Using a household-structured branching process to analyse contact tracing in the SARS-CoV-2 pandemic

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.

Looking under the lamp-post: quantifying the performance of contact tracing in the United States during the SARS-CoV-2 pandemic

Contact tracing forms a crucial part of the public-health toolbox in mitigating and understanding emergent pathogens and nascent disease outbreaks. Contact tracing in the United States was conducted during the pre-Omicron phase of the ongoing COVID-19 pandemic. This tracing relied on voluntary reporting and responses, often using rapid antigen tests due to lack of accessibility to PCR tests. These limitations, combined with SARS-CoV-2's propensity for asymptomatic transmission, raise the question "how reliable was contact tracing for COVID-19 in the United States"? We answered this question using a Markov model to examine the efficiency with which transmission could be detected based on the design and response rates of contact tracing studies in the United States. Our results suggest that contact tracing protocols in the U.S. are unlikely to have identified more than 1.65% (95% uncertainty interval: 1.62-1.68%) of transmission events with PCR testing and 1.00% (95% uncertainty interval 0.98-1.02%) with rapid antigen testing. When considering a more robust contact tracing scenario, based on compliance rates in East Asia with PCR testing, this increases to 62.7% (95% uncertainty interval: 62.6-62.8%). We did not assume presence of asymptomatic transmission or superspreading, making our estimates upper bounds on the actual percentages traced. These findings highlight the limitations in interpretability for studies of SARS-CoV-2 disease spread based on U.S. contact tracing and underscore the vulnerability of the population to future disease outbreaks, for SARS-CoV-2 and other pathogens.

The impacts of spatial-temporal heterogeneity of human-to-human contacts on the extinction probability of infectious disease from branching process model

In this study, we focus on the impacts of spatial-temporal heterogeneity of human-to-human contacts on the spread of infectious diseases and develop a multi-type branching process model by introducing random human-to-human contact mode into a structured population. We provide the general formulas of the generation size, extinction probability, and basic reproduction number of the proposed branching process model. The result shows that the natural temporal heterogeneity (i.e. random contacts over time) can lead to a higher extinction probability while remains the same basic reproduction number and generation size. This is also numerically verified by choosing the real contact distributions from different circumstances of four countries. In addition, we observe a non-monotonic pattern of the differences, against the transmission probability and the mean contact rate, between the extinction probabilities under the constant and random contact patterns. Given the spatial heterogeneity, we show that it can contribute to the increase of basic reproduction number, but also increase the extinction probability of the infectious disease. This study adds novel insights to the course of the impact of heterogeneity on the transmission dynamics and also provides additional evidence for the limited role of reproduction numbers.

Diversity of symptom phenotypes in SARS-CoV-2 community infections observed in multiple large datasets

Variability in case severity and in the range of symptoms experienced has been apparent from the earliest months of the COVID-19 pandemic. From a clinical perspective, symptom variability might indicate various routes/mechanisms by which infection leads to disease, with different routes requiring potentially different treatment approaches. For public health and control of transmission, symptoms in community cases were the prompt upon which action such as PCR testing and isolation was taken. However, interpreting symptoms presents challenges, for instance, in balancing the sensitivity and specificity of individual symptoms with the need to maximise case finding, whilst managing demand for limited resources such as testing. For both clinical and transmission control reasons, we require an approach that allows for the possibility of distinct symptom phenotypes, rather than assuming variability along a single dimension. Here we address this problem by bringing together four large and diverse datasets deriving from routine testing, a population-representative household survey and participatory smartphone surveillance in the United Kingdom. Through the use of cutting-edge unsupervised classification techniques from statistics and machine learning, we characterise symptom phenotypes among symptomatic SARS-CoV-2 PCR-positive community cases. We first analyse each dataset in isolation and across age bands, before using methods that allow us to compare multiple datasets. While we observe separation due to the total number of symptoms experienced by cases, we also see a separation of symptoms into gastrointestinal, respiratory and other types, and different symptom co-occurrence patterns at the extremes of age. In this way, we are able to demonstrate the deep structure of symptoms of COVID-19 without usual biases due to study design. This is expected to have implications for the identification and management of community SARS-CoV-2 cases and could be further applied to symptom-based management of other diseases and syndromes.

Parameter estimation for contact tracing in graph-based models

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is R0. The estimator is tested in a simulation study and is furthermore applied to COVID-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical COVID-19 data, we compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution fit the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency of the estimates on the reproduction number. Finally, we discuss the relevance of our findings.

Assessment of a SARS-CoV-2 population-wide rapid antigen testing in Italy: a modeling and economic analysis study

BACKGROUND

This study aimed to compare the cost-effectiveness of coronavirus disease 2019 (COVID-19) mass testing, carried out in November 2020 in the Italian Bolzano/Südtirol province, to scenarios without mass testing in terms of hospitalizations averted and quality-adjusted life-year (QALYs) saved.

METHODS

We applied branching processes to estimate the effective reproduction number (Rt) and model scenarios with and without mass testing, assuming Rt = 0.9 and Rt = 0.95. We applied a bottom-up approach to estimate the costs of mass testing, with a mixture of bottom-up and top-down methodologies to estimate hospitalizations averted and incremental costs in case of non-intervention. Lastly, we estimated the incremental cost-effectiveness ratio (ICER), denoted by screening and related social costs, and hospitalization costs averted per outcome derived, hospitalizations averted and QALYs saved.

RESULTS

The ICERs per QALY were €24 249 under Rt = 0.9 and €4604 under Rt = 0.95, considering the official and estimated data on disease spread. The cost-effectiveness acceptability curves show that for the Rt = 0.9 scenario, at the maximum threshold willingness to pay the value of €40 000, mass testing has an 80% probability of being cost-effective compared to no mass testing. Under the worst scenario (Rt = 0.95), at the willingness to pay threshold, mass testing has an almost 100% probability of being cost-effective.

CONCLUSIONS

We provide evidence on the cost-effectiveness and potential impact of mass COVID-19 testing on a local healthcare system and community. Although the intervention is shown to be cost-effective, we believe the initiative should be carried out when there is initial rapid local disease transmission with a high Rt, as shown in our model.

Effectiveness of testing, contact tracing and isolation interventions among the general population on reducing transmission of SARS-CoV-2: a systematic review

We conducted a systematic literature review of general population testing, contact tracing, case isolation and contact quarantine interventions to assess their effectiveness in reducing SARS-CoV-2 transmission, as implemented in real-world settings. We designed a broad search strategy and aimed to identify peer-reviewed studies of any design provided there was a quantitative measure of effectiveness on a transmission outcome. Studies that assessed the effect of testing or diagnosis on disease outcomes via treatment, but did not assess a transmission outcome, were not included. We focused on interventions implemented among the general population rather than in specific settings; these were from anywhere in the world and published any time after 1 January 2020 until the end of 2022. From 26 720 titles and abstracts, 1181 were reviewed as full text, and 25 met our inclusion criteria. These 25 studies included one randomized control trial (RCT) and the remaining 24 analysed empirical data and made some attempt to control for confounding. Studies included were categorized by the type of intervention: contact tracing (seven studies); specific testing strategies (12 studies); strategies for isolating cases/contacts (four studies); and 'test, trace, isolate' (TTI) as a part of a package of interventions (two studies). None of the 25 studies were rated at low risk of bias and many were rated as serious risk of bias, particularly due to the likely presence of uncontrolled confounding factors, which was a major challenge in assessing the independent effects of TTI in observational studies. These confounding factors are to be expected from observational studies during an on-going pandemic, when the emphasis was on reducing the epidemic burden rather than trial design. Findings from these 25 studies suggested an important public health role for testing followed by isolation, especially where mass and serial testing was used to reduce transmission. Some of the most compelling analyses came from examining fine-grained within-country data on contact tracing; while broader studies which compared behaviour between countries also often found TTI led to reduced transmission and mortality, this was not universal. There was limited evidence for the benefit of isolation of cases/contacts away from the home environment. One study, an RCT, showed that daily testing of contacts could be a viable strategy to replace lengthy quarantine of contacts. Based on the scarcity of robust empirical evidence, we were not able to draw any firm quantitative conclusions about the quantitative impact of TTI interventions in different epidemic contexts. While the majority of studies found that testing, tracing and isolation reduced transmission, evidence for the scale of this impact is only available for specific scenarios and hence is not necessarily generalizable. Our review therefore emphasizes the need to conduct robust experimental studies that help inform the likely quantitative impact of different TTI interventions on transmission and their optimal design. Work is needed to support such studies in the context of future emerging epidemics, along with assessments of the cost-effectiveness of TTI interventions, which was beyond the scope of this review but will be critical to decision-making. This article is part of the theme issue 'The effectiveness of non-pharmaceutical interventions on the COVID-19 pandemic: the evidence'.

The value of manual backward contact tracing to control COVID-19 in practice, the Netherlands, February to March 2021: a pilot study

BackgroundContact tracing has been a key component of COVID-19 outbreak control. Backward contact tracing (BCT) aims to trace the source that infected the index case and, thereafter, the cases infected by the source. Modelling studies have suggested BCT will substantially reduce SARS-CoV-2 transmission in addition to forward contact tracing.AimTo assess the feasibility and impact of adding BCT in practice.MethodsWe identified COVID-19 cases who were already registered in the electronic database between 19 February and 10 March 2021 for routine contact tracing at the Public Health Service (PHS) of Rotterdam-Rijnmond, the Netherlands (pop. 1.3 million). We investigated if, through a structured questionnaire by dedicated contact tracers, we could trace additional sources and cases infected by these sources. Potential sources identified by the index were approached to trace the source's contacts. We evaluated the number of source contacts that could be additionally quarantined.ResultsOf 7,448 COVID-19 cases interviewed in the study period, 47% (n = 3,497) indicated a source that was already registered as a case in the PHS electronic database. A potential, not yet registered source was traced in 13% (n = 979). Backward contact tracing was possible in 62 of 979 cases, from whom an additional 133 potential sources were traced, and four were eligible for tracing of source contacts. Two additional contacts traced had to stay in quarantine for 1 day. No new COVID-19 cases were confirmed.ConclusionsThe addition of manual BCT to control the COVID-19 pandemic did not provide added value in our study setting.

Time between symptom and testing in relation to familial transmission of severe acute respiratory syndrome coronavirus 2

Brazil has a huge number of cases and deaths due to coronavirus disease 2019 (COVID-19); however, few studies have dealt with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection among familial contacts in Brazil. Here, we report our findings on transmission in a family-based study in Bauru, São Paulo, Brazil. The study, conducted from July to November 2020, comprised 974 individuals with 233 index patients and 741 familial contacts. Familial contacts were evaluated using the rapid COVID-19 Ag ECO and reverse transcription-polymerase chain reaction (RT-PCR) tests immediately after the index patient diagnosis. The antigen-based rapid test was validated in 121 individuals using RT-PCR as the gold standard. Additionally, 30 days later, familial contacts were evaluated for IgM and IgG antibodies against SARS-CoV-2. We found 333 cases of COVID-19 among familial contacts (44.9%). A positive correlation was observed between the time elapsed from the onset of symptoms until the index patient's COVID-19 testing and the number of family contacts infected by SARS-CoV-2. Early SARS-CoV-2 testing and familial contact evaluation are relevant strategies to contain transmission.

Modelling the impact of non-pharmaceutical interventions on workplace transmission of SARS-CoV-2 in the home-delivery sector

OBJECTIVE

We aimed to use mathematical models of SARS-COV-2 to assess the potential efficacy of non-pharmaceutical interventions on transmission in the parcel delivery and logistics sector.

METHODS

We devloped a network-based model of workplace contacts based on data and consultations from companies in the parcel delivery and logistics sectors. We used these in stochastic simulations of disease transmission to predict the probability of workplace outbreaks in this settings. Individuals in the model have different viral load trajectories based on SARS-CoV-2 in-host dynamics, which couple to their infectiousness and test positive probability over time, in order to determine the impact of testing and isolation measures.

RESULTS

The baseline model (without any interventions) showed different workplace infection rates for staff in different job roles. Based on our assumptions of contact patterns in the parcel delivery work setting we found that when a delivery driver was the index case, on average they infect only 0.14 other employees, while for warehouse and office workers this went up to 0.65 and 2.24 respectively. In the LIDD setting this was predicted to be 1.40, 0.98, and 1.34 respectively. Nonetheless, the vast majority of simulations resulted in 0 secondary cases among customers (even without contact-free delivery). Our results showed that a combination of social distancing, office staff working from home, and fixed driver pairings (all interventions carried out by the companies we consulted) reduce the risk of workplace outbreaks by 3-4 times.

CONCLUSION

This work suggests that, without interventions, significant transmission could have occured in these workplaces, but that these posed minimal risk to customers. We found that identifying and isolating regular close-contacts of infectious individuals (i.e. house-share, carpools, or delivery pairs) is an efficient measure for stopping workplace outbreaks. Regular testing can make these isolation measures even more effective but also increases the number of staff isolating at one time. It is therefore more efficient to use these isolation measures in addition to social distancing and contact reduction interventions, rather than instead of, as these reduce both transmission and the number of people needing to isolate at one time.

English tort law and the pandemic: the dog that has not barked

As of February 2023, no case has been reported in the U.K., either in the law reports or in the media, of a victim of COVID-19 suing in tort a person or organisation alleged to have caused the victim to contract the disease. This article considers the reasons this situation might have arisen. It provisionally concludes that the main legal reasons might lie in the applicable doctrines of factual causation and goes on to discuss whether uncertainty in those doctrines should be resolved in the courts.

Attitudes towards booster, testing and isolation, and their impact on COVID-19 response in winter 2022/2023 in France, Belgium, and Italy: a cross-sectional survey and modelling study

Background

European countries are focusing on testing, isolation, and boosting strategies to counter the 2022/2023 winter surge due to SARS-CoV-2 Omicron subvariants. However, widespread pandemic fatigue and limited compliance potentially undermine mitigation efforts.

Methods

To establish a baseline for interventions, we ran a multicountry survey to assess respondents’ willingness to receive booster vaccination and comply with testing and isolation mandates. Integrating survey and estimated immunity data in a branching process epidemic spreading model, we evaluated the effectiveness and costs of current protocols in France, Belgium, and Italy to manage the winter wave.

Findings

The vast majority of survey participants (N = 4594) was willing to adhere to testing (>91%) and rapid isolation (>88%) across the three countries. Pronounced differences emerged in the declared senior adherence to booster vaccination (73% in France, 94% in Belgium, 86% in Italy). Epidemic model results estimate that testing and isolation protocols would confer significant benefit in reducing transmission (17–24% reduction, from R = 1.6 to R = 1.3 in France and Belgium, to R = 1.2 in Italy) with declared adherence. Achieving a mitigating level similar to the French protocol, the Belgian protocol would require 35% fewer tests (from 1 test to 0.65 test per infected person) and avoid the long isolation periods of the Italian protocol (average of 6 days vs. 11). A cost barrier to test would significantly decrease adherence in France and Belgium, undermining protocols’ effectiveness.

Interpretation

Simpler mandates for isolation may increase awareness and actual compliance, reducing testing costs, without compromising mitigation. High booster vaccination uptake remains key for the control of the winter wave.

Funding

The 10.13039/501100000780European Commission, ANRS–Maladies Infectieuses Émergentes, the Agence Nationale de la Recherche, the Chaires Blaise Pascal Program of the Île-de-France region.

Comparative effectiveness of contact tracing interventions in the context of the COVID-19 pandemic: a systematic review

Contact tracing is a non-pharmaceutical intervention (NPI) widely used in the control of the COVID-19 pandemic. Its effectiveness may depend on a number of factors including the proportion of contacts traced, delays in tracing, the mode of contact tracing (e.g. forward, backward or bidirectional contact training), the types of contacts who are traced (e.g. contacts of index cases or contacts of contacts of index cases), or the setting where contacts are traced (e.g. the household or the workplace). We performed a systematic review of the evidence regarding the comparative effectiveness of contact tracing interventions. 78 studies were included in the review, 12 observational (ten ecological studies, one retrospective cohort study and one pre-post study with two patient cohorts) and 66 mathematical modelling studies. Based on the results from six of the 12 observational studies, contact tracing can be effective at controlling COVID-19. Two high quality ecological studies showed the incremental effectiveness of adding digital contact tracing to manual contact tracing. One ecological study of intermediate quality showed that increases in contact tracing were associated with a drop in COVID-19 mortality, and a pre-post study of acceptable quality showed that prompt contact tracing of contacts of COVID-19 case clusters / symptomatic individuals led to a reduction in the reproduction number R. Within the seven observational studies exploring the effectiveness of contact tracing in the context of the implementation of other non-pharmaceutical interventions, contact tracing was found to have an effect on COVID-19 epidemic control in two studies and not in the remaining five studies. However, a limitation in many of these studies is the lack of description of the extent of implementation of contact tracing interventions. Based on the results from the mathematical modelling studies, we identified the following highly effective policies: (1) manual contact tracing with high tracing coverage and either medium-term immunity, highly efficacious isolation/quarantine and/ or physical distancing (2) hybrid manual and digital contact tracing with high app adoption with highly effective isolation/ quarantine and social distancing, (3) secondary contact tracing, (4) eliminating contact tracing delays, (5) bidirectional contact tracing, (6) contact tracing with high coverage in reopening educational institutions. We also highlighted the role of social distancing to enhance the effectiveness of some of these interventions in the context of 2020 lockdown reopening. While limited, the evidence from observational studies shows a role for manual and digital contact tracing in controlling the COVID-19 epidemic. More empirical studies accounting for the extent of contact tracing implementation are required.

Modelling the impact of repeat asymptomatic testing policies for staff on SARS-CoV-2 transmission potential

Repeat asymptomatic testing in order to identify and quarantine infectious individuals has become a widely-used intervention to control SARS-CoV-2 transmission. In some workplaces, and in particular health and social care settings with vulnerable patients, regular asymptomatic testing has been deployed to staff to reduce the likelihood of workplace outbreaks. We have developed a model based on data available in the literature to predict the potential impact of repeat asymptomatic testing on SARS-CoV-2 transmission. The results highlight features that are important to consider when modelling testing interventions, including population heterogeneity of infectiousness and correlation with test-positive probability, as well as adherence behaviours in response to policy. Furthermore, the model based on the reduction in transmission potential presented here can be used to parameterise existing epidemiological models without them having to explicitly simulate the testing process. Overall, we find that even with different model paramterisations, in theory, regular asymptomatic testing is likely to be a highly effective measure to reduce transmission in workplaces, subject to adherence. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Public perceptions and interactions with UK COVID-19 Test, Trace and Isolate policies, and implications for pandemic infectious disease modelling

Background The efforts to contain SARS-CoV-2 and reduce the impact of the COVID-19 pandemic have been supported by Test, Trace and Isolate (TTI) systems in many settings, including the United Kingdom. Mathematical models of transmission and TTI interventions, used to inform design and policy choices, make assumptions about the public’s behaviour in the context of a rapidly unfolding and changeable emergency. This study investigates public perceptions and interactions with UK TTI policy in July 2021, assesses them against how TTI processes are conceptualised and represented in models, and then interprets the findings with modellers who have been contributing evidence to TTI policy. Methods 20 members of the public recruited via social media were interviewed for one hour about their perceptions and interactions with the UK TTI system. Thematic analysis identified key themes, which were then presented back to a workshop of pandemic infectious disease modellers who assessed these findings against assumptions made in TTI intervention modelling. Workshop members co-drafted this report. Results Themes included education about SARS-CoV-2, perceived risks, trust, mental health and practical concerns. Findings covered testing practices, including the uses of and trust in different types of testing, and the challenges of testing and isolating faced by different demographic groups. This information was judged as consequential to the modelling process, from guiding the selection of research questions, influencing choice of model structure, informing parameter ranges and validating or challenging assumptions, to highlighting where model assumptions are reasonable or where their poor reflection of practice might lead to uninformative results. Conclusions We conclude that deeper engagement with members of the public should be integrated at regular stages of public health intervention modelling.

Kombe I, Ojal J, Parisi A, Keeling MJ, Nokes DJ, Manson-Sawko R, House T. A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

Empirical evidence on the efficiency of backward contact tracing in COVID-19

Standard contact tracing practice for COVID-19 is to identify persons exposed to an infected person during the contagious period, assumed to start two days before symptom onset or diagnosis. In the first large cohort study on backward contact tracing for COVID-19, we extended the contact tracing window by 5 days, aiming to identify the source of the infection and persons infected by the same source. The risk of infection amongst these additional contacts was similar to contacts exposed during the standard tracing window and significantly higher than symptomatic individuals in a control group, leading to 42% more cases identified as direct contacts of an index case. Compared to standard practice, backward traced contacts required fewer tests and shorter quarantine. However, they were identified later in their infectious cycle if infected. Our results support implementing backward contact tracing when rigorous suppression of viral transmission is warranted.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

A Review of Using Mathematical Modeling to Improve Our Understanding of Bacteriophage, Bacteria, and Eukaryotic Interactions

Phage therapy, the therapeutic usage of viruses to treat bacterial infections, has many theoretical benefits in the ‘post antibiotic era.’ Nevertheless, there are currently no approved mainstream phage therapies. One reason for this is a lack of understanding of the complex interactions between bacteriophage, bacteria and eukaryotic hosts. These three-component interactions are complex, with non-linear or synergistic relationships, anatomical barriers and genetic or phenotypic heterogeneity all leading to disparity between performance and efficacy in in vivo versus in vitro environments. Realistic computer or mathematical models of these complex environments are a potential route to improve the predictive power of in vitro studies for the in vivo environment, and to streamline lab work. Here, we introduce and review the current status of mathematical modeling and highlight that data on genetic heterogeneity and mutational stochasticity, time delays and population densities could be critical in the development of realistic phage therapy models in the future. With this in mind, we aim to inform and encourage the collaboration and sharing of knowledge and expertise between microbiologists and theoretical modelers, synergising skills and smoothing the road to regulatory approval and widespread use of phage therapy.

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'.