Optimizing vaccine allocation for COVID-19 vaccines shows the potential role of single-dose vaccination

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.

Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.

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.

Vaccination and its impact on healthcare utilization in two groups of vaccinated and unvaccinated patients with COVID-19: A cross-sectional study in Iran between 2021 and 2022

Background and Aims

One of the main responsibilities of health systems impacted by the global Coronavirus disease 2019 (COVID-19) pandemic, where the first case was discovered in Wuhan, China, in December 2019, is the provision of medical services. The current study looked into the impact of vaccination on the utilization of services provided to COVID-19 patients.

Methods

This study was conducted in Iran between 2021 and 2022, utilizing a cross-sectional research design. The research team collected data on the utilization of provided services and the number of COVID-19 vaccines administered to 1000 patients in Iran through a random sampling approach. The data were analyzed with statistical methods, including the mean difference test, and multiple linear regression.

Results

Regression estimates show that after controlling for confounding variables like age, type of admission, and comorbidities, vaccination reduces the utilization of healthcare services in the general majority of services. The study's results reveal a fall in COVID-19 patients' utilization of services, specifically in patients administered two or three doses of the vaccine. However, the reduction is not statistically significant. Regression models are in contrast to univariate analysis findings that vaccination increases the mean utilization of healthcare services for COVID-19 patients in general. Comorbidities are a crucial factor in determining the utilization of diagnostic and treatment services for COVID-19 patients.

Conclusion

Full COVID-19 vaccination and other implementations, including investing in public health, cooperating globally, and vaccinating high-risk groups for future pandemics, are essential as a critical response to this pandemic as they reduce healthcare service utilization to alleviate the burden on healthcare systems and allocate resources more efficiently.

Covid19Vaxplorer: A free, online, user-friendly COVID-19 vaccine allocation comparison tool

There are many COVID-19 vaccines currently available, however, Low- and middle-income countries (LMIC) still have large proportions of their populations unvaccinated. Decision-makers must decide how to effectively allocate available vaccines (e.g. boosters or primary series vaccination, which age groups to target) but LMIC often lack the resources to undergo quantitative analyses of vaccine allocation, resulting in ad-hoc policies. We developed Covid19Vaxplorer (https://covid19vaxplorer.fredhutch.org/), a free, user-friendly online tool that simulates region-specific COVID-19 epidemics in conjunction with vaccination with the purpose of providing public health officials worldwide with a tool for vaccine allocation planning and comparison. We developed an age-structured mathematical model of SARS-CoV-2 transmission and COVID-19 vaccination. The model considers vaccination with up to three different vaccine products, primary series and boosters. We simulated partial immunity derived from waning of natural infection and vaccination. The model is embedded in an online tool, Covid19Vaxplorer that was optimized for its ease of use. By prompting users to fill information through several windows to input local parameters (e.g. cumulative and current prevalence), epidemiological parameters (e.g basic reproduction number, current social distancing interventions), vaccine parameters (e.g. vaccine efficacy, duration of immunity) and vaccine allocation (both by age groups and by vaccination status). Covid19Vaxplorer connects the user to the mathematical model and simulates, in real time, region-specific epidemics. The tool then produces key outcomes including expected numbers of deaths, hospitalizations and cases, with the possibility of simulating several scenarios of vaccine allocation at once for a side-by-side comparison. We provide two usage examples of Covid19Vaxplorer for vaccine allocation in Haiti and Afghanistan, which had as of Spring 2023, 2% and 33% of their populations vaccinated, and show that for these particular examples, using available vaccine as primary series vaccinations prevents more deaths than using them as boosters.

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.

COVID-19 vaccination strategies in settings with limited rollout capacity: a mathematical modelling case study in Sierra Leone

BACKGROUND

COVID-19 vaccine coverage in low- and middle-income countries continues to be challenging. As supplies increase, coverage is increasingly becoming determined by rollout capacity.

METHODS

We developed a deterministic compartmental model of COVID-19 transmission to explore how age-, risk-, and dose-specific vaccine prioritisation strategies can minimise severe outcomes of COVID-19 in Sierra Leone.

RESULTS

Prioritising booster doses to older adults and adults with comorbidities could reduce the incidence of severe disease by 23% and deaths by 34% compared to the use of these doses as primary doses for all adults. Providing a booster dose to pregnant women who present to antenatal care could prevent 38% of neonatal deaths associated with COVID-19 infection during pregnancy. The vaccination of children is not justified unless there is sufficient supply to not affect doses delivered to adults.

CONCLUSIONS

Our paper supports current WHO SAGE vaccine prioritisation guidelines (released January 2022). Individuals who are at the highest risk of developing severe outcomes should be prioritised, and opportunistic vaccination strategies considered in settings with limited rollout capacity.

Modeling vaccination strategies with limited early COVID-19 vaccine access in low- and middle-income countries: A case study of Thailand

Low- and middle-income countries faced significant challenges in accessing COVID-19 vaccines during the early stages of the pandemic. In this study, we utilized an age-structured modeling approach to examine the implications of various vaccination strategies, vaccine prioritization, and vaccine rollout speeds in Thailand, an upper-middle-income country experiencing vaccine shortages during the early stages of the pandemic. The model directly compares the effectiveness of several vaccination strategies, including the heterologous vaccination where CoronaVac (CV) vaccine was administered as the first dose, followed by ChAdOx1 nCoV-19 (AZ) vaccine as the second dose, under varying disease transmission dynamics. We found that the traditional AZ homologous vaccination was more effective than the CV homologous vaccination, regardless of disease transmission dynamics. However, combining CV and AZ vaccines via either parallel homologous or heterologous vaccinations was more effective than relying solely on AZ homologous vaccination. Additionally, prioritizing vaccination for the elderly aged 60 years and above was the most effective way to reduce mortality when community transmission is well-controlled. On the other hand, prioritizing workers aged 20-59 was most effective in lowering COVID-19 cases, irrespective of the transmission dynamics. Lastly, despite the vaccine prioritization strategy, rapid vaccine rollout speeds were crucial in reducing COVID-19 infections and deaths. These findings suggested that in low- and middle-income countries where early access to high-efficacy vaccines might be limited, obtaining any accessible vaccines as early as possible and using them in parallel with other higher-efficacy vaccines might be a better strategy than waiting for and relying solely on higher-efficacy vaccines.

Covid19Vaxplorer: a free, online, user-friendly COVID-19 Vaccine Allocation Comparison Tool

Background

There are many COVID-19 vaccines currently available, however, Low- and middle-income countries (LMIC) still have large proportions of their populations unvaccinated. Decision-makers must decide how to effectively allocate available vaccines (e.g. boosters or primary series vaccination, which age groups to target) but LMIC often lack the resources to undergo quantitative analyses of vaccine allocation, resulting in ad-hoc policies. We developed Covid19Vaxplorer (https://covid19vaxplorer.fredhutch.org/), a free, user-friendly online tool that simulates region-specific COVID-19 epidemics in conjunction with vaccination with the purpose of providing public health officials worldwide with a tool for vaccine allocation planning and comparison.

Methods

We developed an age-structured mathematical model of SARS-CoV-2 transmission and COVID-19 vaccination. The model considers vaccination with up to three different vaccine products, primary series and boosters. We simulated partial immunity derived from waning of natural infection and vaccination. The model is embedded in an online tool, Covid19Vaxplorer that was optimized for its ease of use. By prompting users to fill information through several windows to input local parameters (e.g. cumulative and current prevalence), epidemiological parameters (e.g basic reproduction number, current social distancing interventions), vaccine parameters (e.g. vaccine efficacy, duration of immunity) and vaccine allocation (both by age groups and by vaccination status). Covid19Vaxplorer connects the user to the mathematical model and simulates, in real time, region-specific epidemics. The tool then produces key outcomes including expected numbers of deaths, hospitalizations and cases, with the possibility of simulating several scenarios of vaccine allocation at once for a side-by-side comparison.

Results

We provide two usage examples of Covid19Vaxplorer for vaccine allocation in Haiti and Afghanistan, which had as of Spring 2023 2% and 33% of their populations vaccinated, and show that for these particular examples, using available vaccine as primary series vaccinations prevents more deaths than using them as boosters. Covid19Vaxplorer allows users in 183 regions in the world to compare several vaccination strategies simultaneously, adjusting parameters to their local epidemics, infrastructure and logistics. Covid19Vaxplorer is an online, free, user-friendly tool that facilitates evidence-based decision making for vaccine distribution.

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.

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.

Estimating the impact of COVID-19 vaccine inequities: a modeling study

Access to COVID-19 vaccines on the global scale has been drastically hindered by structural socio-economic disparities. Here, we develop a data-driven, age-stratified epidemic model to evaluate the effects of COVID-19 vaccine inequities in twenty lower middle and low income countries (LMIC) selected from all WHO regions. We investigate and quantify the potential effects of higher or earlier doses availability. In doing so, we focus on the crucial initial months of vaccine distribution and administration, exploring counterfactual scenarios where we assume the same per capita daily vaccination rate reported in selected high income countries. We estimate that more than 50% of deaths (min-max range: [54-94%]) that occurred in the analyzed countries could have been averted. We further consider scenarios where LMIC had similarly early access to vaccine doses as high income countries. Even without increasing the number of doses, we estimate an important fraction of deaths (min-max range: [6-50%]) could have been averted. In the absence of the availability of high-income countries, the model suggests that additional non-pharmaceutical interventions inducing a considerable relative decrease of transmissibility (min-max range: [15-70%]) would have been required to offset the lack of vaccines. Overall, our results quantify the negative impacts of vaccine inequities and underscore the need for intensified global efforts devoted to provide faster access to vaccine programs in low and lower-middle-income countries.

Strategic planning for the optimal distribution of COVID-19 vaccines

This work presents a multi-objective optimization strategy for fair vaccine allocation through different fairness schemes. The proposed approach considers a diverse series of parameters related to different public health data and social behaviors that influence the correct distribution of vaccines, such as corruption and crime. Simultaneously, the formulation includes prioritizing those groups with the highest risk based on the epidemiological traffic light. Furthermore, the presented strategy involves different budget constraints that allow identifying trade-off solutions through Pareto fronts. Therefore, vaccine allocations are obtained by combining fairness concepts with multi-objective optimization. The applicability of the model is illustrated using the case study of Mexico. The solution to the proposed scenarios was carried out using different justice schemes and an economic objective function. The results show the compromises between a satisfaction index and costs, which are shown through Pareto optimal solutions that allow selecting the solutions that balance the objectives. The solutions provided by the social welfare scheme suggest a greater allocation of vaccines to those states with higher epidemiological risk, which may be helpful in the first stage of vaccination. On the other hand, the Rawlsian scheme provides more balanced solutions that can be useful in situations with lower rates of infection. Finally, the Nash scheme is the one that provides the most balanced solutions, favoring to a lesser extent the areas with the highest epidemiological risk, which may be useful in the later stages of vaccination.

Understanding the impact of disease and vaccine mechanisms on the importance of optimal vaccine allocation

Vaccination is an important epidemic intervention strategy. However, it is generally unclear how the outcomes of different vaccine strategies change depending on population characteristics, vaccine mechanisms and allocation objective. In this paper we develop a conceptual mathematical model to simulate strategies for pre-epidemic vaccination. We extend the SEIR model to incorporate a range of vaccine mechanisms and disease characteristics. We then compare the outcomes of optimal and suboptimal vaccination strategies for three public health objectives (total infections, total symptomatic infections and total deaths) using numerical optimisation. Our comparison shows that the difference in outcomes between vaccinating optimally and suboptimally depends on vaccine mechanisms, disease characteristics, and objective considered. Our modelling finds vaccines that impact transmission produce better outcomes as transmission is reduced for all strategies. For vaccines that impact the likelihood of symptomatic disease or dying due to infection, the improvement in outcome as we decrease these variables is dependent on the strategy implemented. Through a principled model-based process, this work highlights the importance of designing effective vaccine allocation strategies. We conclude that efficient allocation of resources can be just as crucial to the success of a vaccination strategy as the vaccine effectiveness and/or amount of vaccines available.

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 counter-factual 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.

Evaluation of mpox vaccine dose-sparing strategies

The spring-summer 2022 mpox outbreak had over 50,000 cases globally, most of them in gay, bisexual, and other men who have sex with men (MSM). In response to vaccine shortages, several countries implemented dose-sparing vaccination strategies, stretching a full-dose vaccine vial into up to five fractional-dose vaccines. Recent studies have found mixed results regarding the effectiveness of the mpox vaccine, raising the question of the utility of dose-sparing strategies. We used an age- and risk-stratified mathematical model of an urban MSM population in the United States with ∼12% high-risk MSM to evaluate potential benefits from implementing dose-sparing vaccination strategies in which a full dose is divided into 3.5 fractional doses. We found that results strongly depend on the fractional-dose vaccine effectiveness (VE) and vaccine supply. With very limited vaccines available, enough to protect with a full dose approximately one-third of the high-risk population, dose-sparing strategies are more beneficial provided that fractional doses preserved at least 40% of full-dose effectiveness (34% absolute VE), projecting 13% (34% VE) to 70% (68% absolute VE) fewer infections than full-dose strategies. In contrast, if vaccine supply is enough to cover the majority of the high-risk population, dose-sparing strategies can be outperformed by full-dose strategies. Scenarios in which fractional dosing was 34% efficacious resulted in almost three times more infections than full dosing. Our analysis suggests that when mpox vaccine supply is limited and fractional-dose vaccination retains moderate effectiveness, there are meaningful health benefits from providing a smaller dose to a larger number of people in the high-risk population. These findings should inform the public-health response to future mpox outbreaks.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies. Finding the optimal strategy for the vaccination programs is a complex problem due to the large number of variables that affect the outcomes. The constructed mathematical model takes into account demographic risk factors such as age, comorbidity status and social contacts of the population. We perform simulations to assess the performance of more than three million vaccination strategies which vary depending on the vaccine priority of each group. This study focuses on the scenario corresponding to the early vaccination period in the USA, but can be extended to other countries. The results of this study show the importance of designing an optimal vaccination strategy in order to save human lives. The problem is extremely complex due to the large amount of factors, high dimensionality and nonlinearities. We found that for low/moderate transmission rates the optimal strategy prioritizes high transmission groups, but for high transmission rates, the optimal strategy focuses on groups with high CFRs. The results provide valuable information for the design of optimal vaccination programs. Moreover, the results help to design scientific vaccination guidelines for future pandemics.

The global COVID-19 vaccine surplus: tackling expiring stockpiles

BACKGROUND

A global surplus of coronavirus disease 2019 (COVID-19) vaccines exists as a result of difficulties in aligning the demand and supply for vaccine manufacturing and delivery. World leaders have accelerated vaccine development, approval, production and distribution as a pragmatic approach to addressing the immediate public health challenges of the first two and a half years of the pandemic.

MAIN BODY

The currently predominant, highly transmissible Omicron variant of severe acute respiratory syndrome coronavirus 2 has brought us closer to the threshold required to achieve herd immunity by greatly increasing rates of natural infection. Paradoxically, in parallel with rising vaccination levels in industrialized nations, this indirectly reduces the need for mass vaccine campaigns. Principal concerns that contribute to low vaccination rates which persist in several other countries, particularly of the Global South, are vaccine hesitancy and unequal access to vaccination. Social uncertainty fueled by fake news, misinformation, unfounded lay opinions and conspiracy theories has inevitably led to an erosion of public trust in vaccination.

CONCLUSION

To address the current mismatch between supply and demand of COVID-19 vaccines, there should be a focus on three principles: decelerating vaccine production, increasing distribution across communities, and optimizing cost-effectiveness of distribution logistics. Slowing down and switching from large-scale production to effectively 'made to order' is a feasible option, which should be commensurate with management capacity. Transparent and evidence-based data should be widely and freely disseminated to the public through multimedia channels to mitigate miscommunication and conspiracy theories. Use of soon-to-expire stockpiles should be prioritized not only to enhance booster dose rollouts in adults but to expand immunization campaigns to children (especially those aged 5-11 years), subject to national approval. Future research should ideally aim to develop vaccines that only require basic, affordable storage and maintenance procedures as opposed to sophisticated and expensive protocols.

Contact pattern, current immune barrier, and pathogen virulence determines the optimal strategy of further vaccination

Background

The current outbreak of novel coronavirus disease 2019 has caused a serious disease burden worldwide. Vaccines are an important factor to sustain the epidemic. Although with a relatively high-vaccination worldwide, the decay of vaccine efficacy and the arising of new variants lead us to the challenge of maintaining a sufficient immune barrier to protect the population.

Method

A case-contact tracking data in Hunan, China, is used to estimate the contact pattern of cases for scenarios including school, workspace, etc, rather than ordinary susceptible population. Based on the estimated vaccine coverage and efficacy, a multi-group vaccinated-exposed-presymptomatic-symptomatic-asymptomatic-removed model (VEFIAR) with 8 age groups, with each partitioned into 4 vaccination status groups is developed. The optimal dose-wise vaccinating strategy is optimized based on the currently estimated immunity barrier of coverage and efficacy, using the greedy algorithm that minimizes the cumulative cases, population size of hospitalization and fatality respectively in a certain future interval. Parameters of Delta and Omicron variants are used respectively in the optimization.

Results

The estimated contact matrices of cases showed a concentration on middle ages, and has compatible magnitudes compared to estimations from contact surveys in other studies. The VEFIAR model is numerically stable. The optimal controled vaccination strategy requires immediate vaccination on the un-vaccinated high-contact population of age 30-39 to reduce the cumulative cases, and is stable with different basic reproduction numbers ( R 0 ). As for minimizing hospitalization and fatality, the optimized strategy requires vaccination on the un-vaccinated of both aged 30-39 of high contact frequency and the vulnerable older.

Conclusion

The objective of reducing transmission requires vaccination in age groups of the highest contact frequency, with more priority for un-vaccinated than un-fully or fully vaccinated. The objective of reducing total hospitalization and fatality requires not only to reduce transmission but also to protect the vulnerable older. The priority changes by vaccination progress. For any region, if the local contact pattern is available, then with the vaccination coverage, efficacy, and disease characteristics of relative risks in heterogeneous populations, the optimal dose-wise vaccinating process will be obtained and gives hints for decision-making.

Adaptive behaviors and vaccination on curbing COVID-19 transmission: Modeling simulations in eight countries

Current persistent outbreak of COVID-19 is triggering a series of collective responses to avoid infection. To further clarify the impact mechanism of adaptive protection behavior and vaccination, we developed a new transmission model via a delay differential system, which parameterized the roles of adaptive behaviors and vaccination, and allowed to simulate the dynamic infection process among people. By validating the model with surveillance data during March 2020 and October 2021 in America, India, South Africa, Philippines, Brazil, UK, Spain and Germany, we quantified the protection effect of adaptive behaviors by different forms of activity function. The modeling results indicated that (1) the adaptive activity function can be used as a good indicator for fitting the intervention outcome, which exhibited short-term awareness in these countries, and it could reduce the total human infections by 3.68, 26.16, 15.23, 4.23, 7.26, 1.65, 5.51 and 7.07 times, compared with the reporting; (2) for complete prevention, the average proportions of people with immunity should be larger than 90%, 92%, 86%, 71%, 92%, 84%, 82% and 76% with adaptive protection behaviors, or 91%, 97%, 94%, 77%, 92%, 88%, 85% and 90% without protection behaviors; and (3) the required proportion of humans being vaccinated is a sub-linear decreasing function of vaccine efficiency, with small heterogeneity in different countries. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Transmission trends of the global COVID-19 pandemic with combined effects of adaptive behaviours and vaccination

We developed a mechanism model which allows for simulating the novel coronavirus (COVID-19) transmission dynamics with the combined effects of human adaptive behaviours and vaccination, aiming at predicting the end time of COVID-19 infection in global scale. Based on the surveillance information (reported cases and vaccination data) between 22 January 2020 and 18 July 2022, we validated the model by Markov Chain Monte Carlo (MCMC) fitting method. We found that (1) if without adaptive behaviours, the epidemic could sweep the world in 2022 and 2023, causing 3.098 billion of human infections, which is 5.39 times of current number; (2) 645 million people could be avoided from infection due to vaccination; and (3) in current scenarios of protective behaviours and vaccination, infection cases would increase slowly, levelling off around 2023, and it would end completely in June 2025, causing 1.024 billion infections, with 12.5 million death. Our findings suggest that vaccination and the collective protection behaviour remain the key determinants against the global process of COVID-19 transmission.

Optimal spatial evaluation of a pro rata vaccine distribution rule for COVID-19

The COVID-19 Vaccines Global Access (COVAX) is a World Health Organization (WHO) initiative that aims for an equitable access of COVID-19 vaccines. Despite potential heterogeneous infection levels across a country, countries receiving allotments of vaccines may follow WHO's allocation guidelines and distribute vaccines based on a jurisdictions' relative population size. Utilizing economic-epidemiological modeling, we benchmark the performance of this pro rata allocation rule by comparing it to an optimal one that minimizes the economic damages and expenditures over time, including a penalty representing the social costs of deviating from the pro rata strategy. The pro rata rule performs better when the duration of naturally- and vaccine-acquired immunity is short, when there is population mixing, when the supply of vaccine is high, and when there is minimal heterogeneity in demographics. Despite behavioral and epidemiological uncertainty diminishing the performance of the optimal allocation, it generally outperforms the pro rata vaccine distribution rule.

Identification of an Optimal COVID-19 Booster Allocation Strategy to Minimize Hospital Bed-Days with a Fixed Healthcare Budget

Healthcare decision-makers face difficult decisions regarding COVID-19 booster selection given limited budgets and the need to maximize healthcare gain. A constrained optimization (CO) model was developed to identify booster allocation strategies that minimize bed-days by varying the proportion of the eligible population receiving different boosters, stratified by age, and given limited healthcare expenditure. Three booster options were included: B₁, costing US $1 per dose, B₂, costing US $2, and no booster (NB), costing US $0. B₁ and B₂ were assumed to be 55%/75% effective against mild/moderate COVID-19, respectively, and 90% effective against severe/critical COVID-19. Healthcare expenditure was limited to US$2.10 per person; the minimum expected expense using B_1, B_2, or NB for all. Brazil was the base-case country. The model demonstrated that B₁ for those aged <70 years and B₂ for those ≥70 years were optimal for minimizing bed-days. Compared with NB, bed-days were reduced by 75%, hospital admissions by 68%, and intensive care unit admissions by 90%. Total costs were reduced by 60% with medical resource use reduced by 81%. This illustrates that the CO model can be used by healthcare decision-makers to implement vaccine booster allocation strategies that provide the best healthcare outcomes in a broad range of contexts.

Protection against SARS-CoV-2 BA.4 and BA.5 subvariants via vaccination and natural infection: A modeling study

With continuing emergence of new SARS-CoV-2 variants, understanding the proportion of the population protected against infection is crucial for public health risk assessment and decision-making and so that the general public can take preventive measures. We aimed to estimate the protection against symptomatic illness caused by SARS-CoV-2 Omicron variants BA.4 and BA.5 elicited by vaccination against and natural infection with other SARS-CoV-2 Omicron subvariants. We used a logistic model to define the protection rate against symptomatic infection caused by BA.1 and BA.2 as a function of neutralizing antibody titer values. Applying the quantified relationships to BA.4 and BA.5 using two different methods, the estimated protection rate against BA.4 and BA.5 was 11.3% (95% confidence interval [CI]: 0.01-25.4) (method 1) and 12.9% (95% CI: 8.8-18.0) (method 2) at 6 months after a second dose of BNT162b2 vaccine, 44.3% (95% CI: 20.0-59.3) (method 1) and 47.3% (95% CI: 34.1-60.6) (method 2) at 2 weeks after a third BNT162b2 dose, and 52.3% (95% CI: 25.1-69.2) (method 1) and 54.9% (95% CI: 37.6-71.4) (method 2) during the convalescent phase after infection with BA.1 and BA.2, respectively. Our study indicates that the protection rate against BA.4 and BA.5 are significantly lower compared with those against previous variants and may lead to substantial morbidity, and overall estimates were consistent with empirical reports. Our simple yet practical models enable prompt assessment of public health impacts posed by new SARS-CoV-2 variants using small sample-size neutralization titer data to support public health decisions in urgent situations.

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.

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.

Spatial Optimization to Improve COVID-19 Vaccine Allocation

Early distribution of COVID-19 vaccines was largely driven by population size and did not account for COVID-19 prevalence nor location characteristics. In this study, we applied an optimization framework to identify distribution strategies that would have lowered COVID-19 related morbidity and mortality. During the first half of 2021 in the state of Missouri, optimized vaccine allocation would have decreased case incidence by 8% with 5926 fewer COVID-19 cases, 106 fewer deaths, and 4.5 million dollars in healthcare cost saved. As COVID-19 variants continue to be identified, and the likelihood of future pandemics remains high, application of resource optimization should be a priority for policy makers.

Ethnic homophily affects vaccine prioritization strategies

People are more likely to interact with other people of their ethnicity-a phenomenon known as ethnic homophily. In the United States, people of color are known to hold proportionately more high-contact jobs and are thus more at risk of virus infection. At the same time, these ethnic groups are on average younger than the rest of the population. This gives rise to interesting disease dynamics and non-trivial trade-offs that should be taken into consideration when developing prioritization strategies for future mass vaccine roll-outs. Here, we study the spread of COVID-19 through the US population, stratified by age, ethnicity, and occupation, using a detailed, previously-developed compartmental disease model. Based on historic data from the US mass COVID-19 vaccine roll-out that began in December 2020, we show, (i) how ethnic homophily affects the choice of optimal vaccine allocation strategy, (ii) that, notwithstanding potential ethical concerns, differentiating by ethnicity in these strategies can improve outcomes (e.g., fewer deaths), and (iii) that the most likely social context in the United States is very different from the standard assumptions made by models which do not account for ethnicity and this difference affects which allocation strategy is optimal. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Coupling the Within-Host Process and Between-Host Transmission of COVID-19 Suggests Vaccination and School Closures are Critical

Most models of COVID-19 are implemented at a single micro or macro scale, ignoring the interplay between immune response, viral dynamics, individual infectiousness and epidemiological contact networks. Here we develop a data-driven model linking the within-host viral dynamics to the between-host transmission dynamics on a multilayer contact network to investigate the potential factors driving transmission dynamics and to inform how school closures and antiviral treatment can influence the epidemic. Using multi-source data, we initially determine the viral dynamics and estimate the relationship between viral load and infectiousness. Then, we embed the viral dynamics model into a four-layer contact network and formulate an agent-based model to simulate between-host transmission. The results illustrate that the heterogeneity of immune response between children and adults and between vaccinated and unvaccinated infections can produce different transmission patterns. We find that school closures play a significant effect on mitigating the pandemic as more adults get vaccinated and the virus mutates. If enough infected individuals are diagnosed by testing before symptom onset and then treated quickly, the transmission can be effectively curbed. Our multiscale model reveals the critical role played by younger individuals and antiviral treatment with testing in controlling the epidemic.

Effective screening strategies for safe opening of universities under Omicron and Delta variants of COVID-19

As new COVID-19 variants emerge, and disease and population characteristics change, screening strategies may also need to change. We develop a decision-making model that can assist a college to determine an optimal screening strategy based on their characteristics and resources, considering COVID-19 infections/hospitalizations/deaths; peak daily hospitalizations; and the tests required. We also use this tool to generate screening guidelines for the safe opening of college campuses. Our compartmental model simulates disease spread on a hypothetical college campus under co-circulating variants with different disease dynamics, considering: (i) the heterogeneity in disease transmission and outcomes for faculty/staff and students based on vaccination status and level of natural immunity; and (ii) variant- and dose-dependent vaccine efficacy. Using the Spring 2022 academic semester as a case study, we study routine screening strategies, and find that screening the faculty/staff less frequently than the students, and/or the boosted and vaccinated less frequently than the unvaccinated, may avert a higher number of infections per test, compared to universal screening of the entire population at a common frequency. We also discuss key policy issues, including the need to revisit the mitigation objective over time, effective strategies that are informed by booster coverage, and if and when screening alone can compensate for low booster coverage.

A comparison of node vaccination strategies to halt SIR epidemic spreading in real-world complex networks

We compared seven node vaccination strategies in twelve real-world complex networks. The node vaccination strategies are modeled as node removal on networks. We performed node vaccination strategies both removing nodes according to the initial network structure, i.e., non-adaptive approach, and performing partial node rank recalculation after node removal, i.e., semi-adaptive approach. To quantify the efficacy of each vaccination strategy, we used three epidemic spread indicators: the size of the largest connected component, the total number of infected at the end of the epidemic, and the maximum number of simultaneously infected individuals. We show that the best vaccination strategies in the non-adaptive and semi-adaptive approaches are different and that the best strategy also depends on the number of available vaccines. Furthermore, a partial recalculation of the node centrality increases the efficacy of the vaccination strategies by up to 80%.

A COVID-19 model incorporating variants, vaccination, waning immunity, and population behavior

Vaccines for COVID-19 have allowed countries to combat the spread of the disease. However, new variants have resulted in significant spikes in cases and raised severe health and economic concerns. We present a COVID-19 model to predict coupled effects of vaccine multiple-dose roll-out strategies, vaccine efficacy, waning immunity, population level of caution, sense of safety, under-reporting of cases, and highly prevalent variants such as the Delta (B.1.617.2) and Omicron (B.1.1.529). The modeling framework can incorporate new variants as they emerge to give critical insights into the new cases and guide public policy decision-making concerning vaccine roll-outs and reopening strategies. The model is shown to recreate the history of COVID-19 for five countries (Germany, India, Japan, South Africa, and the United States). Parameters for crucial aspects of the pandemic, such as population behavior, new variants, vaccination, and waning immunity, can be adjusted to predict pandemic scenarios. The model was used to conduct trend analysis to simulate pandemic dynamics taking into account the societal level of caution, societal sense of safety, and the proportions of individuals vaccinated with first, second, and booster doses. We used the results of serological testing studies to estimate the actual number of cases across countries. The model allows quantification of otherwise hard to quantify aspects such as the infectious power of variants and the effectiveness of government mandates and population behavior. Some example cases are presented by investigating the competitive nature of COVID variants and the effect of different vaccine distribution strategies between immunity groups.

Estimating the impact of COVID-19 vaccine allocation inequities: a modeling study

Access to COVID-19 vaccines on the global scale has been drastically impacted by structural socio-economic inequities. Here, we develop a data-driven, age-stratified epidemic model to evaluate the effects of COVID-19 vaccine inequities in twenty lower middle and low income countries (LMIC) sampled from all WHO regions. We focus on the first critical months of vaccine distribution and administration, exploring counterfactual scenarios where we assume the same per capita daily vaccination rate reported in selected high income countries. We estimate that, in this high vaccine availability scenario, more than 50% of deaths (min-max range: [56% - 99%]) that occurred in the analyzed countries could have been averted. We further consider a scenario where LMIC had similarly early access to vaccine doses as high income countries; even without increasing the number of doses, we estimate an important fraction of deaths (min-max range: [7% - 73%]) could have been averted. In the absence of equitable allocation, the model suggests that considerable additional non-pharmaceutical interventions would have been required to offset the lack of vaccines (min-max range: [15% - 75%]). Overall, our results quantify the negative impacts of vaccines inequities and call for amplified global efforts to provide better access to vaccine programs in low and lower middle income countries.

Antigenic escape is accelerated by the presence of immunocompromised hosts

The repeated emergence of SARS-CoV-2 escape mutants from host immunity has obstructed the containment of the current pandemic and poses a serious threat to humanity. Prolonged infection in immunocompromised patients has received increasing attention as a driver of immune escape, and accumulating evidence suggests that viral genomic diversity and emergence of immune-escape mutants are promoted in immunocompromised patients. However, because immunocompromised patients comprise a small proportion of the host population, whether they have a significant impact on antigenic evolution at the population level is unknown. We consider an evolutionary epidemiological model that combines antigenic evolution and epidemiological dynamics. Applying this model to a heterogeneous host population, we study the impact of immunocompromised hosts on the evolutionary dynamics of pathogen antigenic escape from host immunity. We derived analytical formulae of the speed of antigenic evolution in heterogeneous host populations and found that even a small number of immunocompromised hosts in the population significantly accelerates antigenic evolution. Our results demonstrate that immunocompromised hosts play a key role in viral adaptation at the population level and emphasize the importance of critical care and surveillance of immunocompromised hosts.

Invited Commentary: Mechanistic and Biologically Based Models in Epidemiology-A Powerful Underutilized Tool

Mechanistic and biologically based mathematical models of chronic and behavioral disease processes aim to capture the main mechanistic or biological features of the disease development and to connect these with epidemiologic outcomes. These approaches have a long history in epidemiologic research and are complementary to traditional epidemiologic or statistical approaches to investigate the role of risk factor exposures on disease risk. Simonetto et al. (Am J Epidemiol. 2022;191(10):1766-1775) present a mechanistic, process-oriented model to investigate the role of smoking, hypertension, and dyslipidemia in the development of atherosclerotic lesions and their progression to myocardial infarction. Their approach builds on and brings to cardiovascular disease the ideas and perspectives of earlier mechanistic and biologically based models for the epidemiology of cancer and other chronic diseases, providing important insights into the mechanisms and epidemiology of smoking related myocardial infarction. We argue that although mechanistic modeling approaches have demonstrated their value and place in epidemiology, they are highly underutilized. We call for efforts to grow mechanistic and biologically based modeling research, expertise, and awareness in epidemiology, including the development of training and collaboration opportunities to attract more students and researchers from science, technology, engineering, and medical field into the epidemiology field.

Non-pharmaceutical interventions and their relevance in the COVID-19 vaccine rollout in Saudi Arabia and Arab Gulf countries

In the early stages of the pandemic, Saudi Arabia and other countries in the Arab Gulf region relied on non-pharmaceutical therapies to limit the effect of the pandemic, much like other nations across the world. In comparison to other nations in the area or globally, these interventions were successful at lowering the healthcare burden. This was accomplished via the deterioration of the economy, education, and a variety of other societal activities. By the end of 2020, the promise of effective vaccinations against SARS-CoV-2 have been realized, and vaccination programs have begun in developed countries, followed by the rest of the world. Despite this, there is still a long way to go in the fight against the disease. In order to explore disease transmission, vaccine rollout and prioritisation, as well as behavioural dynamics, we relied on an age-structured compartmental model. We examine how individual and social behaviour changes in response to the initiation of vaccination campaigns and the relaxation of non-pharmacological treatments. Overall, vaccination remains the most effective method of containing the disease and resuming normal life. Additionally, we evaluate several vaccination prioritisation schemes based on age group, behavioural responses, vaccine effectiveness, and vaccination rollout speed. We applied our model to four Arab Gulf nations (Saudi Arabia, Bahrain, the United Arab Emirates, and Oman), which were chosen for their low mortality rate compared to other countries in the region or worldwide, as well as their demographic and economic settings. We fitted the model using actual pandemic data in these countries. Our results suggest that vaccinations focused on the elderly and rapid vaccine distribution are critical for reducing disease resurgence. Our result also reinforces the cautious note that early relaxation of safety measures may compromise the vaccine's short-term advantages.

Effects of infection fatality ratio and social contact matrices on vaccine prioritization strategies

Effective strategies of vaccine prioritization are essential to mitigate the impacts of severe infectious diseases. We investigate the role of infection fatality ratio (IFR) and social contact matrices on vaccination prioritization using a compartmental epidemic model fueled by real-world data of different diseases and countries. Our study confirms that massive and early vaccination is extremely effective to reduce the disease fatality if the contagion is mitigated, but the effectiveness is increasingly reduced as vaccination beginning delays in an uncontrolled epidemiological scenario. The optimal and least effective prioritization strategies depend non-linearly on epidemiological variables. Regions of the epidemiological parameter space, in which prioritizing the most vulnerable population is more effective than the most contagious individuals, depend strongly on the IFR age profile being, for example, substantially broader for COVID-19 in comparison with seasonal influenza. Demographics and social contact matrices deform the phase diagrams but do not alter their qualitative shapes.

The heterogeneous mixing model of COVID-19 with interventions

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number Rc of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p3 plays a key role in Rc. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Control of COVID-19 Outbreaks under Stochastic Community Dynamics, Bimodality, or Limited Vaccination

Reaching population immunity against COVID-19 is proving difficult even in countries with high vaccination levels. Thus, it is critical to identify limits of control and effective measures against future outbreaks. The effects of nonpharmaceutical interventions (NPIs) and vaccination strategies are analyzed with a detailed community-specific agent-based model (ABM). The authors demonstrate that the threshold for population immunity is not a unique number, but depends on the vaccination strategy. Prioritizing highly interactive people diminishes the risk for an infection wave, while prioritizing the elderly minimizes fatalities when vaccinations are low. Control over COVID-19 outbreaks requires adaptive combination of NPIs and targeted vaccination, exemplified for Germany for January-September 2021. Bimodality emerges from the heterogeneity and stochasticity of community-specific human-human interactions and infection networks, which can render the effects of limited NPIs uncertain. The authors' simulation platform can process and analyze dynamic COVID-19 epidemiological situations in diverse communities worldwide to predict pathways to population immunity even with limited vaccination.

Model-Based Evaluation of Transmissibility and Intervention Measures for a COVID-19 Outbreak in Xiamen City, China

Background

In September 2021, there was an outbreak of coronavirus disease 2019 (COVID-19) in Xiamen, China. Various non-pharmacological interventions (NPIs) and pharmacological interventions (PIs) have been implemented to prevent and control the spread of the disease. This study aimed to evaluate the effectiveness of various interventions and to identify priorities for the implementation of prevention and control measures.

Methods

The data of patients with COVID-19 were collected from 8 to 30 September 2021. A Susceptible-Exposed-Infectious-Recovered (SEIR) dynamics model was developed to fit the data and simulate the effectiveness of interventions (medical treatment, isolation, social distancing, masking, and vaccination) under different scenarios. The effective reproductive number (R_eff) was used to assess the transmissibility and transmission risk.

Results

A total of 236 cases of COVID-19 were reported in Xiamen. The epidemic curve was divided into three phases (R_eff = 6.8, 1.5, and 0). Notably, the cumulative number of cases was reduced by 99.67% due to the preventive and control measures implemented by the local government. In the effective containment stage, the number of cases could be reduced to 115 by intensifying the implementation of interventions. The total number of cases (TN) could be reduced by 29.66–95.34% when patients voluntarily visit fever clinics. When only two or three of these measures are implemented, the simulated TN may be greater than the actual number. As four measures were taken simultaneously, the TN may be <100, which is 57.63% less than the actual number. The simultaneous implementation of five interventions could rapidly control the transmission and reduce the number of cases to fewer than 25.

Conclusion

With the joint efforts of the government and the public, the outbreak was controlled quickly and effectively. Authorities could promptly cut the transmission chain and control the spread of the disease when patients with fever voluntarily went to the hospital. The ultimate effect of controlling the outbreak through only one intervention was not obvious. The combined community control and mask wearing, along with other interventions, could lead to rapid control of the outbreak and ultimately lower the total number of cases. More importantly, this would mitigate the impact of the outbreak on society and socioeconomics.

Modeling the Impact of Vaccination on COVID-19 and Its Delta and Omicron Variants

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example and calculate conditions of herd immunity for multiple vaccines and disease variants. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced if vaccination were available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral, Delta, and Omicron strains. Numerical results demonstrate that the static herd immunity threshold corresponds to one percent of the population requiring hospitalization or isolation at some point in time. We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered while still maintaining the same proportion of cumulative hospitalized/isolated individuals.

Optimizing Spatio-Temporal Allocation of the COVID-19 Vaccine Under Different Epidemiological Landscapes

An efficient and safe vaccine is expected to allow people to return to normal life as soon as possible. However, vaccines for new diseases are likely to be in short supply during the initial deployment due to narrow production capacity and logistics. There is an urgent need to optimize the allocation of limited vaccines to improve the population effectiveness of vaccination. Existing studies mostly address a single epidemiological landscape. The robustness of the effectiveness of other proposed strategies is difficult to guarantee under other landscapes. In this study, a novel vaccination allocation model based on spatio-temporal heterogeneity of epidemiological landscapes is proposed. This model was combined with optimization algorithms to determine the near-optimal spatio-temporal allocation for vaccines with different effectiveness and coverage. We fully simulated the epidemiological landscapes during vaccination, and then minimized objective functions independently under various epidemiological landscapes and degrees of viral transmission. We find that if all subregions are in the middle or late stages of the pandemic, the difference between the effectiveness of the near-optimal and pro-rata strategies is very small in most cases. In contrast, under other epidemiological landscapes, when minimizing deaths, the optimizer tends to allocate the remaining doses to sub-regions with relatively higher risk and expected coverage after covering the elderly. While to minimize symptomatic infections, allocating vaccines first to the higher-risk sub-regions is near-optimal. This means that the pro-rata allocation is a good option when the subregions are all in the middle to late stages of the pandemic. Moreover, we suggest that if all subregions are in the period of rapid virus transmission, vaccines should be administered to older adults in all subregions simultaneously, while when the epidemiological dynamics of the subregions are significantly different, priority can be given to older adults in subregions that are still in the early stages of the pandemic. After covering the elderly in the region, high-risk sub-regions can be prioritized.

Intervention strategies for epidemic spreading on bipartite metapopulation networks

Intervention strategies are of great significance for controlling large-scale outbreaks of epidemics. Since the spread of epidemic depends largely on the movement of individuals and the heterogeneity of the network structure, understanding potential factors that affect the epidemic is fundamental for the design of reasonable intervention strategies to suppress the epidemic. So far, most of previous studies mainly consider intervention strategies on the network composed of a single type of locations, while ignoring the movement behavior of individuals to and from locations that are composed of different types, i.e., residences and public places, which often presents heterogeneous structure. In addition, the transmission rate in public places with different population flows is heterogeneous. Inspired by the above observation, we build a bipartite metapopulation network model and propose intervention strategies based on the importance of public places. With the Markovian Chain approach, we derive the epidemic threshold under intervention strategies. Experimental results show that, compared with the uniform intervention to residences or public places, nonuniform intervention to public places is more effective for suppressing the epidemic with an increased epidemic threshold. Specifically, interventions to public places with large degree can further suppress the epidemic. Our study opens a new path for understanding the spatial epidemic spread and provides guidance for the design of intervention strategies for epidemics in the future.

Dosing interval strategies for two-dose COVID-19 vaccination in 13 middle-income countries of Europe: Health impact modelling and benefit-risk analysis

Background

In settings where the COVID-19 vaccine supply is constrained, extending the intervals between the first and second doses of the COVID-19 vaccine may allow more people receive their first doses earlier. Our aim is to estimate the health impact of COVID-19 vaccination alongside benefit-risk assessment of different dosing intervals in 13 middle-income countries (MICs) of Europe.

Methods

We fitted a dynamic transmission model to country-level daily reported COVID-19 mortality in 13 MICs in Europe (Albania, Armenia, Azerbaijan, Belarus, Bosnia and Herzegovina, Bulgaria, Georgia, Republic of Moldova, Russian Federation, Serbia, North Macedonia, Turkey, and Ukraine). A vaccine product with characteristics similar to those of the Oxford/AstraZeneca COVID-19 (AZD1222) vaccine was used in the base case scenario and was complemented by sensitivity analyses around efficacies similar to other COVID-19 vaccines. Both fixed dosing intervals at 4, 8, 12, 16, and 20 weeks and dose-specific intervals that prioritise specific doses for certain age groups were tested. Optimal intervals minimise COVID-19 mortality between March 2021 and December 2022. We incorporated the emergence of variants of concern (VOCs) into the model and conducted a benefit-risk assessment to quantify the tradeoff between health benefits versus adverse events following immunisation.

Findings

In all countries modelled, optimal strategies are those that prioritise the first doses among older adults (60+ years) or adults (20+ years), which lead to dosing intervals longer than six months. In comparison, a four-week fixed dosing interval may incur 10.1% [range: 4.3% - 19.0%; n = 13 (countries)] more deaths. The rapid waning of the immunity induced by the first dose (i.e. with means ranging 60-120 days as opposed to 360 days in the base case) resulted in shorter optimal dosing intervals of 8-20 weeks. Benefit-risk ratios were the highest for fixed dosing intervals of 8-12 weeks.

Interpretation

We infer that longer dosing intervals of over six months could reduce COVID-19 mortality in MICs of Europe. Certain parameters, such as rapid waning of first-dose induced immunity and increased immune escape through the emergence of VOCs, could significantly shorten the optimal dosing intervals.

Funding

World Health Organization.

Vaccine and inclusion

In majoritarian democracies, popular policies may not be inclusive, and inclusive policies may not be popular. This dilemma raises the crucial question of when it is possible to design a policy that is both inclusive and popular. We address this question in the context of vaccine allocation in a polarized economy facing a pandemic. In such an economy, individuals are organized around distinct networks and groups and have in-group preferences. We provide a complete characterization of the set of inclusive and popular vaccine allocations. The findings imply that the number of vaccine doses necessary to generate an inclusive and popular vaccine allocation is greater than the one necessary to obtain an allocation that is only popular. The analysis further reveals that it is always possible to design the decision-making rule of the economy to implement an inclusive and popular vaccine allocation. Under such a rule, the composition of any group endowed with the veto power should necessarily reflect the diversity of the society.

Injectable Slow-Release Hydrogel Formulation of a Plant Virus-Based COVID-19 Vaccine Candidate

Cowpea mosaic virus (CPMV) is a potent immunogenic adjuvant and epitope display platform for the development of vaccines against cancers and infectious diseases, including coronavirus disease 2019. However, the proteinaceous CPMV nanoparticles are rapidly degraded in vivo. Multiple doses are therefore required to ensure long-lasting immunity, which is not ideal for global mass vaccination campaigns. Therefore, we formulated CPMV nanoparticles in injectable hydrogels to achieve slow particle release and prolonged immunostimulation. Liquid formulations were prepared from chitosan and glycerophosphate (GP) before homogenization with CPMV particles at room temperature. The formulations containing high-molecular-weight chitosan and 0-4.5 mg mL-1 CPMV gelled rapidly at 37 °C (5-8 min) and slowly released cyanine 5-CPMV particles in vitro and in vivo. Importantly, when a hydrogel containing CPMV displaying severe acute respiratory syndrome coronavirus 2 spike protein epitope 826 (amino acid 809-826) was administered to mice as a single subcutaneous injection, it elicited an antibody response that was sustained over 20 weeks, with an associated shift from Th1 to Th2 bias. Antibody titers were improved at later time points (weeks 16 and 20) comparing the hydrogel versus soluble vaccine candidates; furthermore, the soluble vaccine candidates retained Th1 bias. We conclude that CPMV nanoparticles can be formulated effectively in chitosan/GP hydrogels and are released as intact particles for several months with conserved immunotherapeutic efficacy. The injectable hydrogel containing epitope-labeled CPMV offers a promising single-dose vaccine platform for the prevention of future pandemics as well as a strategy to develop long-lasting plant virus-based nanomedicines.

Comparing the longer-term effectiveness of a single dose of the Pfizer-BioNTech and Oxford-AstraZeneca COVID-19 vaccines across the age spectrum

BACKGROUND

A single dose strategy may be adequate to confer population level immunity and protection against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, especially in low- and middle-income countries where vaccine supply remains limited. We compared the effectiveness of a single dose strategy of the Oxford-AstraZeneca or Pfizer-BioNTech vaccines against SARS-CoV-2 infection across all age groups and over an extended follow-up period.

METHODS

Individuals vaccinated in North-West London, UK, with either the first dose of the Oxford-AstraZeneca or Pfizer-BioNTech vaccines between January 12, 2021 and March 09, 2021, were matched to each other by demographic and clinical characteristics. Each vaccinated individual was additionally matched to an unvaccinated control. Study outcomes included SARS-CoV-2 infection of any severity, COVID-19 hospitalisation, COVID-19 death, and all-cause mortality.

FINDINGS

Amongst matched individuals, 63,608 were in each of the vaccine groups and 127,216 were unvaccinated. Between 14 and 84 days of follow-up after matching, there were 534 SARS-CoV-2 infections, 65 COVID-19 hospitalisations, and 190 deaths, of which 29 were categorized as due to COVID-19. The incidence rate ratio (IRR) for SARS-CoV-2 infection was 0.85 (95% confidence interval [CI], 0.69 to 1.05) for Oxford-Astra-Zeneca, and 0.69 (0.55 to 0.86) for Pfizer-BioNTech. The IRR for both vaccines was the same at 0.25 (0.09 to 0.55) and 0.14 (0.02 to 0.58) for reducing COVID-19 hospitalization and COVID-19 mortality, respectively. The IRR for all-cause mortality was 0.25 (0.15 to 0.39) and 0.18 (0.10 to 0.30) for the Oxford-Astra-Zeneca and Pfizer-BioNTech vaccines, respectively. Age was an effect modifier of the association between vaccination and SARS-CoV-2 infection of any severity; lower hazard ratios for increasing age.

INTERPRETATION

A single dose strategy, for both vaccines, was effective at reducing COVID-19 mortality and hospitalization rates. The magnitude of vaccine effectiveness was comparatively lower for SARS-CoV-2 infection, although this was variable across the age range, with higher effectiveness seen with older adults. Our results have important implications for health system planning -especially in low resource settings where vaccine supply remains constrained.

Adaptive and optimized COVID-19 vaccination strategies across geographical regions and age groups

We evaluate the efficiency of various heuristic strategies for allocating vaccines against COVID-19 and compare them to strategies found using optimal control theory. Our approach is based on a mathematical model which tracks the spread of disease among different age groups and across different geographical regions, and we introduce a method to combine age-specific contact data to geographical movement data. As a case study, we model the epidemic in the population of mainland Finland utilizing mobility data from a major telecom operator. Our approach allows to determine which geographical regions and age groups should be targeted first in order to minimize the number of deaths. In the scenarios that we test, we find that distributing vaccines demographically and in an age-descending order is not optimal for minimizing deaths and the burden of disease. Instead, more lives could be saved by using strategies which emphasize high-incidence regions and distribute vaccines in parallel to multiple age groups. The level of emphasis that high-incidence regions should be given depends on the overall transmission rate in the population. This observation highlights the importance of updating the vaccination strategy when the effective reproduction number changes due to the general contact patterns changing and new virus variants entering.