Modelling the epidemiological implications for SARS-CoV-2 of Christmas household bubbles in England.

The emergence of SARS-CoV-2 saw severe detriments to public health being inflicted by COVID-19 disease throughout 2020. In the lead up to Christmas 2020, the UK Government sought an easement of social restrictions that would permit spending time with others over the Christmas period, whilst limiting the risk of spreading SARS-CoV-2. In November 2020, plans were published to allow individuals to socialise within 'Christmas bubbles' with friends and family. This policy involved a planned easing of restrictions in England between 23-27 December 2020, with Christmas bubbles allowing people from up to three households to meet throughout the holiday period. We estimated the epidemiological impact of both this and alternative bubble strategies that allowed extending contacts beyond the immediate household. We used a stochastic individual-based model for a synthetic population of 100,000 households, with demographic and SARS-CoV-2 epidemiological characteristics comparable to England as of November 2020. We evaluated five Christmas bubble scenarios for the period 23-27 December 2020, assuming our populations of households did not have symptomatic infection present and were not in isolation as the eased social restrictions began. Assessment comprised incidence and cumulative infection metrics. We tested the sensitivity of the results to a situation where it was possible for households to be in isolation at the beginning of the Christmas bubble period and also when there was lower adherence to testing, contact tracing and isolation interventions. We found that visiting family and friends over the holiday period for a shorter duration and in smaller groups was less risky than spending the entire five days together. The increases in infection from greater amounts of social mixing disproportionately impacted the eldest. We provide this account as an illustration of a real-time contribution of modelling insights to a scientific advisory group, the Scientific Pandemic Influenza Group on Modelling, Operational sub-group (SPI-M-O) for the Scientific Advisory Group for Emergencies (SAGE) in the UK, during the COVID-19 pandemic. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Area-level socioeconomic deprivation, non-national residency, and Covid-19 incidence: A longitudinal spatiotemporal analysis in Germany.

Background: Socioeconomic conditions affect the dynamics of the Covid-19 pandemic. We analysed the association between area-level socioeconomic deprivation, proportion of non-nationals, and incidence of Covid-19 infections in Germany. Methods: Using linked nationally representative data at the level of 401 German districts from three waves of infection (January-2020 to May-2021), we fitted Bayesian spatiotemporal models to assess the association between socioeconomic deprivation, and proportion of non-nationals with Covid-19 incidence, controlling for age, sex, vaccination coverage, settlement structure, and spatial and temporal effects. We estimated risk ratios (RR) and corresponding 95% credible intervals (95% CrI). We further examined the deprivation domains (education, income, occupation), interactions between deprivation, sex and the proportion of non-nationals, and explored potential pathways from deprivation to Covid-19 incidence. Findings: Covid-19 incidence risk was 15% higher (RR=1·15, 95%-CrI=1·06-1·24) in areas classified with the highest deprivation quintile (Q5) compared to the least deprived areas (Q1). Medium-low (Q2), medium (Q3), and medium-high (Q4) deprived districts showed 6% (1·06, 1·00-1·12), 8% (1·08, 1·01-1·15), and 5% (1·05, 0·98-1·13) higher risk, respectively, compared to the least deprived. Districts with higher proportion of non-nationals showed higher incidence risk compared to districts with lowest proportion, but the association weakened across the three waves. During the first wave, an inverse association was observed with highest incidence risk in least deprived areas (Q1). Deprivation interacted with sex, but not with the proportion of non-nationals. Interpretation: Socioeconomic deprivation, and proportion of non-nationals are independently associated with the incidence of Covid-19. Regional planning of non-pharmaceutical interventions and vaccination strategies would benefit from consideration of area-level deprivation and non-national residency. Funding: The study was funded by the German Ministry of Health (ZMV I 1 - 25 20 COR 410).

Data pipelines in a public health emergency: The human in the machine.

In an emergency epidemic response, data providers supply data on a best-faith effort to modellers and analysts who are typically the end user of data collected for other primary purposes such as to inform patient care. Thus, modellers who analyse secondary data have limited ability to influence what is captured. During an emergency response, models themselves are often under constant development and require both stability in their data inputs and flexibility to incorporate new inputs as novel data sources become available. This dynamic landscape is challenging to work with. Here we outline a data pipeline used in the ongoing COVID-19 response in the UK that aims to address these issues. A data pipeline is a sequence of steps to carry the raw data through to a processed and useable model input, along with the appropriate metadata and context. In ours, each data type had an individual processing report, designed to produce outputs that could be easily combined and used downstream. Automated checks were in-built and added as new pathologies emerged. These cleaned outputs were collated at different geographic levels to provide standardised datasets. Finally, a human validation step was an essential component of the analysis pathway and permitted more nuanced issues to be captured. This framework allowed the pipeline to grow in complexity and volume and facilitated the diverse range of modelling approaches employed by researchers. Additionally, every report or modelling output could be traced back to the specific data version that informed it ensuring reproducibility of results. Our approach has been used to facilitate fast-paced analysis and has evolved over time. Our framework and its aspirations are applicable to many settings beyond COVID-19 data, for example for other outbreaks such as Ebola, or where routine and regular analyses are required.

On the interplay of regional mobility, social connectedness and the spread of COVID-19 in Germany.

Since the primary mode of respiratory virus transmission is person-to-person interaction, we are required to reconsider physical interaction patterns to mitigate the number of people infected with COVID-19. While research has shown that non-pharmaceutical interventions (NPI) had an evident impact on national mobility patterns, we investigate the relative regional mobility behaviour to assess the effect of human movement on the spread of COVID-19. In particular, we explore the impact of human mobility and social connectivity derived from Facebook activities on the weekly rate of new infections in Germany between 3 March and 22 June 2020. Our results confirm that reduced social activity lowers the infection rate, accounting for regional and temporal patterns. The extent of social distancing, quantified by the percentage of people staying put within a federal administrative district, has an overall negative effect on the incidence of infections. Additionally, our results show spatial infection patterns based on geographical as well as social distances.

Voluntary risk mitigation behaviour can reduce impact of SARS-CoV-2: a real-time modelling study of the January 2022 Omicron wave in England.

BACKGROUND: Predicting the likely size of future SARS-CoV-2 waves is necessary for public health planning. In England, voluntary "plan B" mitigation measures were introduced in December 2021 including increased home working and face coverings in shops but stopped short of restrictions on social contacts. The impact of voluntary risk mitigation behaviours on future SARS-CoV-2 burden is unknown. METHODS: We developed a rapid online survey of risk mitigation behaviours ahead of the winter 2021 festive period and deployed in two longitudinal cohort studies in the UK (Avon Longitudinal Study of Parents and Children (ALSPAC) and TwinsUK/COVID Symptom Study (CSS) Biobank) in December 2021. Using an individual-based, probabilistic model of COVID-19 transmission between social contacts with SARS-CoV-2 Omicron variant parameters and realistic vaccine coverage in England, we predicted the potential impact of the SARS-CoV-2 Omicron wave in England in terms of the effective reproduction number and cumulative infections, hospital admissions and deaths. Using survey results, we estimated in real-time the impact of voluntary risk mitigation behaviours on the Omicron wave in England, if implemented for the entire epidemic wave. RESULTS: Over 95% of survey respondents (NALSPAC = 2686 and NTwins = 6155) reported some risk mitigation behaviours, with vaccination and using home testing kits reported most frequently. Less than half of those respondents reported that their behaviour was due to "plan B". We estimate that without risk mitigation behaviours, the Omicron variant is consistent with an effective reproduction number between 2.5 and 3.5. Due to the reduced vaccine effectiveness against infection with the Omicron variant, our modelled estimates suggest that between 55% and 60% of the English population could be infected during the current wave, translating into between 12,000 and 46,000 cumulative deaths, depending on assumptions about severity and vaccine effectiveness. The actual number of deaths was 15,208 (26 November 2021-1 March 2022). We estimate that voluntary risk reduction measures could reduce the effective reproduction number to between 1.8 and 2.2 and reduce the cumulative number of deaths by up to 24%. CONCLUSIONS: Predicting future infection burden is affected by uncertainty in disease severity and vaccine effectiveness estimates. In addition to biological uncertainty, we show that voluntary measures substantially reduce the projected impact of the SARS-CoV-2 Omicron variant but that voluntary measures alone would be unlikely to completely control transmission.

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.

Predicting epidemics and the impact of interventions in heterogeneous settings: Standard SEIR models are too pessimistic

The basic reproduction number (R0) is an established concept to describe the potential for an infectious disease to cause an epidemic and to derive estimates of the required effect of interventions for successful control. Calculating R0 from simple deterministic transmission models may result in biased estimates when important sources of heterogeneity related to transmission and control are ignored. Using stochastic simulations with a geographically stratified individual-based SEIR (susceptible, exposed, infectious, recovered) model, we illustrate that if heterogeneity is ignored (i.e. no or too little assumed interindividual variation or assortative mixing) this may substantially overestimate the transmission rate and the potential course of the epidemic. Consequently, predictions for the impact of interventions then become relatively pessimistic. However, should such an intervention be suspended, then the potential for a consecutive epidemic wave will depend strongly on assumptions about heterogeneity, with more heterogeneity resulting in lower remaining epidemic potential, due to selection and depletion of high-risk individuals during the early stages of the epidemic. These phenomena have likely also affected current model predictions regarding COVID-19, as most transmission models assume homogeneous mixing or at most employ a simple age stratification, thereby leading to overcautious predictions of durations of lockdowns and required vaccine coverage levels. © 2022 The Authors. Journal of the Royal Statistical Society: Series A (Statistics in Society) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society.

Learning transmission dynamics modelling of COVID-19 using comomodels.

The COVID-19 epidemic continues to rage in many parts of the world. In the UK alone, an array of mathematical models have played a prominent role in guiding policymaking. Whilst considerable pedagogical material exists for understanding the basics of transmission dynamics modelling, there is a substantial gap between the relatively simple models used for exposition of the theory and those used in practice to model the transmission dynamics of COVID-19. Understanding these models requires considerable prerequisite knowledge and presents challenges to those new to the field of epidemiological modelling. In this paper, we introduce an open-source R package, comomodels, which can be used to understand the complexities of modelling the transmission dynamics of COVID-19 through a series of differential equation models. Alongside the base package, we describe a host of learning resources, including detailed tutorials and an interactive web-based interface allowing dynamic investigation of the model properties. We then use comomodels to illustrate three key lessons in the transmission of COVID-19 within R Markdown vignettes.

Reducing disease spread through optimization: Limiting mixture of the population is more important than limiting group sizes

One of the most efficient tools for limiting the disease spread during a pandemic is to limit the contacts between people. However, too strict restrictions may seriously affect the economy, health, education, and well-being of people. Hence, in this paper we study the use of individualized strategies instead of uniform restrictions for the organisation of activities that include close contacts. Concretely, we study how to schedule a set of activities where the participants meet, and hence can spread infection. Those could be classroom teaching, sports activities, work shifts, etc. Formulating the contacts resulting from the assignment of participants to scheduled activities as a graph, we propose to search for graph structures that limit the disease spread. We develop a mathematical algorithm for identifying such favorable graphs by limiting the distinct contacts the individuals meet during an activity. The quality of a contact graph is evaluated using an agent-based model where individual disease progress is defined according to the so-called SEIR (Susceptible, Exposed, Infectious or Removed) model. A computational study targeted towards the re-opening of physical lecturing at a major university, using real-life data from a course database, demonstrates the ability of this algorithm to limit the spread of a disease under several realistic setups, and shows that the infection can be significantly reduced while also limiting the part of population in quarantine when using this algorithm versus just a general group size limitation. Specifically, it shows that individualized re-opening strategies that limit the mixing of populations can be more powerful in reducing disease spread than limiting group size.

COVID-19 Seroprevalence in Canada Modelling Waning and Boosting COVID-19 Immunity in Canada a Canadian Immunization Research Network Study.

COVID-19 seroprevalence changes over time, with infection, vaccination, and waning immunity. Seroprevalence estimates are needed to determine when increased COVID-19 vaccination coverage is needed, and when booster doses should be considered, to reduce the spread and disease severity of COVID-19 infection. We use an age-structured model including infection, vaccination and waning immunity to estimate the distribution of immunity to COVID-19 in the Canadian population. This is the first mathematical model to do so. We estimate that 60-80% of the Canadian population has some immunity to COVID-19 by late Summer 2021, depending on specific characteristics of the vaccine and the waning rate of immunity. Models results indicate that increased vaccination uptake in age groups 12-29, and booster doses in age group 50+ are needed to reduce the severity COVID-19 Fall 2021 resurgence.

Comparing approaches for modelling indirect contact transmission of infectious diseases.

Mathematical models describing indirect contact transmission are an important component of infectious disease mitigation and risk assessment. A model that tracks microorganisms between compartments by coupled ordinary differential equations or a Markov chain is benchmarked against a mechanistic interpretation of the physical transfer of microorganisms from surfaces to fingers and subsequently to a susceptible person's facial mucosal membranes. The primary objective was to compare these models in their estimates of doses and changes in microorganism concentrations on hands and fomites over time. The abilities of the models to capture the impact of episodic events, such as hand hygiene, and of contact patterns were also explored. For both models, greater doses were estimated for the asymmetrical scenarios in which a more contaminated fomite was touched more often. Differing representations of hand hygiene in the Markov model did not notably impact estimated doses but affected pathogen concentration dynamics on hands. When using the Markov model, losses due to hand hygiene should be handled as separate events as opposed to time-averaging expected losses. The discrete event model demonstrated the effect of hand-to-mouth contact timing on the dose. Understanding how model design influences estimated doses is important for advancing models as reliable risk assessment tools.

Modelling the impact of shutdowns on resurging SARS-CoV-2 transmission in Canada.

BACKGROUND: Shutdowns are enacted when alternative public health measures are insufficient to control the epidemic and the population is largely susceptible. An age-stratified agent-based model was developed to explore the impact of shutdowns to control SARS-CoV-2 transmission in Canada under the assumption that current efforts to control the epidemic remains insufficient and in the absence of a vaccine. METHODS: We estimated the current levels of interventions in Canada to generate a baseline scenario from 7 February to 7 September 2020. Four aspects of shutdowns were explored in scenarios that ran from 8 September 2020 to 7 January 2022, these included the impact of how quickly shutdowns are implemented, the duration of shutdowns, the minimum break (delays) between shutdowns and the types of sectors to shutdown. Comparisons among scenarios were made using cases, hospitalizations, deaths and shutdown days during the 700-day model runs. RESULTS: We found a negative relationship between reducing SARS-CoV-2 transmission and the number of shutdown days. However, we also found that for shutdowns to be optimally effective, they need to be implemented fast with minimal delay, initiated when community transmission is low, sustained for an adequate period and be stringent and target multiple sectors, particularly those driving transmission. By applying shutdowns in this manner, the total number of shutdown days could be reduced compared to delaying the shutdowns until further into the epidemic when transmission is higher and/or implementing short insufficient shutdowns that would require frequent re-implementation. This paper contrasts a range of shutdown strategies and trade-offs between health outcomes and economic metrics that need to be considered within the local context. INTERPRETATION: Given the immense socioeconomic impact of shutdowns, they should be avoided where possible and used only when other public health measures are insufficient to control the epidemic. If used, the time it buys to delay the epidemic should be used to enhance other equally effective, but less disruptive, public health measures.

COVID-19 modelling by time-varying transmission rate associated with mobility trend of driving via Apple Maps.

Compartment-based infectious disease models that consider the transmission rate (or contact rate) as a constant during the course of an epidemic can be limiting regarding effective capture of the dynamics of infectious disease. This study proposed a novel approach based on a dynamic time-varying transmission rate with a control rate governing the speed of disease spread, which may be associated with the information related to infectious disease intervention. Integration of multiple sources of data with disease modelling has the potential to improve modelling performance. Taking the global mobility trend of vehicle driving available via Apple Maps as an example, this study explored different ways of processing the mobility trend data and investigated their relationship with the control rate. The proposed method was evaluated based on COVID-19 data from six European countries. The results suggest that the proposed model with dynamic transmission rate improved the performance of model fitting and forecasting during the early stage of the pandemic. Positive correlation has been found between the average daily change of mobility trend and control rate. The results encourage further development for incorporation of multiple resources into infectious disease modelling in the future.

Modelling that shaped the early COVID-19 pandemic response in the UK.

Infectious disease modelling has played an integral part of the scientific evidence used to guide the response to the COVID-19 pandemic. In the UK, modelling evidence used for policy is reported to the Scientific Advisory Group for Emergencies (SAGE) modelling subgroup, SPI-M-O (Scientific Pandemic Influenza Group on Modelling-Operational). This Special Issue contains 20 articles detailing evidence that underpinned advice to the UK government during the SARS-CoV-2 pandemic in the UK between January 2020 and July 2020. Here, we introduce the UK scientific advisory system and how it operates in practice, and discuss how infectious disease modelling can be useful in policy making. We examine the drawbacks of current publishing practices and academic credit and highlight the importance of transparency and reproducibility during an epidemic emergency. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Monitoring the spatiotemporal epidemiology of Covid-19 incidence and mortality: A small-area analysis in Germany.

Timely monitoring of incidence risks of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and associated deaths at small-area level is essential to inform containment strategies. We analysed the spatiotemporal epidemiology of the SARSCoV- 2 pandemic at district level in Germany to develop a tool for disease monitoring. We used a Bayesian spatiotemporal model to estimate the district-specific risk ratios (RR) of SARS-CoV-2 incidence and the posterior probability (PP) for exceedance of RR thresholds 1, 2 or 3. Of 220 districts (55% of 401 districts) showing a RR > 1, 188 (47%) exceed the RR threshold with sufficient certainty (PP ≥ 80%) to be considered at high risk. 47 districts show very high (RR > 2, PP ≥ 80%) and 15 extremely high (RR > 3, PP ≥ 80%) risks. The spatial approach for monitoring the risk of SARS-CoV-2 provides an informative basis for local policy planning.

Epidemiological characteristics of COVID-19 cases and estimates of the reproductive numbers 1 month into the epidemic, Italy, 28 January to 31 March 2020.

BackgroundOn 20 February 2020, a locally acquired coronavirus disease (COVID-19) case was detected in Lombardy, Italy. This was the first signal of ongoing transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the country. The number of cases in Italy increased rapidly and the country became the first in Europe to experience a SARS-CoV-2 outbreak.AimOur aim was to describe the epidemiology and transmission dynamics of the first COVID-19 cases in Italy amid ongoing control measures.MethodsWe analysed all RT-PCR-confirmed COVID-19 cases reported to the national integrated surveillance system until 31 March 2020. We provide a descriptive epidemiological summary and estimate the basic and net reproductive numbers by region.ResultsOf the 98,716 cases of COVID-19 analysed, 9,512 were healthcare workers. Of the 10,943 reported COVID-19-associated deaths (crude case fatality ratio: 11.1%) 49.5% occurred in cases older than 80 years. Male sex and age were independent risk factors for COVID-19 death. Estimates of R0 varied between 2.50 (95% confidence interval (CI): 2.18-2.83) in Tuscany and 3.00 (95% CI: 2.68-3.33) in Lazio. The net reproduction number Rt in northern regions started decreasing immediately after the first detection.ConclusionThe COVID-19 outbreak in Italy showed a clustering onset similar to the one in Wuhan, China. R0 at 2.96 in Lombardy combined with delayed detection explains the high case load and rapid geographical spread. Overall, Rt in Italian regions showed early signs of decrease, with large diversity in incidence, supporting the importance of combined non-pharmacological control measures.

Reconciling model predictions with low reported cases of COVID-19 in Sub-Saharan Africa: insights from Madagascar.

COVID-19 has wreaked havoc globally with particular concerns for sub-Saharan Africa (SSA), where models suggest that the majority of the population will become infected. Conventional wisdom suggests that the continent will bear a higher burden of COVID-19 for the same reasons it suffers from other infectious diseases: ecology, socio-economic conditions, lack of water and sanitation infrastructure, and weak health systems. However, so far SSA has reported lower incidence and fatalities compared to the predictions of standard models and the experience of other regions of the world. There are three leading explanations, each with different implications for the final epidemic burden: (1) low case detection, (2) differences in epidemiology (e.g. low R 0 ), and (3) policy interventions. The low number of cases have led some SSA governments to relaxing these policy interventions. Will this result in a resurgence of cases? To understand how to interpret the lower-than-expected COVID-19 case data in Madagascar, we use a simple age-structured model to explore each of these explanations and predict the epidemic impact associated with them. We show that the incidence of COVID-19 cases as of July 2020 can be explained by any combination of the late introduction of first imported cases, early implementation of non-pharmaceutical interventions (NPIs), and low case detection rates. We then re-evaluate these findings in the context of the COVID-19 epidemic in Madagascar through August 2020. This analysis reinforces that Madagascar, along with other countries in SSA, remains at risk of a growing health crisis. If NPIs remain enforced, up to 50,000 lives may be saved. Even with NPIs, without vaccines and new therapies, COVID-19 could infect up to 30% of the population, making it the largest public health threat in Madagascar for the coming year, hence the importance of clinical trials and continually improving access to healthcare.