Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Retrospective analysis of equity-based optimization for COVID-19 vaccine allocation

Marginalized racial and ethnic groups in the United States were disproportionally affected by the COVID-19 pandemic. To study these disparities, we construct an age-and-race-stratified mathematical model of SARS-CoV-2 transmission fitted to age-and-race-stratified data from 2020 in Oregon and analyze counterfactual vaccination strategies in early 2021. We consider two racial groups: non-Hispanic White persons and persons belonging to BIPOC groups (including non-Hispanic Black persons, non-Hispanic Asian persons, non-Hispanic American-Indian or Alaska-Native persons, and Hispanic or Latino persons). We allocate a limited amount of vaccine to minimize overall disease burden (deaths or years of life lost), inequity in disease outcomes between racial groups (measured with five different metrics), or both. We find that, when allocating small amounts of vaccine (10% coverage), there is a trade-off between minimizing disease burden and minimizing inequity. Older age groups, who are at a greater risk of severe disease and death, are prioritized when minimizing measures of disease burden, and younger BIPOC groups, who face the most inequities, are prioritized when minimizing measures of inequity. The allocation strategies that minimize combinations of measures can produce middle-ground solutions that similarly improve both disease burden and inequity, but the trade-off can only be mitigated by increasing the vaccine supply. With enough resources to vaccinate 20% of the population the trade-off lessens, and with 30% coverage, we can optimize both equity and mortality. Our goal is to provide a race-conscious framework to quantify and minimize inequity that can be used for future pandemics and other public health interventions.

Evaluating vaccine allocation strategies using simulation-assisted causal modeling

We develop a model to retrospectively evaluate age-dependent counterfactual vaccine allocation strategies against the coronavirus disease 2019 (COVID-19) pandemic. To estimate the effect of allocation on the expected severe-case incidence, we employ a simulation-assisted causal modeling approach that combines a compartmental infection-dynamics simulation, a coarse-grained causal model, and literature estimates for immunity waning. We compare Israel's strategy, implemented in 2021, with counterfactual strategies such as no prioritization, prioritization of younger age groups, or a strict risk-ranked approach; we find that Israel's implemented strategy was indeed highly effective. We also study the impact of increasing vaccine uptake for given age groups. Because of its modular structure, our model can easily be adapted to study future pandemics. We demonstrate this by simulating a pandemic with characteristics of the Spanish flu. Our approach helps evaluate vaccination strategies under the complex interplay of core epidemic factors, including age-dependent risk profiles, immunity waning, vaccine availability, and spreading rates.

Optimizing COVID-19 vaccine allocation considering the target population

Vaccine allocation strategy for COVID-19 is an emerging and important issue that affects the efficiency and control of virus spread. In order to improve the fairness and efficiency of vaccine distribution, this paper studies the optimization of vaccine distribution under the condition of limited number of vaccines. We pay attention to the target population before distributing vaccines, including attitude toward the vaccination, priority groups for vaccination, and vaccination priority policy. Furthermore, we consider inventory and budget indexes to maximize the precise scheduling of vaccine resources. A mixed-integer programming model is developed for vaccine distribution considering the target population from the viewpoint of fairness and efficiency. Finally, a case study is provided to verify the model and provide insights for vaccine distribution.

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.

FMD vaccine allocation and surveillance resourcing options for a potential Australian incursion

Australian Animal Disease Spread (AADIS) epidemiological simulation modelling of potential foot-and-mouth disease outbreaks in the state of Victoria, Australia examined the targeted use of limited vaccine supplies in combination with varying surveillance resources. Updated, detailed estimates of government response costs were prepared based on state level data inputs of required and available resources. Measures of outbreak spread such as duration and numbers of animals removed through depopulation of infected and vaccinated herds from the epidemiological modelling were compared to summed government response costs. This comparison illustrated the trade-offs between targeted control strategies combining vaccination-to-remove and varying surveillance capacities and their corresponding costs. For this intensive cattle and sheep producing region: (1) Targeting vaccination toward intensive production areas or toward specialized cattle operations had outbreak control and response cost advantages similar to vaccination of all species. The median duration was reduced by 27% and response costs by 11%. (2) Adding to the pool of outbreak surveillance resources available further decreased outbreak duration and outbreak response costs. The median duration was reduced by an additional 13% and response costs declined by an additional 8%. (3) Pooling of vaccine resources overcame the very early binding constraints under proportional allocation of vaccines to individual states with similar reductions in outbreak duration to those with additional surveillance resources. However, government costs rose substantially by over 40% and introduced additional risk of a negative consumer response. Increased knowledge of the outbreak situation obtained from more surveillance led to better-informed vaccination deployment decisions in the short timeframe they needed to be made.

How can age-based vaccine allocation strategies be optimized? A multi-objective optimization framework

Human life is deeply influenced by infectious diseases. A vaccine, when available, is one of the most effective ways of controlling the spread of an epidemic. However, vaccine shortage and uncertain vaccine effectiveness in the early stage of vaccine production make vaccine allocation a critical issue. To tackle this issue, we propose a multi-objective framework to optimize the vaccine allocation strategy among different age groups during an epidemic under vaccine shortage in this study. Minimizing total disease onsets and total severe cases are the two objectives of this vaccine allocation optimization problem, and the multistage feature of vaccine allocation are considered in the framework. An improved Strength Pareto Evolutionary Algorithm (SPEA2) is used to solve the optimization problem. To evaluate the two objectives under different strategies, a deterministic age-stratified extended SEIR model is developed. In the proposed framework, different combinations of vaccine effectiveness and vaccine production capacity are investigated, and it is identified that for COVID-19 the optimal strategy is highly related to vaccine-related parameters. When the vaccine effectiveness is low, allocating most of vaccines to 0-19 age group or 65+ age group is a better choice under a low production capacity, while allocating most of vaccines to 20-49 age group or 50-64 age group is a better choice under a relatively high production capacity. When the vaccine effectiveness is high, a better strategy is to allocate vaccines to 65+ age group under a low production capacity, while to allocate vaccines to 20-49 age group under a relatively high production capacity.

Choosing to Die

Two articles in the September-October 2022 issue of the Hastings Center Report discuss health-related reasons that people might have to actively bring their lives to an end. In one, Brent Kious considers the situation of a person who, because of illness, becomes a burden on loved ones. A person in such a situation might prefer to die, and Kious argues that, while there is no obligation to hasten one's death, the choice to do so could sometimes be reasonable. In a second article, Henri Wijsbek and Thomas Nys discuss a case in the Netherlands in which a woman with severe dementia was euthanized at a point when her advance euthanasia directive did not align with what she said, when asked, about death. Wijsbek and Nys defend the authority of her advance directive against a range of objections. In a third article, Henry Silverman and Patrick Odonkor, physicians at the University of Maryland Medical Center, where the first pig-to-human heart transplantation was performed in early 2022, develop recommendations for clinical trials of porcine heart transplantation. And an essay in the issue criticizes the allocation recommendations developed for Covid-19 vaccines by the U.S. Centers for Disease Control and Prevention's Advisory Committee on Immunization Practices.

Comparative performance of between-population vaccine allocation strategies with applications for emerging pandemics

Vaccine allocation decisions during emerging pandemics have proven to be challenging due to competing ethical, practical, and political considerations. Complicating decision making, policy makers need to consider vaccine allocation strategies that balance needs both within and between populations. Due to limited vaccine stockpiles, vaccine doses should be allocated in locations where their impact will be maximized. Using a susceptible-exposed-infectious-recovered (SEIR) model we examine optimal vaccine allocation decisions across two populations considering the impact of population size, underlying immunity, continuous vaccine roll-out, heterogeneous population risk structure, and differences in disease transmissibility. We find that in the context of an emerging pathogen where many epidemiologic characteristics might not be known, equal vaccine allocation between populations performs optimally in most scenarios. In the specific case considering heterogeneous population risk structure, first targeting individuals at higher risk of transmission or death due to infection leads to equal resource allocation across populations.

Effect of COVID-19 vaccine allocation strategies on vaccination refusal: A national survey

Currently, one of the most pressing public health challenges is encouraging people to get vaccinated against COVID-19. Due to limited supplies, some people have had to wait for the COVID-19 vaccine. Consumer research has suggested that people who are overlooked in initial distribution of desired goods may no longer be interested. Here, we therefore examined people's preferences for proposed vaccine allocation strategies, as well as their anticipated responses to being overlooked. After health-care workers, most participants preferred prioritizing vaccines for high-risk individuals living in group-settings (49%) or with families (29%). We also found evidence of reluctance if passed over. After random assignment to vaccine allocation strategies that would initially overlook them, 37% of participants indicated that they would refuse the vaccine. The refusal rate rose to 42% when the vaccine allocation strategy prioritized people in areas with more COVID-19 - policies that were implemented in many areas. Even among participants who did not self-identify as vaccine hesitant, 22% said they would not want to vaccine in that case. Logistic regressions confirmed that vaccine refusal would be largest if vaccine allocation strategies targeted people who live in areas with more COVID-19 infections. In sum, once people are overlooked by vaccine allocation, they may no longer want to get vaccinated, even if they were not originally vaccine hesitant. Vaccine allocation strategies that prioritize high-infection areas and high-risk individuals in group-settings may enhance these concerns.

Cost-Effectiveness of Pertussis Vaccination Schedule in Israel

Pertussis is a highly contagious bacterial disease that primarily affects infants. To optimize the pertussis vaccination schedule in Israel and evaluate the cost-effectiveness of alternative strategies that add or remove booster doses, we developed an age-structured model for pertussis transmission. Our model was calibrated using 16 years of data from laboratory-confirmed pertussis cases in Israel. Costs and quality-adjusted life years (QALYs) projected by the model within 12 years from the implementation of the considered interventions were compared with the current vaccination schedule. We found that by using the same number of vaccines administered today, the targeting of children at the age of six instead of seven would be predicted to be the optimal schedule to decrease both outpatient visits and hospitalizations. We also found that any increase in maternal vaccination coverage is likely to be cost-effective, with an incremental cost-effectiveness ratio of $77,000–$97,000 per QALY. By contrast, the contribution of the second booster dose is limited, with a probability of only 0.6 to be cost-effective at $110,000/QALY saved. Additional effort should be invested to encourage maternal vaccination against pertussis. We recommend moving the first booster to age six and prudently considering the necessity of the second booster dose.

Ethical Considerations in Vaccine Allocation

In an effort to establish a consensus position on the ethical principles and ideals that should guide vaccine allocation during the Covid-19 pandemic, various organizations, including the Centers for Disease Control (CDC) and National Academies of Science, Engineering, and Medicine, released sample allocation frameworks to help guide government entities charged with distributing vaccine doses. One area of agreement among these reports is that front line health care workers, especially those who come into regular contact with Covid-19 patients, ought to be afforded highest priority. But this convergence, though significant, raises questions concerning the ethics of vaccine distribution among those highest-priority health care workers: If a hospital has inadequate supply to vaccinate its entire workforce, which of its essential workers should it prioritize? In this paper, we begin with a general overview of ethical questions of vaccine administration before narrowing our focus to some of the most pressing theoretical and practical issues hospital officials must face in building justifiable and actionable frameworks for vaccinating their workers. We discuss and assess some potential ambitions of hospital allocation plans, concentrating especially on the goal of protecting the community from catastrophic loss of life. Finally, we consider some specific questions hospitals will encounter when developing distribution guidelines that aim to realize this aspiration.

Out of Africa: A Solidarity-Based Approach to Vaccine Allocation

This article sets forth a solidaristic approach to global distribution of vaccines against the SARS-CoV-2 virus. Our approach draws inspiration from African ethics and from the characterization of the Covid-19 crisis as a syndemic, a convergence of biosocial forces that interact with one another to produce and exacerbate clinical disease and prognosis. The first section elaborates the twin ideas of syndemic and solidarity. The second section argues that these ideas lend support to global health alliances to distribute vaccines beyond national borders. The third section introduces ethical criteria to guide global distribution, emphasizing priority to low- and middle-income countries, which have the least ability to obtain vaccines on their own. It also justifies giving priority to people at high risk of infection and high risk of severe disease and death.

Out of Africa: A Solidarity-Based Approach to Vaccine Allocation

This article sets forth a solidaristic approach to global distribution of vaccines against the SARS-CoV-2 virus. Our approach draws inspiration from African ethics and from the characterization of the Covid-19 crisis as a syndemic, a convergence of biosocial forces that interact with one another to produce and exacerbate clinical disease and prognosis. The first section elaborates the twin ideas of syndemic and solidarity. The second section argues that these ideas lend support to global health alliances to distribute vaccines beyond national borders. The third section introduces ethical criteria to guide global distribution, emphasizing priority to low- and middle-income countries, which have the least ability to obtain vaccines on their own. It also justifies giving priority to people at high risk of infection and high risk of severe disease and death.

ASHP principles for COVID-19 vaccine distribution, allocation, and mass immunization

In an effort to expedite the publication of articles related to the COVID-19 pandemic, AJHP is posting these manuscripts online as soon as possible after acceptance. Accepted manuscripts have been peer-reviewed and copyedited, but are posted online before technical formatting and author proofing. These manuscripts are not the final version of record and will be replaced with the final article (formatted per AJHP style and proofed by the authors) at a later time.

Optimal vaccine allocation during the mumps outbreak in two SIR centres

The aim of this work is to investigate the optimal vaccine sharing between two susceptible, infected, removed (SIR) centres in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q=\int _0^{t_f}I(t)\,{\textrm{d}}t$, where $I(t)$ stands for the number of infectives at time $t$. We explain the behaviour of the optimal allocation, which depends on the model parameters and the amount of vaccine available $V$.

Model-based reconstruction of an epidemic using multiple datasets: understanding influenza A/H1N1 pandemic dynamics in Israel

Intensified surveillance during the 2009 A/H1N1 influenza pandemic in Israel resulted in large virological and serological datasets, presenting a unique opportunity for investigating the pandemic dynamics. We employ a conditional likelihood approach for fitting a disease transmission model to virological and serological data, conditional on clinical data. The model is used to reconstruct the temporal pattern of the pandemic in Israel in five age-groups and evaluate the factors that shaped it. We estimate the reproductive number at the beginning of the pandemic to beR= 1.4. We find that the combined effect of varying absolute humidity conditions and school vacations (SVs) is responsible for the infection pattern, characterized by three epidemic waves. Overall attack rate is estimated at 32% (28-35%) with a large variation among the age-groups: the highest attack rates within school children and the lowest within the elderly. This pattern of infection is explained by a combination of the age-group contact structure and increasing immunity with age. We assess that SVs increased the overall attack rates by prolonging the pandemic into the winter. Vaccinating school children would have been the optimal strategy for minimizing infection rates in all age-groups.

Challenges and changes: immunization program managers share perspectives in a 2012 national survey about the US immunization system since the H1N1 pandemic response

In mid-2012 we conducted survey of immunization program managers (IPMs) for the purpose of describing relationships between immunization programs and emergency preparedness programs, IPM's perceptions of challenges encountered and changes made or planned in programmatic budgeting, vaccine allocation and pandemic plans as a result of the H1N1 vaccination campaign. Over 95% of IPMs responded (61/64) to the survey. IPMs reported that a primary budget-related challenge faced during H1N1 included staff-related restrictions that limited the ability to hire extra help or pay regular staff overtime resulting in overworked regular staff. Other budget-related challenges related to operational budget shortfalls and vaccine procurement delays. IPMs described overcoming these challenges by increasing staff where possible, using executive order or other high-level support by officials to access emergency funds and make policy changes, as well as expedite hiring and spending processes according to their pandemic influenza plan or by direction from leadership. Changes planned for response to future pandemic vaccine allocation strategies were to "tailor the strategy to the event" taking into account disease virulence, vaccine production rates and public demand, having flexible vaccine allocation strategies, clarifying priority groups for vaccine receipt to providers and the public, and having targeted clinics such as through pharmacies or schools. Changes already made to pandemic plans were improving strategies for internal and external communication, improving vaccine allocation efficiency, and planning for specific scenarios. To prepare for future pandemics, programs should ensure well-defined roles, collaborating during non-emergency situations, sustaining continuity in preparedness funding, and improved technologies.