 4, or 5 sites, given a daily vaccination rate of 200 (orange), 400
(violet), or 100 (blue). Full-size
DOI: 10.7717/peerj.14151/fig-5
Table 3 Summary of results for the nonlinear integer programming using genetic algorithm
compared with the enumerative approach for L = 1, 2,…7 sites.
Number of vaccination
sites L
Optimal index/indices
using genetic algorithm
Optimal index/indices
using enumerative approach
154 54
2 [3, 9] [3, 9]
3 [1, 3, 24], [1, 3, 52] [1, 3, 24], [1, 3, 52]
4 [ 1, 2, 24, 59], [1, 2, 52, 59] [ 1, 2, 24, 59], [1, 2, 52, 59]
5 [1, 2, 15, 52, 59] [1, 2, 15, 24, 59], [1, 2, 15, 52, 59]
6 [1, 12, 15, 24, 30, 33] [1, 12, 15, 24, 30, 33], [1, 12, 15, 30, 33, 52]
7 [1, 9, 12, 14, 30, 51, 62] Not solvable
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 14/23
If the municipality intends to identify a large number of vaccination sites, GA can be
used. This can be useful for big municipalities or small cities. We have shown that if GA is
given enough number of runs, the solution obtained can be the same as in the enumerative
method.
For the bi-objective minimization problem, the Pareto optimal set is located at the lower
left corner of Fig. 6. The Pareto set for L¼2 contains five combinations of sites that
minimize the distance to the barangays and maximize the population within e-distance
from the sites. The users are free to choose which combination of sites they prefer. If they
prioritize proximity over population, then they may choose the sites with lower y-values.
Otherwise, they can choose the combination with lower x-values. Observe also that the
single-objective optimal solution for L4 is a member of the Pareto optimal set, which
confirms that the single and bi-objective problems are consistent with each other. In Fig. 7,
as Lincreases, the Pareto sets move further to the lower left area of the figure. This is
expected because having more vaccination sites brings the sites closer to the barangays.
Figure 6 Cost function values and Pareto optimal set of the bi-objective optimization problem for
L=2sites. The optimal solution of the single-objective (enumerative) optimization problem is also
shown as a red star. Full-size
DOI: 10.7717/peerj.14151/fig-6
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 15/23
That is, the total distance of the sites to the barangays is reduced and the population
covered by the sites within a fixed radius is increased. While this is not the case for L¼5,
the single-objective solution is still close to the Pareto set. If one wishes to see that the
optimal solution for L¼5 is in the Pareto set, then one can vary the radius eof the site to
the barangays.
The dynamic optimization approach shows how the proposed scheme can be modified
when the number of vaccination sites changes during the program. In this way, the
vaccination sites can be relocated after a certain amount of time so that barangays which
have not completed their vaccination program can gain more access to the vaccines.
In this study, we only considered minimizing the distance travelled and maximizing the
population coverage because the scale of the study is small, and our main goal is to
make the vaccination sites more accessible. This study does not consider other costs
associated to vaccine delivery such as cold chain storage, waste management,
transportation expenses, and technical assistance. Other factors which are not included in
Figure 7 Pareto optimal sets of the bi-objective optimization problem for L = 2, 3, 4, or 5 sites. The
optimal solutions for each Lof the single-objective (enumerative) optimization problem are also shown.
Note that for L = 3, 4, 5, two vaccination site combinations obtained the optimal value, so they are
represented as an overlapping star and diamond. Full-size
DOI: 10.7717/peerj.14151/fig-7
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 16/23
Figure 8 (A–F) Solutions of the dynamic optimization approach for 6 months. The vaccination sites are relocated after 1 month to move them
closer to villages which have not completed their vaccination program. The red stars indicate the optimal vaccination sites while the circular nodes
denote the location of the villages. A circular node is marked white when the vaccination program is finished. Otherwise, it is marked black.
Full-size
DOI: 10.7717/peerj.14151/fig-8
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 17/23
the costs can be due to coordination and planning, social mobilization, training of
personnel, physician’s fee, and other miscellaneous costs (Siedner et al., 2022).
We recognize that although these factors are important, these costs can be assumed to be
the same for all the vaccination sites since the study is done at the municipal level.
In this way, the costs will have no bearing in the formulated optimization problem. If the
method is applied to a larger scale (provincial or national), then these costs may vary, and
the problem should be reformulated. These are limitations of the study which may be
pursued in future research.
CONCLUSIONS
In this study, we proposed an approach to strategically select COVID-19 vaccination sites
from already existing facilities at the municipal level. In finding the optimal location of the
COVID-19 vaccination sites, the method considers the location of the sites, population
density of the municipality, and number of COVID-19 cases. An open-access program has
been created to make the results reproducible. The code only requires two files, one is a list
of possible vaccination sites and the other is a list of the barangays. Our numerical
simulations show the strategic placements of vaccination sites to urge the people to get
vaccinated as soon as possible. The method can be beneficial to underdeveloped rural
municipalities in developing countries, where public transportation is not reliable or in
some cases, not available.
Because the problem can be solved for a greater number of vaccination sites using GA,
this approach can be extended not only to other municipalities, but also to big cities
and provinces. Exploring other algorithms that can solve the proposed optimization
problems is a research direction that can also be pursued. Moreover, one can extend the
results of this study to find the optimal locations of new vaccination sites.
Although the method is intended for COVID-19 vaccinations, the method is general
enough that it can be applied to formulating immunization or drug delivery strategies of
other diseases. For example, if mass drug administration is to be implemented for
school-age children 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.
ADDITIONAL INFORMATION AND DECLARATIONS
Funding
This work is funded by the project titled “Funding for the establishment of a
computational research laboratory in the University of the Philippines Diliman Institute of
Mathematics, pursuant to section 10(x) of Republic Act No. 11494”under the category
“Grant for research on COVID-19 in the Philippines”. The funders had no role in study
design, data collection and analysis, decision to publish, or preparation of the manuscript.
Cabanilla et al. (2022), PeerJ, DOI 10.7717/peerj.14151 18/23
Grant Disclosures
The following grant information was disclosed by the authors:
Grant for research on COVID-19 in the Philippines.
Competing Interests
The authors declare that they have no competing interests.
Author Contributions
Kurt Izak Cabanilla conceived and designed the experiments, performed the
experiments, analyzed the data, prepared figures and/or tables, authored or reviewed
drafts of the article, and approved the final draft.
Erika Antonette T Enriquez conceived and designed the experiments, performed the
experiments, analyzed the data, prepared figures and/or tables, authored or reviewed
drafts of the article, and approved the final draft.
Arrianne Crystal Velasco conceived and designed the experiments, performed the
experiments, analyzed the data, prepared figures and/or tables, authored or reviewed
drafts of the article, and approved the final draft.
Victoria May P Mendoza conceived and designed the experiments, performed the
experiments, analyzed the data, prepared figures and/or tables, authored or reviewed
drafts of the article, and approved the final draft.
Renier Mendoza conceived and designed the experiments, performed the experiments,
analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the
article, and approved the final draft.
Data Availability
The following information was supplied regarding data availability:
The data is available in the Supplemental File.
The codes are available at GitHub:
- Cabanilla KI. 2021. Covid-Site-Optimization. https://github.com/kurtizak/Covid-Site-
Optimization
- Enriquez EA. 2022. COVID-Vaccination-Sites. https://github.com/ErikaAntonette/
COVID-Vaccination-Sites
Supplemental Information
Supplemental information for this article can be found online at http://dx.doi.org/10.7717/
peerj.14151#supplemental-information.
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