Vaccine escape in a heterogeneous population: insights for SARS-CoV-2 from a simple model

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.

Modelling COVID-19 mutant dynamics: understanding the interplay between viral evolution and disease transmission dynamics

Understanding virus mutations is critical for shaping public health interventions. These mutations lead to complex multi-strain dynamics often under-represented in models. Aiming to understand the factors influencing variants' fitness and evolution, we explore several scenarios of virus spreading to gain qualitative insight into the factors dictating which variants ultimately predominate at the population level. To this end, we propose a two-strain stochastic model that accounts for asymptomatic transmission, mutations and the possibility of disease import. We find that variants with milder symptoms are likely to spread faster than those with severe symptoms. This is because severe variants can prompt affected individuals to seek medical help earlier, potentially leading to quicker identification and isolation of cases. However, milder or asymptomatic cases may spread more widely, making it harder to control the spread. Therefore, increased transmissibility of milder variants can still result in higher hospitalizations and fatalities due to widespread infection. The proposed model highlights the interplay between viral evolution and transmission dynamics. Offering a nuanced view of factors influencing variant spread, the model provides a foundation for further investigation into mitigating strategies and public health interventions.

Prioritising older individuals for COVID-19 booster vaccination leads to optimal public health outcomes in a range of socio-economic settings

The rapid development of vaccines against SARS-CoV-2 altered the course of the COVID-19 pandemic. In most countries, vaccinations were initially targeted at high-risk populations, including older individuals and healthcare workers. Now, despite substantial infection- and vaccine-induced immunity in host populations worldwide, waning immunity and the emergence of novel variants continue to cause significant waves of infection and disease. Policy makers must determine how to deploy booster vaccinations, particularly when constraints in vaccine supply, delivery and cost mean that booster vaccines cannot be administered to everyone. A key question is therefore whether older individuals should again be prioritised for vaccination, or whether alternative strategies (e.g. offering booster vaccines to the individuals who have most contacts with others and therefore drive infection) can instead offer indirect protection to older individuals. Here, we use mathematical modelling to address this question, considering SARS-CoV-2 transmission in a range of countries with different socio-economic backgrounds. We show that the population structures of different countries can have a pronounced effect on the impact of booster vaccination, even when identical booster vaccination targeting strategies are adopted. However, under the assumed transmission model, prioritising older individuals for booster vaccination consistently leads to the most favourable public health outcomes in every setting considered. This remains true for a range of assumptions about booster vaccine supply and timing, and for different assumed policy objectives of booster vaccination.

Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study

In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multiscale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multiscale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.

Modelling the Interplay between Responsive Individual Vaccination Decisions and the Spread of SARS-CoV-2

The uptake of COVID-19 vaccines remains low despite their high effectiveness. Epidemic models that represent decision-making psychology can provide insight into the potential impact of vaccine promotion interventions in the context of the COVID-19 pandemic. We coupled a network-based mathematical model of SARS-CoV-2 transmission in Georgia, USA with a social-psychological vaccination decision-making model in which vaccine side effects, post-vaccination infections, and other unidentified community-level factors could "nudge" individuals towards vaccine resistance while hospitalization spikes could nudge them towards willingness. Combining an increased probability of hospitalization-prompted resistant-to-willing switches with a decreased probability of willing-to-resistant switches prompted by unidentified community-level factors increased vaccine uptake and decreased SARS-CoV-2 incidence by as much as 30.7% and 24.0%, respectively. The latter probability had a greater impact than the former. This illustrates the disease prevention potential of vaccine promotion interventions that address community-level factors influencing decision-making and anticipate the case curve instead of reacting to it.

Evolutionary implications of SARS-CoV-2 vaccination for the future design of vaccination strategies

Once the first SARS-CoV-2 vaccine became available, mass vaccination was the main pillar of the public health response to the COVID-19 pandemic. It was very effective in reducing hospitalizations and deaths. Here, we discuss the possibility that mass vaccination might accelerate SARS-CoV-2 evolution in antibody-binding regions compared to natural infection at the population level. Using the evidence of strong genetic variation in antibody-binding regions and taking advantage of the similarity between the envelope proteins of SARS-CoV-2 and influenza, we assume that immune selection pressure acting on these regions of the two viruses is similar. We discuss the consequences of this assumption for SARS-CoV-2 evolution in light of mathematical models developed previously for influenza. We further outline the implications of this phenomenon, if our assumptions are confirmed, for the future design of SARS-CoV-2 vaccination strategies.

The importance of vaccinated individuals to population-level evolution of pathogens

Virus evolution shapes the epidemiological patterns of infectious disease, particularly via evasion of population immunity. At the individual level, host immunity itself may drive viral evolution towards antigenic escape. Using compartmental SIR-style models with imperfect vaccination, we allow the probability of immune escape to differ in vaccinated and unvaccinated hosts. As the relative contribution to selection in these different hosts varies, the overall effect of vaccination on the antigenic escape pressure at the population level changes. We find that this relative contribution to escape is important for understanding the effects of vaccination on the escape pressure and we draw out some fairly general patterns. If vaccinated hosts do not contribute much more than unvaccinated hosts to the escape pressure, then increasing vaccination always reduces the overall escape pressure. In contrast, if vaccinated hosts contribute significantly more than unvaccinated hosts to the population level escape pressure, then the escape pressure is maximised for intermediate vaccination levels. Past studies find only that the escape pressure is maximal for intermediate levels with fixed extreme assumptions about this relative contribution. Here we show that this result does not hold across the range of plausible assumptions for the relative contribution to escape from vaccinated and unvaccinated hosts. We also find that these results depend on the vaccine efficacy against transmission, particularly through the partial protection against infection. This work highlights the potential value of understanding better how the contribution to antigenic escape pressure depends on individual host immunity.

Which vaccination strategy against COVID-19?

BACKGROUND

Bottlenecks in the production and supply pipeline of vaccines against coronavirus disease 2019 have led some countries to consider the option of dose-sparing strategies (e.g., increasing the number of people who receive some vaccine by halving the dose or increasing the interval between doses). In this study we assess the contribution of vaccination strategies to reducing the mortality induced by severe acute respiratory syndrome coronavirus 2.

METHODS

This study focuses on the evolution of the pandemic and related vaccination efforts in five countries that have adopted different vaccination strategies or have experienced a bottleneck in their vaccine supply. The analysis is conducted using an autoregressive time-series approach through a system of simultaneous equations.

RESULTS

The outcome of the early months of the vaccination campaign in containing the number of deaths induced by the epidemic varies across our sample. Overall, our results highlight the effective role played by the vaccine in containing the death toll induced by the epidemic. We could not find evidence of reduced effectiveness of the second dose in the presence of an extended inter-dose interval. The effectiveness of the vaccination campaign results appears to be strongly affected by the stability of vaccine supply.

CONCLUSIONS

The vaccine is effective in containing the deaths caused by the virus, particularly when multiple doses have been administered. The stability of the vaccine pipeline plays a critical role in determining the effectiveness of the vaccination campaign.

The impacts of SARS-CoV-2 vaccine dose separation and targeting on the COVID-19 epidemic in England

In late 2020, the JCVI (the Joint Committee on Vaccination and Immunisation, which provides advice to the Department of Health and Social Care, England) made two important recommendations for the initial roll-out of the COVID-19 vaccine. The first was that vaccines should be targeted to older and vulnerable people, with the aim of maximally preventing disease rather than infection. The second was to increase the interval between first and second doses from 3 to 12 weeks. Here, we re-examine these recommendations through a mathematical model of SARS-CoV-2 infection in England. We show that targeting the most vulnerable had the biggest immediate impact (compared to targeting younger individuals who may be more responsible for transmission). The 12-week delay was also highly beneficial, estimated to have averted between 32-72 thousand hospital admissions and 4-9 thousand deaths over the first ten months of the campaign (December 2020-September 2021) depending on the assumed interaction between dose interval and efficacy.

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".

Non-pharmaceutical interventions and the emergence of pathogen variants

Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs.

Novel coronavirus mutations: Vaccine development and challenges

The ongoing global pandemic of novel coronavirus pneumonia (COVID-19) caused by the SARS-CoV-2 has a significant impact on global health and economy system. In this context, there have been some landmark advances in vaccine development. Over 100 new coronavirus vaccine candidates have been approved for clinical trials, with ten WHO-approved vaccines including four inactivated virus vaccines, two mRNA vaccines, three recombinant viral vectored vaccines and one protein subunit vaccine on the "Emergency Use Listing". Although the SARS-CoV-2 has an internal proofreading mechanism, there have been a number of mutations emerged in the pandemic affecting its transmissibility, pathogenicity and immunogenicity. Of these, mutations in the spike (S) protein and the resultant mutant variants have posed new challenges for vaccine development and application. In this review article, we present an overview of vaccine development, the prevalence of new coronavirus variants and their impact on protective efficacy of existing vaccines and possible immunization strategies coping with the viral mutation and diversity.

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.

Assessing COVID-19 vaccination strategies in varied demographics using an individual-based model

Background

New variants of SARS-CoV-2 are constantly discovered. Administration of COVID-19 vaccines and booster doses, combined with the application of non-pharmaceutical interventions (NPIs), is often used to prevent outbreaks of emerging variants. Such outbreak dynamics are further complicated by the population's behavior and demographic composition. Hence, realistic simulations are needed to estimate the efficiency of proposed vaccination strategies in conjunction with NPIs.

Methods

We developed an individual-based model of COVID-19 dynamics that considers age-dependent parameters such as contact matrices, probabilities of symptomatic and severe disease, and households' age distribution. As a case study, we simulate outbreak dynamics under the demographic compositions of two Israeli cities with different household sizes and age distributions. We compare two vaccination strategies: vaccinate individuals in a currently prioritized age group, or dynamically prioritize neighborhoods with a high estimated reproductive number. Total infections and hospitalizations are used to compare the efficiency of the vaccination strategies under the two demographic structures, in conjunction with different NPIs.

Results

We demonstrate the effectiveness of vaccination strategies targeting highly infected localities and of NPIs actively detecting asymptomatic infections. We further show that different optimal vaccination strategies exist for each sub-population's demographic composition and that their application is superior to a uniformly applied strategy.

Conclusion

Our study emphasizes the importance of tailoring vaccination strategies to subpopulations' infection rates and to the unique characteristics of their demographics (e.g., household size and age distributions). The presented simulation framework and findings can help better design future responses against the following emerging variants.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

The impact of vaccination on the modeling of COVID-19 dynamics: a fractional order model

The coronavirus disease 2019 (COVID-19) is a recent outbreak of respiratory infections that have affected millions of humans all around the world. Initially, the major intervention strategies used to combat the infection were the basic public health measure, nevertheless, vaccination is an effective strategy and has been used to control the incidence of many infectious diseases. Currently, few safe and effective vaccines have been approved to control the inadvertent transmission of COVID-19. In this paper, the modeling approach is adopted to investigate the impact of currently available anti-COVID vaccines on the dynamics of COVID-19. A new fractional-order epidemic model by incorporating the vaccination class is presented. The fractional derivative is considered in the well-known Caputo sense. Initially, the proposed vaccine model for the dynamics of COVID-19 is developed via integer-order differential equations and then the Caputo-type derivative is applied to extend the model to a fractional case. By applying the least square method, the model is fitted to the reported cases in Pakistan and some of the parameters involved in the models are estimated from the actual data. The threshold quantity ( R 0 ) is computed by the Next-generation method. A detailed analysis of the fractional model, such as positivity of model solution, equilibrium points, and stabilities on both disease-free and endemic states are discussed comprehensively. An efficient iterative method is utilized for the numerical solution of the proposed model and the model is then simulated in the light of vaccination. The impact of important influential parameters on the pandemic dynamics is shown graphically. Moreover, the impact of different intervention scenarios on the disease incidence is depicted and it is found that the reduction in the effective contact rate (up to 30%) and enhancement in vaccination rate (up to 50%) to the current baseline values significantly reduced the disease new infected cases.

Assessing Public Health and Social Measures Against COVID-19 in Japan From March to June 2021

Background

Public health and social measures (PHSM) against COVID-19 in Japan involve requesting the public to voluntarily reduce social contact; these measures are not legally binding. The effectiveness of such PHSM has been questioned with emergence of the SARS-CoV-2 Alpha variant (B.1.1.7), which exhibited elevated transmissibility.

Materials and Methods

We investigated the epidemic dynamics during the fourth epidemic wave in Japan from March to June 2021 involving pre-emergency measures and declaration of a state of emergency (SoE). We estimated the effective reproduction number (R_t) before and after these interventions, and then analyzed the relationship between lower R_t values and each PHSM.

Results

With implementation of pre-emergency measures (PEM) in 16 prefectures, the R_t was estimated to be < 1 in six prefectures; its average relative reduction ranged from 2 to 19%. During the SoE, 8 of 10 prefectures had an estimated R_t < 1, and the average relative reduction was 26%–39%. No single intervention was identified that uniquely resulted in an R_t value < 1.

Conclusion

An SoE can substantially reduce the R_t and may be required to curb a surge in cases caused by future SARS-CoV-2 variants of concern with elevated transmissibility. More customized interventions did not reduce the R_t value to < 1 in this study, but that may be partly attributable to the greater transmissibility of the Alpha variant.

A herd immunity approach to the COVID-19 pandemic?

Viral contamination is one of the most urgent and important topics of environmental pollution. COVID-19 is primarily transmitted from person to person, but can also be transmitted from person to animal. Herd immunity must meet the requirements in order to fulfill the goal of mitigating and ending COVID-19. This paper shows five reasons or conditions why herd immunity is not achieved in the present policies without proposed effective strategies in this paper. Unless one of the five reasons for the herd immunity model is met, the promise of herd immunity will not be fulfilled. Many COVID-19 policies worldwide with current vaccines do not meet the requirements. Policymakers have been relying on unreliable R. The number of daily deaths instead of the number of cases is a good indicator of the pandemic which will be mainly used in this paper. Currently, even in vaccinated countries, resurgences are being observed with new variants with spike mutations and immune escape. This paper proposes an effective multipronged approach such as a pharmacological approach and a non-pharmacological approach including digital fencing. Two tools such as scorecovid and deathdaily were used for justifying the claims. Digital fencing as well as pharmacological approaches may be able to overcome the pandemic. Two tools such as scorecovid and deathdaily showed that the proposed multipronged approach will be effective for mitigating the pandemic.

Evolution of resistance to COVID-19 vaccination with dynamic social distancing

The greatest hope for a return to normalcy following the COVID-19 pandemic is worldwide vaccination. Yet, a relaxation of social distancing that allows increased transmissibility, coupled with selection pressure due to vaccination, will probably lead to the emergence of vaccine resistance. We analyse the evolutionary dynamics of COVID-19 in the presence of dynamic contact reduction and in response to vaccination. We use infection and vaccination data from six different countries. We show that under slow vaccination, resistance is very likely to appear even if social distancing is maintained. Under fast vaccination, the emergence of mutants can be prevented if social distancing is maintained during vaccination. We analyse multiple human factors that affect the evolutionary potential of the virus, including the extent of dynamic social distancing, vaccination campaigns, vaccine design, boosters and vaccine hesitancy. We provide guidelines for policies that aim to minimize the probability of emergence of vaccine-resistant variants.

Evaluating strategies for spatial allocation of vaccines based on risk and centrality

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritize some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritization include strategies that target those regions most at risk of importing the pathogen, and strategies that target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network and vaccine availability. We conclude that when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

Targeted vaccination and the speed of SARS-CoV-2 adaptation

The limited supply of vaccines against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) raises the question of targeted vaccination. Many countries have opted to vaccinate older and more sensitive hosts first to minimize the disease burden. However, what are the evolutionary consequences of targeted vaccination? We clarify the consequences of different vaccination strategies through the analysis of the speed of viral adaptation measured as the rate of change of the frequency of a vaccine-adapted variant. We show that such a variant is expected to spread faster if vaccination targets individuals who are likely to be involved in a higher number of contacts. We also discuss the pros and cons of dose-sparing strategies. Because delaying the second dose increases the proportion of the population vaccinated with a single dose, this strategy can both speed up the spread of the vaccine-adapted variant and reduce the cumulative number of deaths. Hence, strategies that are most effective at slowing viral adaptation may not always be epidemiologically optimal. A careful assessment of both the epidemiological and evolutionary consequences of alternative vaccination strategies is required to determine which individuals should be vaccinated first.

Vaccinating adolescents against SARS-CoV-2 in England: a risk-benefit analysis

OBJECTIVE

To offer a quantitative risk-benefit analysis of two doses of SARS-CoV-2 vaccination among adolescents in England.

SETTING

England.

DESIGN

Following the risk-benefit analysis methodology carried out by the US Centers for Disease Control, we calculated historical rates of hospital admission, Intensive Care Unit admission and death for ascertained SARS-CoV-2 cases in children aged 12-17 in England. We then used these rates alongside a range of estimates for incidence of long COVID, vaccine efficacy and vaccine-induced myocarditis, to estimate hospital and Intensive Care Unit admissions, deaths and cases of long COVID over a period of 16 weeks under assumptions of high and low case incidence.

PARTICIPANTS

All 12-17 year olds with a record of confirmed SARS-CoV-2 infection in England between 1 July 2020 and 31 March 2021 using national linked electronic health records, accessed through the British Heart Foundation Data Science Centre.

MAIN OUTCOME MEASURES

Hospitalisations, Intensive Care Unit admissions, deaths and cases of long COVID averted by vaccinating all 12-17 year olds in England over a 16-week period under different estimates of future case incidence.

RESULTS

At high future case incidence of 1000/100,000 population/week over 16 weeks, vaccination could avert 4430 hospital admissions and 36 deaths over 16 weeks. At the low incidence of 50/100,000/week, vaccination could avert 70 hospital admissions and two deaths over 16 weeks. The benefit of vaccination in terms of hospitalisations in adolescents outweighs risks unless case rates are sustainably very low (below 30/100,000 teenagers/week). Benefit of vaccination exists at any case rate for the outcomes of death and long COVID, since neither have been associated with vaccination to date.

CONCLUSIONS

Given the current (as at 15 September 2021) high case rates (680/100,000 population/week in 10-19 year olds) in England, our findings support vaccination of adolescents against SARS-CoV2.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed.

Methods

Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel.

Results

We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility.

Conclusions

Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain.

Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.

Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics

Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed.