Modelling herd immunity requirements in Queensland: impact of vaccination effectiveness, hesitancy and variants of SARS-CoV-2.

Long-term control of SARS-CoV-2 outbreaks depends on the widespread coverage of effective vaccines. In Australia, two-dose vaccination coverage of above 90% of the adult population was achieved. However, between August 2020 and August 2021, hesitancy fluctuated dramatically. This raised the question of whether settings with low naturally derived immunity, such as Queensland where less than [Formula: see text] of the population is known to have been infected in 2020, could have achieved herd immunity against 2021's variants of concern. To address this question, we used the agent-based model Covasim. We simulated outbreak scenarios (with the Alpha, Delta and Omicron variants) and assumed ongoing interventions (testing, tracing, isolation and quarantine). We modelled vaccination using two approaches with different levels of realism. Hesitancy was modelled using Australian survey data. We found that with a vaccine effectiveness against infection of 80%, it was possible to control outbreaks of Alpha, but not Delta or Omicron. With 90% effectiveness, Delta outbreaks may have been preventable, but not Omicron outbreaks. We also estimated that a decrease in hesitancy from 20% to 14% reduced the number of infections, hospitalizations and deaths by over 30%. Overall, we demonstrate that while herd immunity may not be attainable, modest reductions in hesitancy and increases in vaccine uptake may greatly improve health outcomes. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Herd immunity under individual variation and reinfection.

We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model.

LSTM-Based Prediction of COVID-19 Vaccination Drive in India

The vaccination drive for the much dangerous and contagious Coronavirus (COVID-19) has started successfully in India. This paper proposes to predict the vaccination drive of COVID-19 using the time series data for India. The proposed model was used for predicting the number of people to be vaccinated once per day in the country. The proposed model was compared with the direct input-based Long Short Term Memory (LSTM) cell model using various performance parameters and the proposed model was found to perform better. The actual closeness of the model's prediction from the actual data was depicted through line graphs. The proposed model was further used to predict the short-term and long-term future values. Herd immunity is another key ongoing research area when it comes to COVID-19. The Herd Immunity Threshold (HIT) of COVID-19 has not been found yet. However, this paper has proposed the expected number of days for different population thresholds. The proposed model predicts 174 days for obtaining a population threshold of 50% and 319 days for obtaining a population threshold of 90%. © 2021 IEEE.

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

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.

COVID-19 vaccine strategies for Aotearoa New Zealand: a mathematical modelling study.

Background: COVID-19 elimination measures, including border closures have been applied in New Zealand. We have modelled the potential effect of vaccination programmes for opening borders. Methods: We used a deterministic age-stratified Susceptible, Exposed, Infectious, Recovered (SEIR) model. We minimised spread by varying the age-stratified vaccine allocation to find the minimum herd immunity requirements (the effective reproduction number Reff<1 with closed borders) under various vaccine effectiveness (VE) scenarios and R0 values. We ran two-year open-border simulations for two vaccine strategies: minimising Reff and targeting high-risk groups. Findings: Targeting of high-risk groups will result in lower hospitalisations and deaths in most scenarios. Reaching the herd immunity threshold (HIT) with a vaccine of 90% VE against disease and 80% VE against infection requires at least 86•5% total population uptake for R0=4•5 (with high vaccination coverage for 30-49-year-olds) and 98•1% uptake for R0=6. In a two-year open-border scenario with 10 overseas cases daily and 90% total population vaccine uptake (including 0-15 year olds) with the same vaccine, the strategy of targeting high-risk groups is close to achieving HIT, with an estimated 11,400 total hospitalisations (peak 324 active and 36 new daily cases in hospitals), and 1,030 total deaths. Interpretation: Targeting high-risk groups for vaccination will result in fewer hospitalisations and deaths with open borders compared to targeting reduced transmission. With a highly effective vaccine and a high total uptake, opening borders will result in increasing cases, hospitalisations, and deaths. Other public health and social measures will still be required as part of an effective pandemic response. Funding: This project was funded by the Health Research Council [20/1018]. Research in context.

Vaccines and variants: Modelling insights into emerging issues in COVID-19 epidemiology.

Mathematical modelling has played a pivotal role in understanding the epidemiology of and guiding public health responses to the ongoing coronavirus disease of 2019 (COVID-19) pandemic. Here, we review the role of epidemiological models in understanding evolving epidemic characteristics, including the effects of vaccination and Variants of Concern (VoC). We highlight ways in which models continue to provide important insights, including (1) calculating the herd immunity threshold and evaluating its limitations; (2) verifying that nascent vaccines can prevent severe disease, infection, and transmission but may be less efficacious against VoC; (3) determining optimal vaccine allocation strategies under efficacy and supply constraints; and (4) determining that VoC are more transmissible and lethal than previously circulating strains, and that immune escape may jeopardize vaccine-induced herd immunity. Finally, we explore how models can help us anticipate and prepare for future stages of COVID-19 epidemiology (and that of other diseases) through forecasts and scenario projections, given current uncertainties and data limitations.