Immunity Threshold Research Articles

Emerging SARS-CoV-2 Variants, Inequitable Vaccine Distribution, and Implications for COVID-19 Control in Sub-Saharan Africa

Since the onset of the COVID-19 pandemic, four SARS-CoV-2 variants of concern have emerged, which have shifted the clinical and epidemiological characteristics of the disease. Of concern is the impact of the emerging variants on COVID-19 vaccination programmes, with vaccination perceived as a key global pandemic control strategy. Variants of concern can reduce the effectiveness of the currently available vaccines, shift herd immunity thresholds, and promote wider vaccine inequities as richer countries hoard vaccines for booster shots for their populations without accounting for the needs of the underdeveloped countries of sub-Saharan Africa. Currently, Africa lags far behind the rest of the world, with most sub-Saharan Africa countries still to reach 50% vaccination of their eligible populations against global herd immunity thresholds of 70–90%. As long as the vaccination gap between sub-Saharan Africa and the rest of the world persists, SARS-CoV-2 will most likely persist as a significant global health threat, with continued emergence of variants of concern. Therefore, strategies to ensure wider reach of different types of vaccines on the African continent are urgently required alongside fighting vaccine hesitancy and logistical barriers to access for the marginalized populations. Sub-Saharan Africa must look for opportunities to manufacture vaccines on the continent and enhance genomic sequencing capacity as key pandemic-control strategies.

Vaccination with partial transmission and social distancing on contact networks

We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so, we extend the cavity method to study networks where nodes have heterogeneous transmissibility. We find that vaccination with partial transmission still provides herd immunity and show how the herd immunity threshold depends upon the assortativity between nodes of different transmissibility. In addition, we study the impact of social distancing via bond percolation and show that percolation targeting links between nodes of high transmissibility can reduce the risk of an epidemic greater than targeting links between nodes of high degree. Finally, we extend recent methods to compute the distributional equations of risk in populations with heterogeneous transmissibility and show how targeted social distancing measures may reduce overall risk greater than untargeted vaccination campaigns, by comparing the effect of random and targeted strategies of node and link deletion on the risk distribution.

SARS-CoV-2 vaccine research and immunization strategies for improved control of the COVID-19 pandemic.

The record speed at which Chinese scientists identified severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) and shared its genomic sequence with the world, has greatly facilitated the development of coronavirus disease (COVID-19) diagnostics, drugs, and vaccines. It is unprecedented in pandemic control history to develop a dozen successful vaccines in the first year and to immunize over half of the global population in the second year, due to the efforts of the scientific community, biopharmaceutical industry, and regulatory agencies worldwide. The challenges are both great and multidimensional due to the rapid emergence of virus variants and waning of vaccine immunity. Vaccination strategies need to adapt to these challenges to keep population immunity above the herd immunity threshold, by increasing vaccine coverage, especially for older adults and young people, and providing timely booster doses with homologous or heterologous vaccine boosts. Further research should be undertaken to develop more effective vaccines against SARS-CoV-2 variants and to understand the best prime-boost vaccine combinations and immunization strategies to provide sufficient and sustainable immune protection against COVID-19.

Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold

Individual variation in susceptibility and exposure is subject to selection by natural infection, accelerating the acquisition of immunity, and reducing herd immunity thresholds and epidemic final sizes. This is a manifestation of a wider population phenomenon known as “frailty variation”. Despite theoretical understanding, public health policies continue to be guided by mathematical models that leave out considerable variation and as a result inflate projected disease burdens and overestimate the impact of interventions. Here we focus on trajectories of the coronavirus disease (COVID-19) pandemic in England and Scotland until November 2021. We fit models to series of daily deaths and infer relevant epidemiological parameters, including coefficients of variation and effects of non-pharmaceutical interventions which we find in agreement with independent empirical estimates based on contact surveys. Our estimates are robust to whether the analysed data series encompass one or two pandemic waves and enable projections compatible with subsequent dynamics. We conclude that vaccination programmes may have contributed modestly to the acquisition of herd immunity in populations with high levels of pre-existing naturally acquired immunity, while being crucial to protect vulnerable individuals from severe outcomes as the virus becomes endemic.

A COVID-19 vaccination model for Aotearoa New Zealand

We develop a mathematical model to estimate the effect of New Zealand’s vaccine rollout on the potential spread and health impacts of COVID-19. The main purpose of this study is to provide a basis for policy advice on border restrictions and control measures in response to outbreaks that may occur during the vaccination roll-out. The model can be used to estimate the theoretical population immunity threshold, which represents a point in the vaccine rollout at which border restrictions and other controls could be removed and only small, occasional outbreaks would take place. We find that, with a basic reproduction number of 6, approximately representing the Delta variant of SARS-CoV-2, and under baseline vaccine effectiveness assumptions, reaching the population immunity threshold would require close to 100% of the total population to be vaccinated. Since this coverage is not likely to be achievable in practice, relaxing controls completely would risk serious health impacts. However, the higher vaccine coverage is, the more collective protection the population has against adverse health outcomes from COVID-19, and the easier it will become to control outbreaks. There remains considerable uncertainty in model outputs, in part because of the potential for the evolution of new variants. If new variants arise that are more transmissible or vaccine resistant, an increase in vaccine coverage will be needed to provide the same level of protection.

Modelling of Waning of Immunity and Reinfection Induced Antibody Boosting of SARS-CoV-2 in Manaus, Brazil

It was reported that the Brazilian city, Manaus, likely exceeded the herd immunity threshold (presumably 60–70%) in November 2020 after the first wave of COVID-19, based on the serological data of a routine blood donor. However, a second wave started in November 2020, when an even higher magnitude of deaths hit the city. The arrival of the second wave coincided with the emergence of the Gamma (P.1) variant of SARS-CoV-2, with higher transmissibility, a younger age profile of cases, and a higher hospitalization rate. Prete et al. (2020 MedRxiv 21256644) found that 8 to 33 of 238 (3.4–13.9%) repeated blood donors likely were infected twice in Manaus between March 2020 and March 2021. It is unclear how this finding can be used to explain the second wave. We propose a simple model which allows reinfection to explain the two-wave pattern in Manaus. We find that the two waves with 30% and 40% infection attack rates, respectively, and a reinfection ratio at 3.4–13.9%, can explain the two waves well. We argue that the second wave was likely because the city had not exceeded the herd immunity level after the first wave. The reinfection likely played a weak role in causing the two waves.

Modeling the Interplay Between Seasonal Flu Outcomes and Individual Vaccination Decisions.

Seasonal influenza presents an ongoing challenge to public health. The rapid evolution of the flu virus necessitates annual vaccination campaigns, but the decision to get vaccinated or not in a given year is largely voluntary, at least in the USA, and many people decide against it. In some early attempts to model these yearly flu vaccine decisions, it was often assumed that individuals behave rationally, and do so with perfect information-assumptions that allowed the techniques of classical economics and game theory to be applied. However, these assumptions are not fully supported by the emerging empirical evidence about human decision-making behavior in this context. We develop a simple model of coupled disease spread and vaccination dynamics that instead incorporates experimental observations from social psychology to model annual vaccine decision-making more realistically. We investigate population-level effects of these new decision-making assumptions, with the goal of understanding whether the population can self-organize into a state of herd immunity, and if so, under what conditions. Our model agrees with the established results while also revealing more subtle population-level behavior, including biennial oscillations about the herd immunity threshold.

A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics.

Simple SummaryPredicting the spreading trend of the COVID-19 epidemic is one of the hot topics in the modeling field. In this study, we applied a continuous Markov-chain model to simulate the spread of the COVID-19 epidemic. The results of this study indicate that the herd immunity threshold should be significantly higher than 1 − 1/R0. Taking the immunity waning effect into consideration, the model could predict an epidemic resurgence after the herd immunity threshold. Meanwhile, this Markov-chain approach could also forecast the epidemic distribution and predict the epidemic hotspots at different times. It is implied from our model that it is significantly challenging to eradicate SARS-CoV-2 in the short term. The actual epidemic development is consistent with our prediction. In the end, this method displayed great potential as an alternative approach to traditional compartment models.To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number R0. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/R0. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results.

Prevalence of measles antibodies among migrant workers in Singapore: a serological study to identify susceptible population subgroups

BackgroundIn 2019, two clusters of measles cases were reported in migrant worker dormitories in Singapore. We conducted a seroprevalence study to measure the level of susceptibility to measles among migrant workers in Singapore.MethodsOur study involved residual sera of migrant workers from seven Asian countries (Bangladesh, China, India, Indonesia, Malaysia, Myanmar and the Philippines) who had participated in a survey between 2016 and 2019. Immunoglobulin G (IgG) antibody levels were first measured using a commercial enzyme-linked immunosorbent assay (ELISA) test kit. Those with equivocal or negative IgG results were further evaluated using plaque reduction neutralization test (PRNT).ResultsA total of 2234 migrant workers aged 20–49 years were included in the study. The overall prevalence of measles IgG antibodies among migrant workers from the seven Asian countries was 90.5% (95% confidence interval 89.2–91.6%). The country-specific seroprevalence ranged from 80.3 to 94.0%. The seroprevalence was significantly higher among migrant workers born in 1965–1989 than those born in 1990–1999 (95.3% vs. 86.6%, p < 0.0005), whereas there was no significant difference by gender (90.8% in men vs. 89.9% in women, p = 0.508). 195 out of 213 samples with equivocal or negative ELISA results were tested positive using PRNT.ConclusionThe IgG seroprevalence in migrant workers was below the herd immunity threshold of 95% for measles. Sporadic outbreaks may occur in susceptible individuals due to high transmissibility of measles virus. Seroprevalence surveys can help identify susceptible subgroups for vaccination.

Great Expectations of COVID-19 Herd Immunity.

ABSTRACTThere is a common preconception that reaching an estimated herd immunity threshold through vaccination will end the COVID-19 pandemic. However, the mathematical models underpinning this estimate make numerous assumptions that may not be met in the real world. The protection afforded by vaccines is imperfect, particularly against asymptomatic infection, which can still result in transmission and propagate pandemic viral spread. Immune responses wane and SARS-COV-2 has the capacity to mutate over time to become more infectious and resistant to vaccine elicited immunity. Human behavior and public health restrictions also vary over time and among different populations, impacting the transmissibility of infection. These ever-changing factors modify the number of secondary cases produced by an infected individual, thereby necessitating constant revision of the herd immunity threshold. Even so, vaccination remains a powerful strategy to slow down the pandemic, save lives, and alleviate the burden on limited health care resources.

Immunity boosters in COVID-19: Reality or myth?

COVID-19 pandemic has posed an unprecedented threat to human beings. The emergence of pathogens always had been a threat as the designing and verification of treatment strategies and vaccines take time. In such a scenario, the use of strategies, formulations, or chemicals to improve immunity can provide protection, at least partially. The use of some traditional or folk medicinal preparations and other supplements derived from plants are among the most common agents used for keeping immunity tidy and tough. They are used by many with the belief that being herbal in origin these agents are safe. These formulations/preparations are regarded as “Immunity Boosters.” Revolving information and advertisements in bulk and the strategies of “the attention economy” also propagate this belief. The term “Immunity Booster” is a misnomer for these agents and is scientifically not approved. However, the benefits of these herbal formulations cannot be denied. Few of these herbal formulations have benefits in preventive and therapeutic management infections including those of SARS-CoV-2. Due to lifestyle, diet habits, deficiencies and neuropsychological stress, the immunity of a large fraction of the population is not optimal. Uncertainty and fear prevalent in the time of pandemic also negatively affect the immunity threshold. Many phytochemicals have been proven to aid in maintaining the threshold of immune response to an optimal level in subjects with compromised states of immunity. The immunomodulatory potential of these traditional herbal formulations also offers advantages when used along with standard operating procedures in COVID-19. Proposed formulations and their components also have disadvantageous effects and must be used under supervision with scientific methods. Excessive use of these agents may not only affect the organ and tissues deleteriously, but it can also invite immunopathology. Experimental verification of benefits being offered by these herbal agents will aid in their rightful exploitation in the therapy of human ailments including COVID-19.

Estimates of Presumed Population Immunity to SARS-CoV-2 by State in the United States, August 2021.

BackgroundInformation is needed to monitor progress toward a level of population immunity to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sufficient to disrupt viral transmission. We estimated the percentage of the US population with presumed immunity to SARS-CoV-2 due to vaccination, natural infection, or both as of August 26, 2021.MethodsPublicly available data as of August 26, 2021, from the Centers for Disease Control and Prevention were used to calculate presumed population immunity by state. Seroprevalence data were used to estimate the percentage of the population previously infected with SARS-CoV-2, with adjustments for underreporting. Vaccination coverage data for both fully and partially vaccinated persons were used to calculate presumed immunity from vaccination. Finally, we estimated the percentage of the total population in each state with presumed immunity to SARS-CoV-2, with a sensitivity analysis to account for waning immunity, and compared these estimates with a range of population immunity thresholds.ResultsIn our main analysis, which was the most optimistic scenario, presumed population immunity varied among states (43.1% to 70.6%), with 19 states with ≤60% of their population having been infected or vaccinated. Four states had presumed immunity greater than thresholds estimated to be sufficient to disrupt transmission of less infectious variants (67%), and none were greater than the threshold estimated for more infectious variants (≥78%).ConclusionsThe United States remains a distance below the threshold sufficient to disrupt viral transmission, with some states remarkably low. As more infectious variants emerge, it is critical that vaccination efforts intensify across all states and ages for which the vaccines are approved.

Continual Versus Occasional Spreading In Networks

Epidemic processes are widely used as an abstraction for various real-world phenomena - human infections, computer viruses, rumors, information broadcasts, etc. [5, 1, 3]. Under the SIR model (susceptible-infected-removed/recovered) in finite networks, the effective reproduction number, R(), decreases as nodes become infected and removed. Hence, the spread process remains active for a while but eventually dies out (following R &lt; 1, "herd-immunity"). Such threshold phenomena have been observed empirically. In these special days of COVID-19, estimations of the spreadinduced Herd Immunity Threshold (HIT) are a key factor in directing strategic decisions concerning the fight against the pandemic.

Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States.

Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number , the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of relates to a herd immunity threshold (HIT), which is given by . When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21 January 2020 to 21 June 2020. Our estimates characterize the infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we found that no state had achieved herd immunity as of 20 September 2021.

Vaccination Schedule under Conditions of Limited Vaccine Production Rate.

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective actions with a herd immunity threshold (PDPAHIT) also includes a variable probability of infection, i.e., the situation when herd immunity is obtained. The results of computational experiments are reported and the potential of the models is illustrated with examples.

Caveats on COVID-19 herd immunity threshold: the Spain case

After a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

Accuracy assessment of total or IgG Immunoglobulin to hepatitis A virus tests around immunity threshold.

Anti-hepatitis A virus (HAV) antibody titers at 20 IU/L are assumed to correlate with protection against HAV challenge. We examined the accuracy and precision of currently in use immunoassays for total or anti-HAV IgG determination, by repeated testing of dilutions of the international anti-HAV standard, within a 10-50 IU/mL concentration range. Eight immunoassays were evaluated. All could confidently identify people who need to be vaccinated, or who might benefit from a booster vaccine: no positive interpretation for the 10 and 15 IU/mL concentrations. However, qualitative interpretation may differ from test to test in the 15-30 IU/mL range. This variation has to be taken into account when comparing seroprevalence data.

Optimal single-interval control for SIR-type systems

Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets, few of them present a formal dynamic characterization in terms of the two main indexes: the infected peak prevalence (IPP) and the final epidemic size (EFS). These indices are directly related to equilibrium sets and stability, which are crucial concepts to understand what kind of non-pharmaceutical interventions (social distancing, isolation measures, mask-wearing, etc.) can be implemented to handle an epidemic. The objective of this work is to provide a theoretical single-interval control strategy that simultaneously minimizes the EFS while maintaining the IPP arbitrary low, according to health system capacity limitations. Several simulations illustrate the true role of the herd immunity threshold and provide new insight into the way authorities may act.

Time Dynamics of the Spread of Virus Mutants with Increased Infectiousness in Austria

In spring 2021, it became eminent that the emergence of higher infectious virus mutants of SARS-CoV-2 is an unpredictable and omnipresent threat for fighting the pandemic and has wide-ranging implications on containment policies and herd immunity goals. To quantify the risk related to a more infectious virus variant, extensive surveillance and proper data analysis are required. Key observable of the analysis is the excess infectiousness defined as the quotient between the effective reproduction rate of the new and the previous variants. A proper estimate of this parameter allows forecasts for the epidemic situation after the new variant has taken over and enables estimates by how much the new variant will increase the herd immunity threshold. Here, we present and analyse methods to estimate this crucial parameter based on surveillance data. We specifically focus on the time dynamics of the ratio of mutant infections among the new confirmed cases and discuss, how the excess infectiousness can be estimated based on surveillance data for this ratio. We apply a modified susceptible-infectious-recovered approach and derive formulas which can be used to estimate this parameter. We will provide adaptations of the formulas which are able to cope with imported cases and different generation-times of mutant and previous variants and furthermore fit the formulas to surveillance data from Austria. We conclude that the derived methods are well capable of estimating the excess infectiousness, even in early phases of the replacement process. Yet, a high ratio of imported cases from regions with higher variant prevalence may cause a major overestimation of the excess infectiousness, if not considered. Consequently, the analysis of Austrian data allowed a proper estimate for the Alpha variant, but results for the Delta variant are inconclusive.

A tentative tracking of the SARS-Cov2 pandemic in France, based on a corrected SIR model including vaccination effects

We developed successive extensions of the SIR model in order to track the dynamics of the SARS-Cov2 disease. The analysis of health system available data is published in a chronicle accessible on the net: https://corona-circule.github.io/lettres/. This chronicle was initiated on late march 2020 and up to now contains 50 issues. A constant concern was the reliability of the data: for instance, we very soon evidenced that the number of confirmed cases, because of the asymptomatic carriers and the erratic testing policy, was hugely underestimated. By the end of 2020 we made a basic change in the model which consisted in accounting for a constant contagiousness time (SIR-tcc) instead of the probabilistic evolution of the end of the infection assumed so far. Recently we completed this SIR-tcc model for the vaccination effects in order to properly track the evolution of the group immunity threshold. Calculations were performed using the Excel facility (Microsoft), allowing a manual fitting of the model parameters. The results have dealt with a large number of countries, but we focus here on the data regarding France. Further pieces of information are also presented, in order to help elucidating some the factors responsible for the complex history of the pandemic dynamics. (submitted dec 14th 2021)