Multi-period vaccine allocation model in a pandemic: A case study of COVID-19 in Australia

Balancing fairness and efficiency in dynamic vaccine allocation during major infectious disease outbreaks

The outbreak of novel infectious diseases presents major public health challenges, highlighting the urgency of accelerating vaccination efforts to reduce morbidity and mortality. Vaccine allocation has become a crucial societal concern. This paper introduces a dynamic vaccine allocation model that considers demand uncertainty and vaccination willingness, focusing on the trade-off between fairness and efficiency. We develop a multi-period dynamic vaccine allocation model, evaluating optimal strategies over different periods. The model addresses structural differences among vaccination groups, strategy selection, dynamic demand, and vaccination willingness. Our findings suggest that prioritizing efficiency in the initial outbreak stages may lead to inequitable distribution, causing adverse social impacts, while overemphasizing fairness can undermine overall utility. Therefore, we propose a dynamic optimization-based strategy balancing fairness and efficiency at different pandemic stages. Our results indicate that allocation strategies should shift from efficiency to fairness as the pandemic evolves to enhance vaccine utility. Additionally, macro-level interventions like reducing free-rider behavior and increasing vaccination convenience can improve total vaccine utility. This study offers new perspectives and methodologies for dynamic vaccine allocation, highlighting the trade-off between fairness and efficiency, providing crucial insights for policy formulation and pandemic response.

An integrated blockchain-enabled multi-channel vaccine supply chain network under hybrid uncertainties

The recent pandemic caused by COVID-19 is considered an unparalleled disaster in history. Developing a vaccine distribution network can provide valuable support to supply chain managers. Prioritizing the assigned available vaccines is crucial due to the limited supply at the final stage of the vaccine supply chain. In addition, parameter uncertainty is a common occurrence in a real supply chain, and it is essential to address this uncertainty in planning models. On the other hand, blockchain technology, being at the forefront of technological advancements, has the potential to enhance transparency within supply chains. Hence, in this study, we develop a new mathematical model for designing a COVID-19 vaccine supply chain network. In this regard, a multi-channel network model is designed to minimize total cost and maximize transparency with blockchain technology consideration. This addresses the uncertainty in supply, and a scenario-based multi-stage stochastic programming method is presented to handle the inherent uncertainty in multi-period planning horizons. In addition, fuzzy programming is used to face the uncertain price and quality of vaccines. Vaccine assignment is based on two main policies including age and population-based priority. The proposed model and method are validated and tested using a real-world case study of Iran. The optimum design of the COVID-19 vaccine supply chain is determined, and some comprehensive sensitivity analyses are conducted on the proposed model. Generally, results demonstrate that the multi-stage stochastic programming model meaningfully reduces the objective function value compared to the competitor model. Also, the results show that one of the efficient factors in increasing satisfied demand and decreasing shortage is the price of each type of vaccine and its agreement.

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.

Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach

COVID-19 is an infectious disease that causes millions of deaths worldwide, and it is the principal leading cause of morbidity and mortality in all nations. Although the governments of developed and developing countries are enforcing their universal control strategies, more precise and cost-effective single or combination interventions are required to control COVID-19 outbreaks. Using proper optimal control strategies with appropriate cost-effectiveness analysis is important to simulate, examine, and forecast the COVID-19 transmission phase. In this study, we developed a COVID-19 mathematical model and considered two important features including direct link between vaccination and latently population, and practical healthcare cost by separation of infections into Mild and Critical cases. We derived basic reproduction numbers and performed mesh and contour plots to explore the impact of different parameters on COVID-19 dynamics. Our model fitted and calibrated with number of cases of the COVID-19 data in Bangladesh as a case study to determine the optimal combinations of interventions for particular scenarios. We evaluated the cost-effectiveness of varying single and combinations of three intervention strategies, including transmission control, treatment, and vaccination, all within the optimal control framework of the single-intervention policies; enhanced transmission control is the most cost-effective and prompt in declining the COVID-19 cases in Bangladesh. Our finding recommends that a three-intervention strategy that integrates transmission control, treatment, and vaccination is the most cost-effective compared to single and double intervention techniques and potentially reduce the overall infections. Other policies can be implemented to control COVID-19 depending on the accessibility of funds and policymakers' judgments.

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.

A robust optimization problem for drone-based equitable pandemic vaccine distribution with uncertain supply

Widespread vaccination is the only way to overcome the COVID-19 global crisis. However, given the vaccine scarcity during the early outbreak of the pandemic, ensuring efficient and equitable distribution of vaccines, particularly in rural areas, has become a significant challenge. To this end, this study develops a two-stage robust vaccine distribution model that addresses the supply uncertainty incurred by vaccine shortages. The model aims to optimize the social and economic benefits by jointly deciding vaccination facility location, transportation capacity, and reservation plan in the first stage, and rescheduling vaccinations in the second stage after the confirmation of uncertainty. To hedge vaccine storage and transportation difficulties in remote areas, we consider using drones to deliver vaccines in appropriate and small quantities to vaccination points. Two tailored column-and-constraint generation algorithms are proposed to exactly solve the robust model, in which the subproblems are solved via the vertex traversal and the dual methods, respectively. The superiority of the dual method is further verified. Finally, we use real-world data to demonstrate the necessity to account for uncertain supply and equitable distribution, and analyze the impacts of several key parameters. Some managerial insights are also produced for 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.

A reliable emergency logistics network for COVID-19 considering the uncertain time-varying demands

The evolving COVID-19 epidemic pose significant threats and challenges to emergency response operations. This paper focuses on designing an emergency logistic network, including the deployment of emergency facilities and the allocation of supplies to satisfy the time-varying demands. A Demand prediction-Network optimization-Decision adjustment framework is proposed for the emergency logistic network design. We first present an improved short-term epidemic model to predict the evolutionary trajectory of the epidemic. Then, considering the uncertainty of the estimated demands, we construct a capacitated multi-period, multi-echelon facility deployment and resource allocation robust optimization model to improve the reliability of the decisions. To address the conservativeness of robust solutions during the evolution of the epidemic, an uncertainty budget adjustment strategy is proposed and integrated into the rolling horizon optimization approach. The results of the case study show that (i) the short-term prediction method has higher accuracy and the accuracy increases with the amount of observed data; (ii) considering the demand uncertainty, the proposed robust optimization model combined with uncertainty budget adjustment strategy can improve the performance of the emergency logistic network; (iii) the proposed solution method is more efficient than its benchmark, especially for large-scale cases. Moreover, some managerial insights related to the emergency logistics network design problem are presented.

Modeling a closed-loop vaccine supply chain with transshipments to minimize wastage and threats to the public: a system dynamics approach

Purpose

This study aims to focus on building a conceptual closed-loop vaccine supply chain (CLVSC) to decrease vaccine wastage and counterfeit/fake vaccines.

Design/methodology/approach

Through a focused literature review, the framework for the CLVSC is described, and the system dynamics (SD) research methodology is used to build a causal loop diagram (CLD) of the proposed model.

Findings

In the battle against COVID-19, waste management systems have become overwhelmed, which has created negative environmental and extremely hazardous societal impacts. A key contributing factor is unused vaccine doses, shown as a source for counterfeit/fake vaccines. The findings identify a CLVSC design and transshipment operations to decrease vaccine wastage and the potential for vaccine theft.

Research limitations/implications

This study contributes to establishing a pandemic-specific VSC structure. The proposed model informs the current COVID-19 pandemic as well as potential future pandemics.

Social implications

A large part of the negative impact of counterfeit/fake vaccines is on human well-being, and this can be avoided with proper CLVSC.

Originality/value

This study develops a novel overarching SD CLD by integrating the epidemic model of disease transmission, VSC and closed-loop structure. This study enhances the policymakers’ understanding of the importance of vaccine waste collection, proper handling and threats to the public, which are born through illicit activities that rely on stolen vaccine doses.

Optimizing two-dose vaccine resource allocation to combat a pandemic in the context of limited supply: The case of COVID-19

The adequate vaccination is a promising solution to mitigate the enormous socio-economic costs of the ongoing COVID-19 pandemic and allow us to return to normal pre-pandemic activity patterns. However, the vaccine supply shortage will be inevitable during the early stage of the vaccine rollout. Public health authorities face a crucial challenge in allocating scarce vaccines to maximize the benefits of vaccination. In this paper, we study a multi-period two-dose vaccine allocation problem when the vaccine supply is highly limited. To address this problem, we constructed a novel age-structured compartmental model to capture COVID-19 transmission and formulated as a nonlinear programming (NLP) model to minimize the total number of deaths in the population. In the NLP model, we explicitly take into account the two-dose vaccination procedure and several important epidemiologic features of COVID-19, such as pre-symptomatic and asymptomatic transmission, as well as group heterogeneity in susceptibility, symptom rates, severity, etc. We validated the applicability of the proposed model using a real case of the 2021 COVID-19 vaccination campaign in the Midlands of England. We conducted comparative studies to demonstrate the superiority of our method. Our numerical results show that prioritizing the allocation of vaccine resources to older age groups is a robust strategy to prevent more subsequent deaths. In addition, we show that releasing more vaccine doses for first-dose recipients could lead to a greater vaccination benefit than holding back second doses. We also find that it is necessary to maintain appropriate non-pharmaceutical interventions (NPIs) during the vaccination rollout, especially in low-resource settings. Furthermore, our analysis indicates that starting vaccination as soon as possible is able to markedly alleviate the epidemic impact when the vaccine resources are limited but are currently available. Our model provides an effective tool to assist policymakers in developing adaptive COVID-19 likewise vaccination strategies for better preparedness against future pandemic threats.

Analysis of performance of Covid-19 vaccine supply chain in India

Purpose

This study aims to analyse the structure of the Indian vaccine supply chain (SC) during the Covid-19 crisis and explore the underlying challenges at each stage in the network. It also brings out the difference in performance of various constituent states.

Design/methodology/approach

This study relied on both primary and secondary data for the analyses. For the primary data, the study gathered experts’ opinions to validate the authors’ inferences. For the secondary data, it relies on government data provided in websites.

Findings

Based on the quartile analysis and cluster analysis of the secondary data, the authors find that the constituent states responded differently during the first and second waves. This was due to the differences in SC characteristics attributed to varied demographics and administrative efficiency.

Research limitations/implications

This paper’s analyses is primarily limited to secondary information and inferences are based on them. The study has important implications for implementing the large-scale vaccination drives by government and constituent states for better coordination and last-mile delivery.

Originality/value

The contribution is unique in studying the performance of constituent states using statistical techniques, with secondary data from authentic sources. It is also unique in combining this observation with validation from experts.