key: cord-1013853-ooobm21c
authors: Xu, Xinglu; Rodgers, Mark D.; Guo, Weihong
title: A Hub-and-spoke Design for Ultra-cold COVID-19 Vaccine Distribution
date: 2021-08-25
journal: Vaccine
DOI: 10.1016/j.vaccine.2021.08.069
sha: 067b7b0cb920ea27c4c4e3ddf9f30eb26cadb94c
doc_id: 1013853
cord_uid: ooobm21c

An orderly and effective vaccination campaign is essential in combating the global COVID-19 pandemic. As one of the pioneers, the U.S. Center for Disease Control proposes a phased plan to promote the vaccination process. This plan starts with vaccinating the high-priority population in Phase I, then turns to the remainder of the public in Phase II, and ends with a scale-back network in Phase III. The phased plan not only provides a sense of hope to impacted communities that this global pandemic can be defeated, but can serve as a template for other countries. To enhance this plan, this paper develops a generalizable framework for designing a hub-and-spoke vaccination dispensing network to achieve the goals in the Phase 2, which aims to expand the vaccination coverage for the general public. We introduce a new coverage index to measure the priority of different potential dispensing sites based on geo-data and develop an optimization model for network design. The hub-and-spoke network enhances the accessibility of the vaccines to various communities and helps to overcome the challenges related to ultra-cold storage facility shortage. A case study of Middlesex County in New Jersey is presented to demonstrate the application of the framework and provide insights for the Phase 2. Results from the baseline scenario show that increasing the driving time limit from 10 minutes to 25 minutes can improve the total coverage index from 40.8 to 55.9. Additionally, we explore how the changes of parameters impact the network design and discuss potential solutions for some special cases. When we allow 4 outreach nodes per hub, all potential 45 outreach points can be covered in the vaccination network within a 20-minute drive, and the total coverage index reaches its maximum value of 58.3.

3 infrastructure investment from two aspects. First, the vicinity of local dispensing sites in the hub-and-spoke network design enables local inventory sharing, thus helping to use up a batch of vaccines within the short shelf-life, reducing the risk of vaccine wastage due to expiration. Second, the short-trip transfers within the regional hub-and-spoke network can help reduce the risk of temperature excursion in transportation.

In order to simultaneously ensure fair and equitable access to vaccines for all communities, we apply a newly proposed vaccination coverage optimization model that seeks to design the optimal configuration for the hub-and-spoke vaccination network.

This research serves as a generalized framework that can be adopted in various regions of the globe, especially in low-income countries, with inadequate cold chain infrastructure.

Next, subsection A presents additional details about the current phased vaccination plan in the U.S. Subsection B reviews recent works of literature and identifies existing research gaps. Subsequently, in section II, we will state the potential advantages of the new configuration and present our model in detail. A case study is presented in section III. Finally, we conclude in section IV.

As one of the countries in the first vaccine roll-out echelon, the U.S. government proposed a phased vaccination plan [5] , as given in Fig. 1 . Considering that the supply and demand for vaccines are highly stochastic, the CDC outlines three phases:

 Phase 1 focuses on distributing the vaccine to high-priority populations, including the critical infrastructure workforce, and people at increased risk for severe COVID-19 illness.

 Phase 2 aims to expand vaccine access to the general public by adding more dispensing sites in the provider network.

 Phase 3, upon covering most of the population, CDC plans to scale back these efforts, since the demand for vaccines would be dramatically reduced This phased vaccination plan streamlines the immunization progress in midst of the pandemic, while also providing a good template for other countries that are mounting a strategy to defeat COVID-19. This plan was made ahead of the EUA of the first vaccine in the U.S., with the CDC providing the strategic framework, and leaving operational details to the local governments to FIGURE 1. An illustration of phased vaccination plan in the U.S 4 execute [11] . At the time of writing, most regions of the U.S. are still in Phase 1. Several states announced plans to transition into Phase 2, however, there is a lack of guidance on how to successfully accomplish this task. Our proposed research not only helps to address this gap for the U.S. but may also help other countries to deploy a phased immunization program.

To promote global immunization, various studies have been conducted. This subsection first reviews the existing studies related to common vaccine distribution, then presents recent studies on the COVID-19 vaccination campaign. Research gaps are identified after reviewing from both the problem perspective and the methodology perspective. Lastly, we briefly outline how this paper addresses the current challenge in ultra-cold vaccine distribution and overcomes the drawbacks of existing coverage model.

De Boeck et al. [12] provide a review of studies related to the vaccine distribution chain. Based on the review, existing studies can be divided into three categories according to their research scope and decision variables. The first topic is about long-term strategic decisions including the facility location and allocation decisions. For example, Lee et al. [13] use a computational simulation model to re-design the vaccine supply chain in Mozambique by comparing two simulation outputs: the vaccine availability and unit logistics cost. Lim et al. [14] focus on comparing the differences of applying different coverage models in the objective function when optimizing the location of dispensing sites. Hirsh Bar Gai et al. [15] develop a model to find out the optimal locations and capacities for local hub vaccine warehouses to minimize the total traveling distance. Based on the real data of Nigeria, they compare the performance of different scenarios. As for the second topic, some researchers focus on tactical decisions such as shipping policies and transportation modes. Han et al. [16] optimize the routing problem in an existing threelayer supply chain to minimize the total transportation cost for emergency material delivery. Chen et al. [17] propose a planning model for optimizing the vaccine quantities of each delivery trip in a directed WHO-EPI vaccine distribution network in lowincome countries. Their model aims to maximize the number of fully immunized children under known demand. Rabta et al. [18] study the last-mile distribution problem by drones in the humanitarian supply chain. An optimization model is presented in their paper to minimize the total traveling distance. Lin et al. [19] discuss the distributor's transportation decision on using a cold chain for vaccines or not. Meanwhile, they analyze the impact of retailer's inspections on the aforementioned distributor's decisions.

The third topic is operational decisions including administration policies and inventory policies at the final dispensing sites. A mixed-integer programming model is developed by Proano et al. [20] which focuses on optimizing the number of doses in a combination vaccine. Their model aims to maximize manufacturing profits and customer surplus. Mofrad et al. [21] study the vaccine administration policies considering the non-stationary demand and delayed service. The goal of their work is to reduce 5 the "open vial waste". Azadi et al. [22] develop a two-stage stochastic programming model to optimize the combination of vaccine vials in a different size, and decide whether to open a new vial or not in face of the uncertain patient arrivals.

Most recently, studies about immunization during COVID-19 have received a lot of attention. COTFAS et al. [23] explore how the COVID-19 vaccination opinions changes in social media network. Risanger et al. [24] present an inventory-location optimization model to optimize the allocation of influenza vaccines during the pandemic. Corey et al. [25] qualitatively discuss possible challenges for both the endpoints and the manufactures in developing COVID-19 vaccines. Similarly, Mills and Salisbury [26] discuss the potential challenges of distributing COVID-19 vaccines. Aruffo et al. [27] introduce a compartmental model to study the vaccination strategy for COVID-19 under scenarios with different vaccine coverage, effectiveness, and waning immunity. Roy et al. [28] use an epidemic model to study the allocation of limited vaccines. Several other studies focus on identifying the population group that has the priority to be vaccinated [29] .

With an overview of the previous studies, the following research gaps can be identified:

(1) Previous studies related to vaccine distribution mostly focus on designing or optimizing networks that minimize cost or traveling distance for permanent routine vaccination. The existing network design models or strategies cannot be used directly in the phased COVID-19 campaign that network changes over time to achieve different goals. Moreover, previous research fails to address the challenges associated with the newly-presented ultra-cold vaccine distribution such as how to facilitate vaccination when most of the sites do not have the appropriate storage facilities for ultra-cold requirement.

(2) When developing models, there is a lack of a generalized framework that can capture local characteristics (e.g., local transportation accessibility, economics) and be used in different regions of the world. Promoting immunization progress is a global topic. Without loss of generality, there is a clear need for these models to capture the local characteristics to better inform their vaccine distribution strategies.

In addressing these gaps, this paper will develop a network design methodology for the phased vaccination campaign.

Considering the very short shelf-life of ultra-cold vaccines, we introduce a hub-and-spoke network configuration in which dispensing sites can share their vaccine inventory, use up the ultra-cold vaccines quickly, and further reduce the vaccine waste.

This hub-and-spoke network configuration allows more flexible network expansion or reduction in each vaccination campaign phase when needed. Moreover, to compare the coverage of different dispensing sites, we introduce a coverage index calculation model which considers not only the population lived around a dispensing site, but also the local travel and economic characteristics that impact vaccination wiliness.

Vaccines are strategic stockpiles controlled by a special national division. In general, vaccines are produced by authorized domestic manufacturers and then sent into the vaccine distribution network [13] . For some low-income countries, due to the lack of technology and raw materials, vaccines may be imported from other countries instead of producing locally [17] . In the vaccine distribution system, the specified national division such as the Division of Strategic National Stockpile in the U.S. will manage the allocation and distribution of vaccines. Generally, vaccine distribution involves multiple sectors from the national warehouse to the local warehouse. After vaccines arrive at the local warehouse, local stockpile divisions will take over the vaccines and allocate them to the final dispensing sites where people can be vaccinated [30] . In some cases, vaccine manufactures can directly send vaccines to the final dispensing sites if resources are allowed. In this paper, we focus on the final step of the vaccine distribution network where the vaccines are delivered from manufacturers or local warehouses to the final dispensing sites.

As shown in Fig. 2 , the final vaccine delivery in the current point-to-point configuration is from the upstream sector directly to each dispensing site. This configuration is very effective and easy to manage for routine vaccines that can be stored at room temperature or refrigerator. A batch of vaccines is delivered to each dispensing site and stored in the required environment until they are administrated to people. However, when it comes to vaccines that require ultra-cold storage, the point-to-point configuration may cause huge waste. Since ordinary refrigerated trucks cannot reach the required ultra-low temperature, passive refrigerators are widely used along the ultra-cold chain [17, 31] . Due to cost reasons, one passive refrigerator container contains a number of vaccine vials. In the point-to-point configuration, upstream sectors ship such containers to each dispensing site. Since there is no ultra-cold freezer in dispensing sites, once a container is opened at the dispensing site, all vaccines in the container start to defrost. Outside the ultra-cold environment, vaccines are only good for a short time once thawed. Hence, the administrations of these vaccines become a race against time. However, it's highly likely that the number of vaccines in one container is more than the amount that most of the dispensing sites could reasonably expect to use. For example, the current Pfizer's storage container holds from 1,000 to 5,000 doses of the shot [6] . These vaccines need to be used within five days in standard refrigeration. There are different kinds of dispensing sites such as big hospitals, health care centers, doctor offices, and pharmacies. Based on the data in New Jersey's vaccination plan published by the New Jersey Department of Health [32] , the expected administration capacity per day at one site varies from 50 to 400. That is to say, most of the dispensing sites cannot use up the vaccines in one container before they are out-of-date.

At the time of writing, the U.S. promotes the COVID-19 vaccination rollout process by sending vaccines (point-to-point) to several large, centralized vaccination centers which can rapidly go through all doses. This solution seems to be all right at this phase (Phase 1) whose target is to vaccinate the high-priority population [5] . However, once we step into the second phase aiming to cover as many people as possible, the centralized sites with point-to-point configuration will be unfavorable. These centralized dispensing sites are usually located in densely populated regions and are spread out. People may need to travel a long way to get to an available centralized dispensing site. According to a recent survey conducted in Uganda, one of the most crucial factors determining people's willingness to be vaccinated is convenience [33] . Long traveling time to a vaccination site will decrease people's willingness to be vaccinated. So, in addition to using the mega, centralized sites, Phase 2 must expand the provider network by involving more local sites to enhance people's accessibility to vaccines. By doing so, the aim of stimulating more people to get vaccinated can be achieved.

Considering the aforementioned challenges in COVID-19 vaccine distribution, we propose a hub-and-spoke network caused by unused overdue vaccines. This is particularly important for ultra-cold vaccine rollout since the lack of appropriate storage facilities shortens vaccine shelf-life. Second, the use of outreach dispensing sites enhances the convenience of getting people vaccinated by expanding the geographical coverage area of sites, which will stimulate more people to get vaccinated. Third, the proposed hub-and-spoke configuration can help reduce the temperature excursion risks associated with transporting ultra-cold vaccines, since some of the long-distance shipping trips from upstream to dispensing sites will be replaced by short-distance transfer shipping trips between local dispensing sites within the cluster. With these three strengths, this hub-and-spoke configuration can help us overcome the challenges brought by the lack of ultra-cold freezers in vaccine distribution without having to invest in expensive infrastructure. One question then naturally arises: How to design such a hub-and-spoke network based on the current vaccine distribution system?

In this section, an optimization model is proposed for designing a hub-and-spoke network for Phase 2 of COVID-19 vaccine distribution. According to the CDC's vaccine rollout recommendations [5] , Phase 2 includes all other persons aged ≥16 years not already recommended for vaccination in Phase 1, and any authorized COVID-19 vaccine may be used. Some of the large centralized dispensing sites used in Phase 1 will act as the H-DSs in Phase 2 since the distribution of vaccines from upstream to these sites is well established. To cover the larger population in Phase 2, OR-DSs will need to be added to the vaccination network.

These OR-DSs should be strategically selected from the available local dispensing sites and allocated to the existing H-DSs.

An integer programming problem is formulated with a decision variable to determine which local sites are selected to be Then, the total coverage of the hub-and-spoke network, also the objective function to be maximized is equal to

, H

Equations (2) and (3) together establish the hub-and-spoke configuration. Specifically, Equation (2) specifies that an OR-DS can only be assigned to at most one H-DS; Equation (3) specifies that an H-DS is connected with at most OR-DSs. Frequent MAX vaccine transfers occur between the H-DS and its OR-DS. Thus, it is necessary to limit the travel distance from the H-DS to its OR-DS since a long trip will not only shorten the ultra-cold vaccine's shelf life in dispensing sites but also increase the temperature excursion risk. Thus, equation (4) ensures that OR-DS i can be assigned to H-DS j only if the driving time between i and j is within a predetermined upper limit .

The most crucial input in the optimization model is the coverage index (CI for short) of each site. The optimal network should consist of high-CI sites to maximize the total coverage. This section presents how we define and estimate the coverage index by extending the basic concept from literature but customizing it for the COVID-19 vaccine. The original meaning of vaccination coverage is the percentage of vaccinated people [34, 35] . Lim, et al. [14] presented several ways of measuring coverage: The simplest method is the binary coverage model which assumes all the population within a certain distance radius of the site is covered; Extending from the binary coverage model, the variable single coverage model assumes that the fraction of covered people decreases stepwise as the distance radius increases. Risanger, et al. [24] assumed the fraction of covered people decays exponentially as the distance increases. All these models assume straight-line distance when estimating the 

where is the fixed baseline fraction of covered people in k level area from Lim's study [14] , is the total number of public transportation stops (bus stops, subway stops, etc.) around site i, and is the additional "attractiveness" brought by each vaccination because a more socially vulnerable community is at higher risk of COVID-19 and hence is in more urgent need of vaccines. Let denote the social vulnerability index (SVI) of the community that dispensing site i is located in. In order to SVI raise the priority of the more vulnerable regions, we define the final coverage index of site i be 

To demonstrate our framework and gain insights on the Phase 2 vaccination campaign, a case study is conducted in this section.

We take Middlesex County in central New Jersey, U.S., as the case area. Also known as the "Heart of New Jersey," Middlesex County is located squarely in the center of New Jersey [36] . As part of the New York metropolitan area, Middlesex has an estimated population of over 825,000 in 2019 and 523 census block groups [37] . The County is 318 square miles in size, has 25 municipalities ranging from quiet rural towns to vibrant city centers [36] . The case study will develop a hub-and-spoke vaccination network at the county level based on real data. Section A describes the data collection process. Section B provides results of the case study.

The optimization model in this case study is solved by the CPLEX Optimizer.

Two types of data are needed for the optimization model: location of the potential dispensing sites and geographic data and information (also known as geo-data) on local demographics, transportation facilities, economics, etc.

The vaccination plan published by NJDOH in October 2020 provides a list of potential local dispensing sites for each county [32] . According to NJDOH, potential dispensing sites include hospitals, Federally Qualified Health Centers (FQHC), and chain retail pharmacies. The NJDOH's vaccination plan lists a total of 58 potential dispensing sites in Middlesex County, including 6 hospitals, 7 health centers, and 45 retail pharmacies. For convenience, we reasonably assume that all 13 hospitals and health centers , the total residents that live in the coverage level k of dispensing site i. We use the Ρ ( ) Summarize Nearby function in ArcGIS Online to calculate the total population within a specified distance of a dispensing site. As stated in section II, to better capture the local transportation accessibility, we define that distance is measured by driving time. The live speed in a typical peak hour (Monday 8 a.m.) is used to estimate the driving time. Public transportation data are used to obtain the number of nearby bus stops ( . The SVI data layer enables us to calculate the . ) SVI Table I lists the input data to the case study. The K = 3 coverage levels and the values of 's are adopted from Lim's work [14] . According to the 2017 person trips statistics data released by the U.S. Department of Transportation [39] , about 2% of personal trips use public transportation. So, we assume that the estimated additional attractiveness brought to a dispensing site per public transportation stop is 0.02.

The maximum number of OR-DSs that can connect to a H-DS ( ) and the upper limit on the allowed driving time from a MAX H-DS to its OR-DSs ( ) vary in different scenarios. As stated in Section II, is introduced to limit the travel distance

from H-DS to its OR-DS for reducing the on-trip time and the long-trip temperature excursion risks during ultra-cold vaccine delivery. It's reported that the ultra-cold COVID-19 vaccine allows at most 30 minutes under room temperature considering some local transfers may not use refrigerated trucks [6] . So, we let the values range between 10 and 30 minutes. As for , the

baseline scenario allows each hub to be connected with at most 3 OR-DSs ( ), since a cluster with 4 sites (1 hub and 3 MAX = 3 outreach sites) is expected to administer 1,000 doses per day according to NJDOH's estimation [32] , which is the minimum quantity in one Pfizer's container. To investigate how impacts vaccine distribution, we increase to 4 and 5,

respectively, in sensitivity analysis, allowing more OR-DSs to be connected to a hub. For convenience, we name each scenario by its and values. For example, "4OR15DT" represent the scenario with = 4 and = 15 minutes.

This section analyzes the results of the 5 baseline scenarios. Table II presents the total coverage index (TCI, objective function value) and the total number of OR-DSs included in the optimal hub-and-spoke network. As shown in Table II 

In order to take a closer look at the optimal hub-and-spoke network, Table III lists the selection results of the 15 potential OR-DSs with smallest coverage index. Symbol "○" in Table III defined as the number of times out of the 5 baseline scenarios that a site is selected into the optimal hub-and-spoke network. A larger circle indicates the site receives higher preference and that the site is selected into the optimal design more. CI is an input attribute of a site, while preference is an output from optimization. Intuitively, the preference of a site should depend on its CI. are not selected into the optimal design in any of the baseline scenarios. improve the TCI. At , all 45 potential OR-DSs are selected into the optimal hub-and-spoke network for vaccine MAX ≥ 20 distribution. In other words, when the hub-and-spoke network configuration is implemented, ultra-cold vaccines can be delivered to all local dispensing sites from the hubs within its 30-min restriction under room temperature after opening the vaccine container.

Using our analytical framework, we have demonstrated the process of utilizing a geographical information system to determine and improve the coverage index of each dispensing site. Furthermore, within this framework, we adopt a hub-and-spoke design to support vaccination efforts, and apply it to the Phase 2 vaccination campaign in Middlesex County, NJ, the U.S. After evaluating 15 scenarios with varying constraints and parameters, we observe the following key takeaways:

(1) There is a maximum threshold level for the distance limitation which restricts the acceptable driving time from a H-DS to its OR-DSs. While we can expand coverage by increasing the distance limitation, once this threshold is met, any further increases in the distance limitation would not result in expanded coverage. 4) Our framework serves as a decision support tool, which can aid state and local governments in designing vaccination campaigns in the face of a public health crisis. While this framework can be applied to many regions and countries to obtain generalizable insights, we observe that rural and underpopulated areas are at risk of limited coverage under the current assumptions of this framework. For example, Fig. 7 shows the potential dispensing sites in New Jersey's Cape May County. Pharmacies in the highlighted area are far from the county's hub centers. In order to ensure fair and equitable access to vaccines in such cases, public health officials may need to consider alternative options, establishing partnerships with neighboring counties or deploying pop-up vaccine administration sites.

This paper focuses on expanding the COVID-19 vaccination coverage against the backdrop of the phased vaccination campaign in the U.S. In face of the challenges brought by ultra-cold storage requirements, we propose a framework to design a regional huband-spoke vaccine distribution network that can be generalized to support different communities in a public health crisis by enhancing the access to the vaccines. This network configuration is expected to reduce vaccine waste without making infrastructure investments by sharing inventory within each region. Furthermore, we introduce an improved coverage index in the optimization model to measure the priority of each dispensing site. This newly proposed coverage index utilizes a geographical information system to capture local characteristics and demographics. We demonstrate our framework by evaluating 15 different scenarios based on real data, which yields actionable strategies for the upcoming Phase 2 vaccination campaign.

Additionally, our newly proposed framework can be further generalized to support other countries deploying a vaccination campaign in the face of a public health crisis. To accomplish this, our work may be further expanded by considering site-specific demands, flexible administration policies, and new opportunities for secondary distribution such as using drones or smaller containers. Though our solution provides a way to improve vaccine access, it must be noted that enhancing vaccine awareness and acceptance are also essential for a successful vaccination program [40] . Further actions such as funding support and media promotion should be taken simultaneously to improve vaccine acceptance. Future research is required on a case-by-case basis to evaluate individual challenges faced by other regions or countries, and how to combine the framework with other opportunities. The baseline fraction of level 1 coverage 1 2 The baseline fraction of level 2 coverage 0.5 3 The baseline fraction of level 3 coverage 0.2 1 The driving time limit (minutes) of level 1 coverage 5 2 The driving time limit (minutes)of level 2 coverage 8 3 The driving time limit (minutes) of level 3 coverage 10

The additional attractiveness brought to a dispensing site per public 

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