Estimating local outbreak risks and the effects of non-pharmaceutical interventions in age-structured populations: SARS-CoV-2 as a case study

Epidemiological feature analysis of SVEIR model with control strategy and variant evolution

The complex interactions were performed among non-pharmaceutical interventions, vaccinations, and hosts for all epidemics in mainland China during the spread of COVID-19. Specially, the small-scale epidemic in the city described by SVEIR model was less found in the current studies. The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures. In this study, the total population (N) of Jinzhou City was divided into five compartments: the susceptible (S), the vaccinated (V), the exposed (E), the infected (I), and the recovered (R). By surveillance data and the SVEIR model, three methods (maximum likelihood method, exponential growth rate method, next generation matrix method) were governed to estimate basic reproduction number, and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1. Meanwhile, the effective reproduction number for two epidemics were investigated by surveillance data, and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later, and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later. Moreover, the impacts of non-pharmaceutical interventions (awareness delay, peak delay, control intensity) were discussed extensively, the variations of infection scales for Omicron variant and EG.5 variant were also discussed. Furthermore, the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control. The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control, which provided a possible perspective on variant evolution in the future.

Non-pharmaceutical interventions to reduce COVID-19 transmission in the UK: a rapid mapping review and interactive evidence gap map

BACKGROUND

Non-pharmaceutical interventions (NPIs) were crucial in the response to the COVID-19 pandemic, although uncertainties about their effectiveness remain. This work aimed to better understand the evidence generated during the pandemic on the effectiveness of NPIs implemented in the UK.

METHODS

We conducted a rapid mapping review (search date: 1 March 2023) to identify primary studies reporting on the effectiveness of NPIs to reduce COVID-19 transmission. Included studies were displayed in an interactive evidence gap map.

RESULTS

After removal of duplicates, 11 752 records were screened. Of these, 151 were included, including 100 modelling studies but only 2 randomized controlled trials and 10 longitudinal observational studies.Most studies reported on NPIs to identify and isolate those who are or may become infectious, and on NPIs to reduce the number of contacts. There was an evidence gap for hand and respiratory hygiene, ventilation and cleaning.

CONCLUSIONS

Our findings show that despite the large number of studies published, there is still a lack of robust evaluations of the NPIs implemented in the UK. There is a need to build evaluation into the design and implementation of public health interventions and policies from the start of any future pandemic or other public health emergency.

Who acquires infection from whom? A sensitivity analysis of transmission dynamics during the early phase of the COVID-19 pandemic in Belgium

Age-related heterogeneity in a host population, whether due to how individuals mix and contact each other, the nature of host-pathogen interactions defining epidemiological parameters, or demographics, is crucial in studying infectious disease dynamics. Compartmental models represent a popular approach to address the problem, dividing the population of interest into a discrete and finite number of states depending on, for example, individuals' age and stage of infection. We study the corresponding linearised system whose operator, in the context of a discrete-time model, equates to a square matrix known as the next generation matrix. Performing formal perturbation analysis of the entries of the aforementioned matrix, we derive indices to quantify the age-specific variation of its dominant eigenvalue (i.e., the reproduction number) and explore the relevant epidemiological information we can derive from the eigenstructure of the matrix. The resulting method enables the assessment of the impact of age-related population heterogeneity on virus transmission. In particular, starting from an age-structured SEIR model, we demonstrate the use of this approach for COVID-19 dynamics in Belgium. We analyse the early stages of the SARS-CoV-2 spread, with particular attention to the pre-pandemic framework and the lockdown lifting phase initiated as of May 2020. Our results, influenced by our assumption on age-specific susceptibility and infectiousness, support the hypothesis that transmission was only influenced to a small extent by children in the age group [0,18) and adults over 60 years of age during the early phases of the pandemic and up to the end of July 2020.

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.

Workplace absenteeism due to COVID-19 and influenza across Canada: A mathematical model

The continual distress of COVID-19 cannot be overemphasized. The pandemic economic and social costs are alarming, with recent attributed economic loss amounting to billions of dollars globally. This economic loss is partly driven by workplace absenteeism due to the disease. Influenza is believed to be a culprit in reinforcing this phenomenon as it may exist in the population concurrently with COVID-19 during the influenza season. Furthermore, their joint infection may increase workplace absenteeism leading to additional economic loss. The objective of this project will aim to quantify the collective impact of COVID-19 and influenza on workplace absenteeism via a mathematical compartmental disease model incorporating population screening and vaccination. Our results indicate that appropriate PCR testing and vaccination of both COVID-19 and seasonal influenza may significantly alleviate workplace absenteeism. However, with COVID-19 PCR testing, there may be a critical threshold where additional tests may result in diminishing returns. Regardless, we recommend on-going PCR testing as a public health intervention accompanying concurrent COVID-19 and influenza vaccination with the added caveat that sensitivity analyses will be necessary to determine the optimal thresholds for both testing and vaccine coverage. Overall, our results suggest that rates of COVID-19 vaccination and PCR testing capacity are important factors for reducing absenteeism, while the influenza vaccination rate and the transmission rates for both COVID-19 and influenza have lower and almost equal affect on absenteeism. We also use the model to estimate and quantify the (indirect) benefit that influenza immunization confers against COVID-19 transmission.

A practical guide to mathematical methods for estimating infectious disease outbreak risks

Mathematical models are increasingly used throughout infectious disease outbreaks to guide control measures. In this review article, we focus on the initial stages of an outbreak, when a pathogen has just been observed in a new location (e.g., a town, region or country). We provide a beginner's guide to two methods for estimating the risk that introduced cases lead to sustained local transmission (i.e., the probability of a major outbreak), as opposed to the outbreak fading out with only a small number of cases. We discuss how these simple methods can be extended for epidemiological models with any level of complexity, facilitating their wider use, and describe how estimates of the probability of a major outbreak can be used to guide pathogen surveillance and control strategies. We also give an overview of previous applications of these approaches. This guide is intended to help quantitative researchers develop their own epidemiological models and use them to estimate the risks associated with pathogens arriving in new host populations. The development of these models is crucial for future outbreak preparedness. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Pandemic modelling for regions implementing an elimination strategy

During the COVID-19 pandemic, some countries, such as Australia, China, Iceland, New Zealand, Thailand, and Vietnam successfully implemented an elimination strategy, enacting strict border control and periods of lockdowns to end community transmission. Atlantic Canada and Canada's territories implemented similar policies, and reported long periods with no community cases. In Newfoundland and Labrador (NL), Nova Scotia, and Prince Edward Island a median of 80% or more of daily reported cases were travel-related from July 1, 2020 to May 31, 2021. With increasing vaccination coverage, it may be appropriate to exit an elimination strategy, but most existing epidemiological frameworks are applicable only to situations where most cases occur in the community, and are not appropriate for regions that have implemented an elimination strategy. To inform the pandemic response in regions that are implementing an elimination strategy, we extend importation modelling to consider post-arrival travel restrictions, and pharmaceutical and non-pharmaceutical interventions in the local community. We find that shortly after the Omicron variant had begun spreading in Canada, the expected daily number of spillovers, infections spread to NL community members from travellers and their close contacts, was higher than any time previously in the pandemic. By December 24, 2021, the expected number of spillovers was 44% higher than the previous high, which occurred in late July 2021 shortly after travel restrictions were first relaxed. We develop a method to assess the characteristics of potential future community outbreaks in regions that are implementing an elimination strategy. We apply this method to predict the effect of variant and vaccination coverage on the size of hypothetical community outbreaks in Mount Pearl, a suburb of the St. John's metropolitan area in NL. Our methodology can be used to evaluate alternative plans to relax public health restrictions when vaccine coverage is high in regions that have implemented an elimination strategy. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Projecting the COVID-19 immune landscape in Japan in the presence of waning immunity and booster vaccination

Coronavirus disease 2019 (COVID-19) booster vaccination has been implemented globally in the midst of surges in infection due to the Delta and Omicron variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The objective of the present study was to present a framework to estimate the proportion of the population that is immune to symptomatic SARS-CoV-2 infection with the Omicron variant (immune proportion) in Japan, considering the waning of immunity resulting from vaccination and naturally acquired infection. We quantified the decay rate of immunity against symptomatic infection with Omicron conferred by the second and third doses of COVID-19 vaccine. We estimated the current and future vaccination coverage for the second and third vaccine doses from February 17, 2021 to August 1, 2022 and used data on the confirmed COVID-19 incidence from February 17, 2021 to April 10, 2022. From this information, we estimated the age-specific immune proportion over the period from February 17, 2021 to August 1, 2022. Vaccine-induced immunity, conferred by the second vaccine dose in particular, was estimated to rapidly wane. There were substantial variations in the estimated immune proportion by age group because each age cohort experienced different vaccination rollout timing and speed as well as a different infection risk. Such variations collectively contributed to heterogeneous immune landscape trajectories over time and age. The resulting prediction of the proportion of the population that is immune to symptomatic SARS-CoV-2 infection could aid decision-making on when and for whom another round of booster vaccination should be considered. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants

Introduction

A key feature of the COVID-19 pandemic has been the emergence of SARS-CoV-2 variants with different transmission characteristics. However, when a novel variant arrives in a host population, it will not necessarily lead to many cases. Instead, it may fade out, due to stochastic effects and the level of immunity in the population. Immunity against novel SARS-CoV-2 variants may be influenced by prior exposures to related viruses, such as other SARS-CoV-2 variants and seasonal coronaviruses, and the level of cross-reactive immunity conferred by those exposures.

Methods

Here, we investigate the impact of cross-reactive immunity on the emergence of SARS-CoV-2 variants in a simplified scenario in which a novel SARS-CoV-2 variant is introduced after an antigenically related virus has spread in the population. We use mathematical modelling to explore the risk that the novel variant invades the population and causes a large number of cases, as opposed to fading out with few cases.

Results

We find that, if cross-reactive immunity is complete (i.e. someone infected by the previously circulating virus is not susceptible to the novel variant), the novel variant must be more transmissible than the previous virus to invade the population. However, in a more realistic scenario in which cross-reactive immunity is partial, we show that it is possible for novel variants to invade, even if they are less transmissible than previously circulating viruses. This is because partial cross-reactive immunity effectively increases the pool of susceptible hosts that are available to the novel variant compared to complete cross-reactive immunity. Furthermore, if previous infection with the antigenically related virus assists the establishment of infection with the novel variant, as has been proposed following some experimental studies, then even variants with very limited transmissibility are able to invade the host population.

Discussion

Our results highlight that fast assessment of the level of cross-reactive immunity conferred by related viruses against novel SARS-CoV-2 variants is an essential component of novel variant risk assessments.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The heterogeneous mixing model of COVID-19 with interventions

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