Where to locate COVID-19 mass vaccination facilities?

Optimization Modeling for Pandemic Vaccine Supply Chain Management: A Review and Future Research Opportunities

During various stages of the COVID-19 pandemic, countries implemented diverse vaccine management approaches, influenced by variations in infrastructure and socio-economic conditions. This article provides a comprehensive overview of optimization models developed by the research community throughout the COVID-19 era, aimed at enhancing vaccine distribution and establishing a standardized framework for future pandemic preparedness. These models address critical issues such as site selection, inventory management, allocation strategies, distribution logistics, and route optimization encountered during the COVID-19 crisis. A unified framework is employed to describe the models, emphasizing their integration with epidemiological models to facilitate a holistic understanding. This article also summarizes evolving nature of literature, relevant research gaps, and authors' perspectives for model selection. Finally, future research scopes are detailed both in the context of modeling and solutions approaches.

Optimizing the Selection of Mass Vaccination Sites: Access and Equity Consideration

In the early phases of the COVID-19 pandemic, vaccine accessibility was limited, impacting large metropolitan areas such as Los Angeles County, which has over 10 million residents but only nine initial vaccination sites, which resulted in people experiencing long travel times to get vaccinated. We developed a mixed-integer linear model to optimize site selection, considering equitable access for vulnerable populations. Analyzing 277 zip codes between December 2020 and May 2021, our model incorporated factors such as car ownership, ethnic group disease vulnerability, and the Healthy Places Index, alongside travel times by car and public transit. Our optimized model significantly outperformed actual site allocations for all ethnic groups. We observed that White populations faced longer travel times, likely due to their residences being in more remote, less densely populated areas. Conversely, areas with higher Latino and Black populations, often closer to the city center, benefited from shorter travel times in our model. However, those without cars experienced greater disadvantages. While having many vaccination sites might improve access for those dependent on public transit, that advantage is diminished if people must search among many sites to find a location with available vaccines.

Predictive models for health outcomes due to SARS-CoV-2, including the effect of vaccination: a systematic review

BACKGROUND

The interaction between modelers and policymakers is becoming more common due to the increase in computing speed seen in recent decades. The recent pandemic caused by the SARS-CoV-2 virus was no exception. Thus, this study aims to identify and assess epidemiological mathematical models of SARS-CoV-2 applied to real-world data, including immunization for coronavirus 2019 (COVID-19).

METHODOLOGY

PubMed, JSTOR, medRxiv, LILACS, EconLit, and other databases were searched for studies employing epidemiological mathematical models of SARS-CoV-2 applied to real-world data. We summarized the information qualitatively, and each article included was assessed for bias risk using the Joanna Briggs Institute (JBI) and PROBAST checklist tool. The PROSPERO registration number is CRD42022344542.

FINDINGS

In total, 5646 articles were retrieved, of which 411 were included. Most of the information was published in 2021. The countries with the highest number of studies were the United States, Canada, China, and the United Kingdom; no studies were found in low-income countries. The SEIR model (susceptible, exposed, infectious, and recovered) was the most frequently used approach, followed by agent-based modeling. Moreover, the most commonly used software were R, Matlab, and Python, with the most recurring health outcomes being death and recovery. According to the JBI assessment, 61.4% of articles were considered to have a low risk of bias.

INTERPRETATION

The utilization of mathematical models increased following the onset of the SARS-CoV-2 pandemic. Stakeholders have begun to incorporate these analytical tools more extensively into public policy, enabling the construction of various scenarios for public health. This contribution adds value to informed decision-making. Therefore, understanding their advancements, strengths, and limitations is essential.

Modeling geographic vaccination strategies for COVID-19 in Norway

Vaccination was a key intervention in controlling the COVID-19 pandemic globally. In early 2021, Norway faced significant regional variations in COVID-19 incidence and prevalence, with large differences in population density, necessitating efficient vaccine allocation to reduce infections and severe outcomes. This study explored alternative vaccination strategies to minimize health outcomes (infections, hospitalizations, ICU admissions, deaths) by varying regions prioritized, extra doses prioritized, and implementation start time. Using two models (individual-based and meta-population), we simulated COVID-19 transmission during the primary vaccination period in Norway, covering the first 7 months of 2021. We investigated alternative strategies to allocate more vaccine doses to regions with a higher force of infection. We also examined the robustness of our results and highlighted potential structural differences between the two models. Our findings suggest that early vaccine prioritization could reduce COVID-19 related health outcomes by 8% to 20% compared to a baseline strategy without geographic prioritization. For minimizing infections, hospitalizations, or ICU admissions, the best strategy was to initially allocate all available vaccine doses to fewer high-risk municipalities, comprising approximately one-fourth of the population. For minimizing deaths, a moderate level of geographic prioritization, with approximately one-third of the population receiving doubled doses, gave the best outcomes by balancing the trade-off between vaccinating younger people in high-risk areas and older people in low-risk areas. The actual strategy implemented in Norway was a two-step moderate level aimed at maintaining the balance and ensuring ethical considerations and public trust. However, it did not offer significant advantages over the baseline strategy without geographic prioritization. Earlier implementation of geographic prioritization could have more effectively addressed the main wave of infections, substantially reducing the national burden of the pandemic.

Fair-split distribution of multi-dose vaccines with prioritized age groups and dynamic demand: The case study of COVID-19

The emergence of the SARS-CoV-2 virus and new viral variations with higher transmission and mortality rates have highlighted the urgency to accelerate vaccination to mitigate the morbidity and mortality of the COVID-19 pandemic. For this purpose, this paper formulates a new multi-vaccine, multi-depot location-inventory-routing problem for vaccine distribution. The proposed model addresses a wide variety of vaccination concerns: prioritizing age groups, fair distribution, multi-dose injection, dynamic demand, etc. To solve large-size instances of the model, we employ a Benders decomposition algorithm with a number of acceleration techniques. To monitor the dynamic demand of vaccines, we propose a new adjusted susceptible-infectious-recovered (SIR) epidemiological model, where infected individuals are tested and quarantined. The solution to the optimal control problem dynamically allocates the vaccine demand to reach the endemic equilibrium point. Finally, to illustrate the applicability and performance of the proposed model and solution approach, the paper reports extensive numerical experiments on a real case study of the vaccination campaign in France. The computational results show that the proposed Benders decomposition algorithm is 12 times faster, and its solutions are, on average, 16% better in terms of quality than the Gurobi solver under a limited CPU time. In terms of vaccination strategies, our results suggest that delaying the recommended time interval between doses of injection by a factor of 1.5 reduces the unmet demand up to 50%. Furthermore, we observed that the mortality is a convex function of fairness and an appropriate level of fairness should be adapted through the vaccination.

Equitable and effective vaccine access considering vaccine hesitancy and capacity constraints

The COVID-19 pandemic continues to have an unprecedented impact on people's lives and the economy worldwide. Vaccines are the strongest evidence-based defense against the spread of the disease. The release of COVID-19 vaccines to the general public created policy challenges associated with how to best allocate vaccines among different sub-regions. In the United States, after vaccines became widely available for all eligible adults, policymakers faced objectives such as (i ) achieving an equitable allocation to reduce populations' travel times to get vaccinated and (i i ) effectively allocating vaccine doses to minimize waste and unmet need. This problem was further exacerbated by the underlying factors of population vaccine hesitancy and sub-regions' varying capacity levels to administer vaccines to eligible and willing populations. Although simple to implement, commonly used pro rata policies do not capture the complexities of this problem. We propose two alternatives to simple pro rata policies. The first alternative is based on a Mixed-Integer Linear Programming Model that minimizes the maximum travel duration of patients and aims to achieve an equitable and effective allocation of vaccines to sub-regions while considering capacity and vaccine hesitancy. A second alternative is a heuristic approach that may be more palatable for policymakers who (i ) are not familiar with mathematical modeling, (i i ) are reluctant to use black-box models, and (i i i ) prefer algorithms that are easy to understand and implement. We demonstrate the results of our model through a case study based on real data from the state of Alabama and show that substantial improvements in travel time-based equity are achievable through capacity improvements in a small subset of counties. We perform additional computational experiments that compare the proposed methods in terms of several metrics and demonstrate the promising performance of our model and proposed heuristic. We find that while our mathematical model can achieve equitable and effective vaccine allocation, the proposed heuristic performs better if the goal is to minimize average travel duration. Finally, we explore two model extensions that aim to (i ) lower vaccine hesitancy by allocating vaccines, and (i i ) prioritize vaccine access for certain high-risk sub-populations.

Hierarchical Vaccine Allocation Based on Epidemiological and Behavioral Considerations

Vaccines have proven useful in curbing contagion from new strains of the SARS-CoV-2 virus. However, equitable vaccine allocation continues to be a significant challenge worldwide, necessitating a comprehensive allocation strategy incorporating heterogeneity in epidemiological and behavioral considerations. In this paper, we present a hierarchical allocation strategy that assigns vaccines to zones and their constituent neighborhoods cost-effectively, based on their population density, susceptibility, infected count, and attitude towards vaccinations. Moreover, it includes a module that tackles vaccine shortages in certain zones by locally transferring vaccines from zones with surplus vaccines. We leverage the epidemiological, socio-demographic, and social media datasets from Chicago and Greece and their constituent community areas to show that the proposed allocation approach assigns vaccines based on the chosen criteria and captures the effects of disparate vaccine adoption rates. We conclude the paper with a lowdown on future efforts to extend this study to design models for effective public policies and vaccination strategies that curtail vaccine purchase costs.

Two-phase COVID-19 medical waste transport optimisation considering sustainability and infection probability

A safe and effective medical waste transport network is beneficial to control the COVID-19 pandemic and at least decelerate the spread of novel coronavirus. Seldom studies concentrated on a two-phase COVID-19 medical waste transport in the presence of multi-type vehicle selection, sustainability, and infection probability, which is the focus of this paper. This paper aims to identify the priority of sustainable objectives and observe the impacts of multi-phase and infection probability on the results. Thus, such a problem is formulated as a mixed-integer programming model to minimise total potential infection risks, minimise total environmental risks, and maximise total economic benefits. Then, a hybrid solution strategy is designed, incorporating a lexicographic optimisation approach and a linear weighted sum method. A real-world case study from Chongqing is used to illustrate this methodology. Results indicate that the solution strategy guides a good COVID-19 medical waste transport scheme within 1 min. The priority of sustainable objectives is society, economy, and environment in the first and second phases because the total Gap of case No.35 is 3.20%. A decentralised decision mode is preferred to design a COVID-19 medical waste transport network at the province level. Whatever the infection probability is, infection risk is the most critical concern in the COVID-19 medical waste clean-up activities. Environmental and economic sustainability performance also should be considered when infection probability is more than a certain threshold.

Dynamic planning of a two-dose vaccination campaign with uncertain supplies

The ongoing COVID-19 pandemic has led public health authorities to face the unprecedented challenge of planning a global vaccination campaign, which for most protocols entails the administration of two doses, separated by a bounded but flexible time interval. The partial immunity already offered by the first dose and the high levels of uncertainty in the vaccine supplies have been characteristic of most of the vaccination campaigns implemented worldwide and made the planning of such interventions extremely complex. Motivated by this compelling challenge, we propose a stochastic optimization framework for optimally scheduling a two-dose vaccination campaign in the presence of uncertain supplies, taking into account constraints on the interval between the two doses and on the capacity of the healthcare system. The proposed framework seeks to maximize the vaccination coverage, considering the different levels of immunization obtained with partial (one dose only) and complete vaccination (two doses). We cast the optimization problem as a convex second-order cone program, which can be efficiently solved through numerical techniques. We demonstrate the potential of our framework on a case study calibrated on the COVID-19 vaccination campaign in Italy. The proposed method shows good performance when unrolled in a sliding-horizon fashion, thereby offering a powerful tool to help public health authorities calibrate the vaccination campaign, pursuing a trade-off between efficacy and the risk associated with shortages in supply.

A mass vaccination site selection problem: An application of GIS and entropy-based MAUT approach

Coronavirus disease (COVID-19) was recognized in December 2019 and spread very severely throughout the world. In 2022 May, the total death numbers reached 6.28 million people worldwide. During the pandemic, some alternative vaccines were discovered in the middle of 2020. Today, many countries are struggling to supply vaccines and vaccinate their citizens. Besides the difficulties of vaccine supply, mass vaccination is a challenging but mandatory task for the countries. Within this context, determining the mass vaccination site is very important for recovering, thus a five-step approach is generated in this paper to solve this real-life problem. Firstly the mass vaccination site selection criteria are determined, and secondly, the spatial data are collected and mapped by using Geographical Information System (GIS) software. Then, the entropy weighting method (EWM) is used for determining the relative importance levels of criteria and fourthly, the multiple attribute utility theory (MAUT) approach is used for ranking the potential mass vaccination sites. Lastly, ranked alternative sites are analyzed using network analyst tool of GIS in terms of covered population. A case study is conducted in Gaziantep city which is the ninth most population and having above-average COVID-19 patients in Turkey. As a result, the fourth alternative (around the Şehitkamil Monument) is chosen as the best mass vaccination site for the city. It is believed that the outcomes of the paper could be used by city planners and decision-makers.

Pharmacy-based immunization: a systematic review

Background

The coronavirus disease 2019 pandemic has prompted the exploration of new response strategies for such health contingencies in the near future. Over the last 15 years, several pharmacy-based immunization (PBI) strategies have emerged seeking to exploit the potential of pharmacies as immunization, medication sale, and rapid test centers. However, the participation of pharmacies during the last pandemic was very uneven from one country to another, suggesting a lack of consensus on the definition of their roles and gaps between the literature and practice.

Purpose

This study aimed to consolidate the current state of the literature on PBI, document its progress over time, and identify the gaps not yet addressed. Moreover, this study seeks to (i) provide new researchers with an overview of the studies on PBI and (ii) to inform both public health and private organization managers on the range of possible immunization models and strategies.

Methodology

A systematic review of scientific qualitative and quantitative studies on the most important scientific databases was conducted. The Preferred Reporting Items for Systematic Reviews and Meta-analyzes guidelines were followed. Finally, this study discusses the trends, challenges, and limitations on the existing literature on PBI.

Findings

Must studies concluded that PBI is a beneficial strategy for the population, particularly in terms of accessibility and territorial equity. However, the effectiveness of PBI is affected by the economic, political, and/or social context of the region. The collaboration between the public (government and health departments) and private (various pharmacy chains) sectors contributes to PBI's success.

Originality

Unlike previous literature reviews on PBI that compiled qualitative and statistical studies, this study reviewed studies proposing mathematical optimization methods to approach PBI.

Vaccine Allocation and Distribution: A Review with a Focus on Quantitative Methodologies and Application to Equity, Hesitancy, and COVID-19 Pandemic

This review focuses on vaccine distribution and allocation in the context of the current COVID-19 pandemic. The implications discussed are in the areas of equity in vaccine distribution and allocation (at a national level as well as worldwide), vaccine hesitancy, game-theoretic modeling to guide decision-making and policy-making at a governmental level, distribution and allocation barriers (in particular in low-income countries), and operations research (OR) mathematical models to plan and execute vaccine distribution and allocation. To conduct this review, we adopt a novel methodology that consists of three phases. The first phase deploys a bibliometric analysis; the second phase concentrates on a network analysis; and the last phase proposes a refined literature review based on the results obtained by the previous two phases. The quantitative techniques utilized to conduct the first two phases allow describing the evolution of the research in this area and its potential ramifications in future. In conclusion, we underscore the significance of operations research (OR)/management science (MS) research in addressing numerous challenges and trade-offs connected to the current pandemic and its strategic impact in future research.

Bi-objective optimization of a stochastic resilient vaccine distribution network in the context of the COVID-19 pandemic

This paper develops an approach to optimize a vaccine distribution network design through a mixed-integer nonlinear programming model with two objectives: minimizing the total expected number of deaths among the population and minimizing the total distribution cost of the vaccination campaign. Additionally, we assume that a set of input parameters (e.g., death rate, social contacts, vaccine supply, etc.) is uncertain, and the distribution network is exposed to disruptions. We then investigate the resilience of the distribution network through a scenario-based robust-stochastic optimization approach. The proposed model is linearized and finally validated through a real case study of the COVID-19 vaccination campaign in France. We show that the current vaccination strategies are not optimal, and vaccination prioritization among the population and the equity of vaccine distribution depend on other factors than those conceived by health policymakers. Furthermore, we demonstrate that a vaccination strategy mixing the population prioritization and the quarantine restrictions leads to an 8.5% decrease in the total number of deaths.

Location Optimization of COVID-19 Vaccination Sites: Case in Hillsborough County, Florida

The equitable allocation of COVID-19 vaccines is a critical challenge worldwide, given that the pandemic has been disproportionally affecting economically disadvantaged racial and ethnic groups. In the United States, the ongoing implementation efforts at different administrative levels and districts, to some extent, are standing in conflict with commitments to mitigate inequities. In this study, we developed a spatial optimization model to choose the best locations for vaccination sites. The model is a modified two-step maximal covering location problem (MCLP). It aims at maximizing the number of residents who can conveniently access the sites and mitigating inequity issues by prioritizing disadvantaged population groups who live in geographic areas identified through the CDC's Social Vulnerability Index (SVI). We conducted our study using the case of Hillsborough County, Florida. We found that by reserving up to 30% of total vaccines for highly vulnerable communities, our model can optimize location choices for vaccination sites to provide effective coverage for residents at large while prioritizing disadvantaged groups of people. A series of sensitivity analyses have been performed to evaluate the impact of parameters such as site capacity and distance threshold. The model has the potential to guide the future allocation of critical medical resources in the U.S. and other countries.

Bi-objective optimization for a multi-period COVID-19 vaccination planning problem

This work investigates a new multi-period vaccination planning problem that simultaneously optimizes the total travel distance of vaccination recipients (service level) and the operational cost. An optimal plan determines, for each period, which vaccination sites to open, how many vaccination stations to launch at each site, how to assign recipients from different locations to opened sites, and the replenishment quantity of each site. We formulate this new problem as a bi-objective mixed-integer linear program (MILP). We first propose a weighted-sum and an ϵ -constraint methods, which rely on solving many single-objective MILPs and thus lose efficiency for practical-sized instances. To this end, we further develop a tailored genetic algorithm where an improved assignment strategy and a new dynamic programming method are designed to obtain good feasible solutions. Results from a case study indicate that our methods reduce the operational cost and the total travel distance by up to 9.3% and 36.6%, respectively. Managerial implications suggest enlarging the service capacity of vaccination sites can help improve the performance of the vaccination program. The enhanced performance of our heuristic is due to the newly proposed assignment strategy and dynamic programming method. Our findings demonstrate that vaccination programs during pandemics can significantly benefit from formal methods, drastically improving service levels and decreasing operational costs.

Study on the Localization of Fangcang Shelter Hospitals During Pandemic Outbreaks

In the event of pandemic, it is essential for government authority to implement responses to control the pandemic and protect people's health with rapidity and efficicency. In this study, we first develop an evaluation framework consisting of the entropy weight method (EWM) and the technique for order preference by similarity to ideal solution (TOPSIS) to identify the preliminary selection of Fangcang shelter hospitals; next, we consider the timeliness of isolation and treatment of patients with different degrees of severity of the infectious disease, with the referral to and triage in Fangcang shelter hospitals characterized and two optimization models developed. The computational results of Model 1 and Model 2 are compared and analyzed. A case study in Xuzhou, Jiangsu Province, China, is used to demonstrate the real-life applicability of the proposed models. The two-stage localization method gives decision-makers more options in case of emergencies and can effectively designate the location. This article may give recommendations of and new insights into parameter settings in isolation hospital for governments and public health managers.

A Data-Driven Digital Application to Enhance the Capacity Planning of the COVID-19 Vaccination Process

In this paper, a decision support system (DSS) is presented that focuses on the capacity planning of the COVID-19 vaccination process in the Netherlands. With the Dutch national vaccination priority list as the starting point, the DSS aims to minimize the per-class waiting-time with respect to (1) the locations of the medical hubs (i.e., the vaccination locations) and (2) the distribution of the available vaccines and healthcare professionals (over time). As the user is given the freedom to experiment with different starting positions and strategies, the DSS is ideally suited for providing support in the dynamic environment of the COVID-19 vaccination process. In addition to the DSS, a mathematical model to support the assignment of inhabitants to medical hubs is presented. This model has been satisfactorily implemented in practice in close collaboration with the Dutch Municipal and Regional Health Service (GGD GHOR Nederland).

Optimization in the Context of COVID-19 Prediction and Control: A Literature Review

This paper presents an overview of some key results from a body of optimization studies that are specifically related to COVID-19, as reported in the literature during 2020-2021. As shown in this paper, optimization studies in the context of COVID-19 have been used for many aspects of the pandemic. From these studies, it is observed that since COVID-19 is a multifaceted problem, it cannot be studied from a single perspective or framework, and neither can the related optimization models. Four new and different frameworks are proposed that capture the essence of analyzing COVID-19 (or any pandemic for that matter) and the relevant optimization models. These are: (i) microscale vs. macroscale perspective; (ii) early stages vs. later stages perspective; (iii) aspects with direct vs. indirect relationship to COVID-19; and (iv) compartmentalized perspective. To limit the scope of the review, only optimization studies related to the prediction and control of COVID-19 are considered (public health focused), and which utilize formal optimization techniques or machine learning approaches. In this context and to the best of our knowledge, this survey paper is the first in the literature with a focus on the prediction and control related optimization studies. These studies include optimization of screening testing strategies, prediction, prevention and control, resource management, vaccination prioritization, and decision support tools. Upon reviewing the literature, this paper identifies current gaps and major challenges that hinder the closure of these gaps and provides some insights into future research directions.