BACKGROUND:Countries in the World Health Organization (WHO) European Region differ in terms of the COVID-19 vaccine supply conditions. We evaluated the health and economic impact of different age-based vaccine prioritisation strategies across this demographically and socio-economically diverse region.METHODS:We fitted age-specific compartmental models to the reported daily COVID-19 mortality in 2020 to inform the immunity level before vaccine roll-out. Models capture country-specific differences in population structures, contact patterns, epidemic history, life expectancy, and GDP per capita.We examined four strategies that prioritise: all adults (V+), younger (20-59 year-olds) followed by older adults (60+) (V20), older followed by younger adults (V60), and the oldest adults (75+) (V75) followed by incrementally younger age groups. We explored four roll-out scenarios (R1-4) - the slowest scenario (R1) reached 30% coverage by December 2022 and the fastest (R4) 80% by December 2021. Five decision-making metrics were summarised over 2021-22: mortality, morbidity, and losses in comorbidity-adjusted life expectancy, comorbidity- and quality-adjusted life years, and human capital. Six vaccine profiles were tested - the highest performing vaccine has 95% efficacy against both infection and disease, and the lowest 50% against diseases and 0% against infection.FINDINGS:Of the 20 decision-making metrics and roll-out scenario combinations, the same optimal strategy applied to all countries in only one combination; V60 was more or similarly desirable than V75 in 19 combinations. Of the 38 countries with fitted models, 11-37 countries had variable optimal strategies by decision-making metrics or roll-out scenarios. There are greater benefits in prioritising older adults when roll-out is slow and when vaccine profiles are less favourable.INTERPRETATION:The optimal age-based vaccine prioritisation strategies were sensitive to country characteristics, decision-making metrics, and roll-out speeds. A prioritisation strategy involving more age-based stages (V75) does not necessarily lead to better health and economic outcomes than targeting broad age groups (V60). Countries expecting a slow vaccine roll-out may particularly benefit from prioritising older adults.FUNDING:World Health Organization, Bill and Melinda Gates Foundation, the Medical Research Council (United Kingdom), the National Institute of Health Research (United Kingdom), the European Commission, the Foreign, Commonwealth and Development Office (United Kingdom), Wellcome Trust.

England has experienced a heavy burden of COVID-19, with multiple waves of SARS-CoV-2 transmission since early 2020 and high infection levels following the emergence and spread of Omicron variants since late 2021. In response to rising Omicron cases, booster vaccinations were accelerated and offered to all adults in England. Using a model fitted to more than 2 years of epidemiological data, we project potential dynamics of SARS-CoV-2 infections, hospital admissions and deaths in England to December 2022. We consider key uncertainties including future behavioural change and waning immunity, and assess the effectiveness of booster vaccinations in mitigating SARS-CoV-2 disease burden between October 2021 and December 2022. If no new variants emerge, SARS-CoV-2 transmission is expected to decline, with low levels remaining in the coming months. The extent to which projected SARS-CoV-2 transmission resurges later in 2022 depends largely on assumptions around waning immunity and to some extent, behaviour and seasonality.

Summary 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 could let 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 for low- and middle-income countries of Europe. Methods We fitted a dynamic transmission model to country-level daily reported COVID-19 mortality in 13 low- and middle-income countries in the World Health Organization European Region (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 the Oxford/AstraZeneca COVID-19 (AZD1222) vaccine was used in the base case scenario and was complemented by sensitivity analyses around efficacies related 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 into the model, and also conducted a benefit-risk assessment to quantify the trade-off between health benefits versus adverse events following immunisation. Findings In 12 of the 13 countries, optimal strategies are those that prioritise the first doses among older adults (60+ years) or adults (20-59 years). These strategies lead to dosing intervals longer than six months. In comparison, a four-week fixed dosing interval may incur 10.2% [range: 4.0% - 22.5%; n = 13 (countries)] more deaths. There is generally a negative association between dosing interval and COVID-19 mortality within the range we investigated. Assuming a shorter first dose waning duration of 120 days, as opposed to 360 days in the base case, led to shorter optimal dosing intervals of 8-12 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, which are substantially longer than the current label recommendation for most vaccine products, could reduce COVID-19 mortality in low- and middle-income countries of WHO/Europe. Certain vaccine features, such as fast waning of first doses, significantly shorten the optimal dosing intervals. Funding World Health Organization

England has experienced a heavy burden of COVID-19, with multiple waves of SARS-CoV-2 transmission since early 2020 and high infection levels following the emergence and spread of Omicron variants since late 2021. In response to rising Omicron cases, booster vaccinations were accelerated and offered to all adults in England. Using a model fitted to more than 2 years of epidemiological data, we project potential dynamics of SARS-CoV-2 infections, hospital admissions and deaths in England to December 2022. We consider key uncertainties including future behavioural change and waning immunity and assess the effectiveness of booster vaccinations in mitigating SARS-CoV-2 disease burden between October 2021 and December 2022. If no new variants emerge, SARS-CoV-2 transmission is expected to decline, with low levels remaining in the coming months. The extent to which projected SARS-CoV-2 transmission resurges later in 2022 depends largely on assumptions around waning immunity and to some extent, behaviour, and seasonality.

Background COVID-19 outbreaks still occur in English care homes despite the interventions in place. Methods We developed a stochastic compartmental model to simulate the spread of SARS-CoV-2 within an English care home. We quantified the outbreak risk with baseline non-pharmaceutical interventions (NPIs) already in place, the role of community prevalence in driving outbreaks, and the relative contribution of all importation routes into a fully susceptible care home. We also considered the potential impact of additional control measures in care homes with and without immunity, namely: increasing staff and resident testing frequency, using lateral flow antigen testing (LFD) tests instead of polymerase chain reaction (PCR), enhancing infection prevention and control (IPC), increasing the proportion of residents isolated, shortening the delay to isolation, improving the effectiveness of isolation, restricting visitors and limiting staff to working in one care home. We additionally present a Shiny application for users to apply this model to their facility of interest, specifying care home, outbreak and intervention characteristics. Results The model suggests that importation of SARS-CoV-2 by staff, from the community, is the main driver of outbreaks, that importation by visitors or from hospitals is rare, and that the past testing strategy (monthly testing of residents and daily testing of staff by PCR) likely provides negligible benefit in preventing outbreaks. Daily staff testing by LFD was 39% (95% 18–55%) effective in preventing outbreaks at 30 days compared to no testing. Conclusions Increasing the frequency of testing in staff and enhancing IPC are important to preventing importations to the care home. Further work is needed to understand the impact of vaccination in this population, which is likely to be very effective in preventing outbreaks.

We estimate the potential remaining COVID-19 hospitalisation and death burdens in 19 European countries by estimating the proportion of each country’s population that has acquired immunity to severe disease through infection or vaccination. Our results suggest many European countries could still face high burdens of hospitalisations and deaths, particularly those with lower vaccination coverage, less historical transmission and/or older populations. Continued non-pharmaceutical interventions and efforts to achieve high vaccination coverage are required in these countries to limit severe COVID-19 outcomes.

We estimate the potential remaining COVID-19 burden in 19 European countries by estimating the proportion of each country's population that has acquired immunity to severe disease through infection or vaccination. Our results suggest that many European countries could still face a substantial burden of hospitalisations and deaths, particularly those with lower vaccine coverage, less historical transmission, and/or older populations. Continued non-pharmaceutical interventions and efforts to achieve high vaccine coverage are required in these countries to limit severe COVID-19 outcomes.

A new SARS-CoV-2 variant of concern, Omicron (B.1.1.529), has been identified based on genomic sequencing and epidemiological data in South Africa. Presumptive Omicron cases in South Africa have grown extremely rapidly, despite high prior exposure and moderate vaccination coverage. The available evidence suggests that Omicron spread is at least in part due to evasion of this immune protection, though it may also exhibit higher intrinsic transmissibility. Using detailed laboratory and epidemiological data from South Africa, we estimate the constraints on these two characteristics of the new variant and their relationship. Our estimates and associated uncertainties provide essential information to inform projection and scenario modeling analyses, which are crucial planning tools for governments around the world.

We model Step 4 of the UK Government’s Spring 2021 “Roadmap” out of lockdown in England. To capture behavioural changes in response to the easing of restrictions, we consider low, medium and high scenarios for mobility levels resulting from implementing Step 4 of the roadmap. We also consider a number of alternative policy options such as delaying roadmap Step 4, implementing circuit breaker lockdowns and reversing roadmap steps. As the Delta variant of concern (VOC) B.1.617.2 continues to spread in England, our analysis considers a third SARS-CoV-2 variant which exhibits different levels of immune escape and of increased transmissibility relative to the Alpha B.1.1.7 VOC.

We estimate the potential remaining COVID-19 burden in 19 European countries by estimating the proportion of each country’s population that has acquired immunity to severe disease through infection or vaccination. Our results suggest that many European countries could still face a substantial burden of hospitalisations and deaths, particularly those with lower vaccination coverage, less historical transmission, and/or older populations. Continued non-pharmaceutical interventions and efforts to achieve high vaccination coverage are required in these countries to limit severe COVID-19 outcomes. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was funded by the National Insitute for Heatlh Research (NIHR) (NIHR200908) and the Wellcome Trust (206250/Z/17/Z) (LACC, TWR, AJK). The work was partly supported by funding from the European Union's Horizon 2020 research and innovation programme - project EpiPose (101003688: RCB); the FCDO/Wellcome Trust (Epidemic Preparedness Coronavirus research programme 221303/Z/20/Z: KvZ); the Wellcome Trust (210758/Z/18/Z: SA); NIHR (NIHR200929) (NGD); UK MRC (MC\_PC\_19065) (NGD) and UKRI Research England (NGD). The funders had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: This study involves only openly available human data, which can be obtained from: <https://osf.io/mpwjq/> <https://dc-covid.site.ined.fr/en/> <https://www.ecdc.europa.eu/en/covid-19/data> [https://github.com/robert-koch-institut/COVID-19-Impfungen\_in\_Deutschland/][1] <https://coronavirus.data.gov.uk/details/download> <https://covid19.sanger.ac.uk/downloads> <https://serotracker.com/> I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data and code used in this manuscript are available online at [https://github.com/LloydChapman/covid\_remaining\_burden][2] and <https://doi.org/10.5281/zenodo.5772163> or at the links below. [https://github.com/LloydChapman/covid\_remaining\_burden][2] <https://osf.io/mpwjq/> <https://dc-covid.site.ined.fr/en/> <https://www.ecdc.europa.eu/en/covid-19/data> <https://coronavirus.data.gov.uk/details/download> <https://covid19.sanger.ac.uk/downloads> <https://serotracker.com/> <https://doi.org/10.5281/zenodo.5772163> [1]: https://github.com/robert-koch-institut/COVID-19-Impfungen_in_Deutschland/ [2]: https://github.com/LloydChapman/covid_remaining_burden

A novel SARS-CoV-2 variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in November 2020 and is rapidly spreading towards fixation. Using a variety of statistical and dynamic modelling approaches, we estimate that this variant has a 43–90% (range of 95% credible intervals 38–130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine roll-out, COVID-19 hospitalisations and deaths across England in 2021 will exceed those in 2020. Concerningly, VOC 202012/01 has spread globally and exhibits a similar transmission increase (59–74%) in Denmark, Switzerland, and the United States.

Background A second wave of COVID-19 cases in autumn, 2020, in England led to localised, tiered restrictions (so-called alert levels) and, subsequently, a second national lockdown. We examined the impact of these tiered restrictions, and alternatives for lockdown stringency, timing, and duration, on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission and hospital admissions and deaths from COVID-19. Methods We fit an age-structured mathematical model of SARS-CoV-2 transmission to data on hospital admissions and hospital bed occupancy (ISARIC4C/COVID-19 Clinical Information Network, National Health Service [NHS] England), seroprevalence (Office for National Statistics, UK Biobank, REACT-2 study), virology (REACT-1 study), and deaths (Public Health England) across the seven NHS England regions from March 1, to Oct 13, 2020. We analysed mobility (Google Community Mobility) and social contact (CoMix study) data to estimate the effect of tiered restrictions implemented in England, and of lockdowns implemented in Northern Ireland and Wales, in October, 2020, and projected epidemiological scenarios for England up to March 31, 2021. Findings We estimated a reduction in the effective reproduction number (R t) of 2% (95% credible interval [CrI] 0-4) for tier 2, 10% (6-14) for tier 3, 35% (30-41) for a Northern Ireland-stringency lockdown with schools closed, and 44% (37-49) for a Wales-stringency lockdown with schools closed. From Oct 1, 2020, to March 31, 2021, a projected COVID-19 epidemic without tiered restrictions or lockdown results in 280 000 (95% projection interval 274 000-287 000) hospital admissions and 58 500 (55 800-61 100) deaths. Tiered restrictions would reduce hospital admissions to 238 000 (231 000-245 000) and deaths to 48 600 (46 400-50 700). From Nov 5, 2020, a 4-week Wales-type lockdown with schools remaining open-similar to the lockdown measures announced in England in November, 2020-was projected to further reduce hospital admissions to 186 000 (179 000-193 000) and deaths to 36 800 (34 900-38 800). Closing schools was projected to further reduce hospital admissions to 157 000 (152 000-163 000) and deaths to 30 300 (29 000-31 900). A projected lockdown of greater than 4 weeks would reduce deaths but would bring diminishing returns in reducing peak pressure on hospital services. An earlier lockdown would have reduced deaths and hospitalisations in the short term, but would lead to a faster resurgence in cases after January, 2021. In a post-hoc analysis, we estimated that the second lockdown in England (Nov 5-Dec 2) reduced R t by 22% (95% CrI 15-29), rather than the 32% (25-39) reduction estimated for a Wales-stringency lockdown with schools open. Interpretation Lockdown measures outperform less stringent restrictions in reducing cumulative deaths. We projected that the lockdown policy announced to commence in England on Nov 5, with a similar stringency to the lockdown adopted in Wales, would reduce pressure on the health service and would be well timed to suppress deaths over the winter period, while allowing schools to remain open. Following completion of the analysis, we analysed new data from November, 2020, and found that despite similarities in policy, the second lockdown in England had a smaller impact on behaviour than did the second lockdown in Wales, resulting in more deaths and hospitalisations than we originally projected when focusing on a Wales-stringency scenario for the lockdown.

The Omicron B.1.1.529 SARS-CoV-2 variant was first detected in late November 2021 and has since spread to multiple countries worldwide. We model the potential consequences of the Omicron variant on SARS-CoV-2 transmission and health outcomes in England between December 2021 and April 2022, using a deterministic compartmental model fitted to epidemiological data from March 2020 onwards. Because of uncertainty around the characteristics of Omicron, we explore scenarios varying the extent of Omicron's immune escape and the effectiveness of COVID-19 booster vaccinations against Omicron, assuming the level of Omicron's transmissibility relative to Delta to match the growth in observed S gene target failure data in England. We consider strategies for the re-introduction of control measures in response to projected surges in transmission, as well as scenarios varying the uptake and speed of COVID-19 booster vaccinations and the rate of Omicron's introduction into the population. These results suggest that Omicron has the potential to cause substantial surges in cases, hospital admissions and deaths in populations with high levels of immunity, including England. The reintroduction of additional non-pharmaceutical interventions may be required to prevent hospital admissions exceeding the levels seen in England during the previous peak in winter 2020-2021.

A novel SARS-CoV-2 variant, VOC 202012/01, emerged in southeast England in November 2020 and appears to be rapidly spreading towards fixation. We fitted a two-strain mathematical model of SARS-CoV-2 transmission to observed COVID-19 hospital admissions, hospital and ICU bed occupancy, and deaths; SARS-CoV-2 PCR prevalence and seroprevalence; and the relative frequency of VOC 202012/01 in the three most heavily affected NHS England regions (South East, East of England, and London). We estimate that VOC 202012/01 is 56% more transmissible (95% credible interval across three regions 50-74%) than preexisting variants of SARS-CoV-2. We were unable to find clear evidence that VOC 202012/01 results in greater or lesser severity of disease than preexisting variants. Nevertheless, the increase in transmissibility is likely to lead to a large increase in incidence, with COVID-19 hospitalisations and deaths projected to reach higher levels in 2021 than were observed in 2020, even if regional tiered restrictions implemented before 19 December are maintained. Our estimates suggest that control measures of a similar stringency to the national lockdown implemented in England in November 2020 are unlikely to reduce the effective reproduction number Rt to less than 1, unless primary schools, secondary schools, and universities are also closed. We project that large resurgences of the virus are likely to occur following easing of control measures. It may be necessary to greatly accelerate vaccine roll-out to have an appreciable impact in suppressing the resulting disease burden.

The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics, it is well studied and understood. However, it is less so for clustered networks where theoretical results are mostly limited to idealised networks. In this paper we focus on a class of models known as pairwise models where, to our knowledge, no analytical result for the epidemic threshold exists. We show that by exploiting the presence of fast variables and using some standard techniques from perturbation theory we are able to obtain the epidemic threshold analytically. We validate this new threshold by comparing it to the threshold based on the numerical solution of the full system. The agreement is found to be excellent over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. Interestingly, we find that the analytical form of the threshold depends on the choice of closure, highlighting the importance of model selection when dealing with real-world epidemics. Nevertheless, we expect that our method will extend to other systems in which fast variables are present.

The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a dual-layer static-dynamic multiplex network. The static network layer affords tunable clustering and describes an individual's permanent community structure. The dynamic network layer describes the transient connections an individual makes with members of the wider population by imposing constant edge rewiring. We follow the edge-based compartmental modelling approach to derive equations describing the evolution of a susceptible-infected-recovered epidemic spreading through this multiplex network of individuals. We derive the basic reproduction number, measuring the expected number of new infectious cases caused by a single infectious individual in an otherwise susceptible population. We validate model equations by showing convergence to pre-existing edge-based compartmental model equations in limiting cases and by comparison with stochastically simulated epidemics. We explore the effects of altering model parameters and multiplex network attributes on resultant epidemic dynamics. We validate the basic reproduction number by plotting its value against associated final epidemic sizes measured from simulation and predicted by model equations for a number of set-ups. Further, we explore the effect of varying individual model parameters on the basic reproduction number. We conclude with a discussion of the significance and interpretation of the model and its relation to existing research literature. We highlight intrinsic limitations and potential extensions of the present model and outline future research considerations, both experimental and theoretical.

The balance between excitation and inhibition in a neuronal network is considered to be an important determinant of neural excitability. Various processes are thought to maintain this balance across a range of stimuli/conditions. However, how this balance is exactly formed and maintained remains an open question, especially regarding the interplay between network blue-print (the spatial arrangement of excitatory and inhibitory neurons) and homeostatic processes. In this chapter, we use a published model of activity-dependent structural plasticity to show that the ratio between the number of excitatory and inhibitory neurons (E/I ratio) alone cannot accurately predict system behavior but rather it is the combination of this ratio and the underlying spatial arrangement of neurons that determine both activity in, and structure of, the resulting network. In particular, we highlight the role of spatial clustering of inhibitory neurons. We develop measures that allow us to characterize the relationship between this spatial clustering and system behavior in both the one-dimensional and two-dimensional forms of the model. Our results reveal that, for a given E/I ratio, networks with high levels of inhibitory spatial clustering are more likely to experience oscillatory behavior of their connectivity and electrical activity than networks with lower levels of clustering. This instability of the network structure can be thought of as a pathological outcome. We discuss implications these results may have on future modeling studies in this field and speculate about their relationship to neurodevelopmental physiology and pathophysiology.

The balance between excitation and inhibition in a neuronal network is considered to be an important predictor of neural excitability. Various processes are thought to maintain this balance across a range of stimuli/conditions. However, the developmental formation of this balance remains an open question, especially regarding the interplay between network blue-print (the spatial arrangement of excitatory and inhibitory nodes) and homeostatic processes. In this paper, we use a published model of activity-dependent growth to show that the E/I ratio alone cannot accurately predict system behaviour but rather it is the combination of this ratio and the underlying spatial arrangement of neurones that predict both activity in, and structure of, the resulting network. In particular, we highlight the particular role of clustered inter-inhibitory connectivity. We develop a measure that allows us to determine the relationship between inter-inhibitory connectivity clustering and system behaviour in an exhaustive list of spatial arrangements with a given fixed number of excitatory and inhibitory neurones. Our results reveal that, for a given E/I ratio, networks with high levels of inter-inhibitory clustering are more likely to experience oscillatory behaviour than networks with low levels, and we investigate the network attributes which characterise each global behaviour type produced by the model. We identify possible approaches for extensions of the current work, and discuss the implications these results may have on future modelling studies in this field.