Backtracking: Improved methods for identifying the source of a deliberate release of Bacillus anthracis from the temporal and spatial distribution of cases.

Reverse epidemiology is a mathematical modelling tool used to ascertain information about the source of a pathogen, given the spatial and temporal distribution of cases, hospitalisations and deaths. In the context of a deliberately released pathogen, such as Bacillus anthracis (the disease-causing organism of anthrax), this can allow responders to quickly identify the location and timing of the release, as well as other factors such as the strength of the release, and the realized wind speed and direction at release. These estimates can then be used to parameterise a predictive mechanistic model, allowing for estimation of the potential scale of the release, and to optimise the distribution of prophylaxis. In this paper we present two novel approaches to reverse epidemiology, and demonstrate their utility in responding to a simulated deliberate release of B. anthracis in ten locations in the UK and compare these to the standard grid-search approach. The two methods-a modified MCMC and a Recurrent Convolutional Neural Network-are able to identify the source location and timing of the release with significantly better accuracy compared to the grid-search approach. Further, the neural network method is able to do inference on new data significantly quicker than either the grid-search or novel MCMC methods, allowing for rapid deployment in time-sensitive outbreaks.

Using mixture density networks to emulate a stochastic within-host model of Francisella tularensis infection.

For stochastic models with large numbers of states, analytical techniques are often impractical, and simulations time-consuming and computationally demanding. This limitation can hinder the practical implementation of such models. In this study, we demonstrate how neural networks can be used to develop emulators for two outputs of a stochastic within-host model of Francisella tularensis infection: the dose-dependent probability of illness and the incubation period. Once the emulators are constructed, we employ Markov Chain Monte Carlo sampling methods to parameterize the within-host model using records of human infection. This inference is only possible through the use of a mixture density network to emulate the incubation period, providing accurate approximations of the corresponding probability distribution. Notably, these estimates improve upon previous approaches that relied on bacterial counts from the lungs of macaques. Our findings reveal a 50% infectious dose of approximately 10 colony-forming units and we estimate that the incubation period can last for up to 11 days following low dose exposure.

Simplified within-host and Dose-response Models of SARS-CoV-2.

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

Check your assumptions: Further scrutiny of basic model frameworks of antimicrobial resistance.

Since the mid-1990s, growing concerns over antimicrobial resistant (AMR) organisms has led to an increase in the use of mathematical models to explore the inter-host transmission of such infections. Previous work reviewing such models categorised them into generic frameworks based on their underlying assumptions. These assumptions dictated the coexistence between AMR and antimicrobial sensitive strains. We add to this work performing stability analyses of the frameworks, along with simulating them deterministically and stochastically. Stability analyses found that many of these assumptions lead to models having the same equilibria, but showed differences in the equilibria's stability between models. Deterministic simulations reveal that assuming replacement of one infecting strain by another leads to an unusual antimicrobial treatment threshold. Increasing beyond this threshold causes a discontinuous increase in disease burden. The cost of AMR to pathogen fitness (lowered transmission) dictates both the threshold of treatment that causes the discontinuous increase in disease burden and the size of that increase. It was also shown that Superinfection states can be biased against resident strains and so favour coexistence of both strains. Stochastic simulations demonstrated that differing scenario starting conditions can guide models to converge upon equilibria that they may not have under deterministic simulation. These findings highlight the importance of checking assumptions when modelling AMR and strain competition more widely.

What effect might border screening have on preventing importation of COVID-19 compared with other infections?: considering the additional effect of post-arrival isolation.

We recently described a simple model through which we assessed what effect subjecting travellers to a single on-arrival test might have on reducing risk of importing disease cases during simulated outbreaks of coronavirus disease 2019 (COVID-19), influenza, severe acute respiratory syndrome (SARS) and Ebola. We build upon this work to allow for the additional requirement that inbound travellers also undergo a period of self-isolation upon arrival, where upon completion the traveller is again tested for signs of infection prior to admission across the border. Prior results indicated that a single on-arrival test has the potential to detect 9% of travellers infected with COVID-19, compared to 35%, 10% and 3% for travellers infected with influenza, SARS and Ebola, respectively. Our extended model shows that testing administered after a 2-day isolation period could detect up to 41%, 97%, 44% and 15% of COVID-19, influenza, SARS and Ebola infected travellers, respectively. Longer self-isolation periods increase detection rates further, with an 8-day self-isolation period suggesting detection rates of up to 94%, 100%, 98% and 62% for travellers infected with COVID-19, influenza, SARS and Ebola, respectively. These results therefore suggest that testing arrivals after an enforced period of self-isolation may present a reasonable method of protecting against case importation during international outbreaks.

Assessing the role of imported cases on the establishment of SARS-CoV-2 Delta variant of concern in Bolton, UK.

This paper presents a method used to rapidly assess the incursion and the establishment of community transmission of suspected SARS-CoV-2 variant of concern Delta (lineage B.1.617.2) into the UK in April and May 2021. The method described is independent of any genetically sequenced data, and so avoids the inherent lag times involved in sequencing of cases. We show that, between 1 April and 12 May 2021, there was a strong correlation between local authorities with high numbers of imported positive cases from India and high COVID-19 case rates, and that this relationship holds as we look at finer geographic detail. Further, we also show that Bolton was an outlier in the relationship, having the highest COVID-19 case rates despite relatively few importations. We use an artificial neural network trained on demographic data, to show that observed importations in Bolton were consistent with similar areas. Finally, using an SEIR transmission model, we show that imported positive cases were a contributing factor to persistent transmission in a number of local authorities, however they could not account for increased case rates observed in Bolton. As such, the outbreak of Delta variant in Bolton was likely not a result of direct importation from overseas, but rather secondary transmission from other regions within the UK.

What effect might border screening have on preventing the importation of COVID-19 compared with other infections? A modelling study.

The effectiveness of screening travellers during times of international disease outbreak is contentious, especially as the reduction in the risk of disease importation can be very small. Border screening typically consists of travellers being thermally scanned for signs of fever and/or completing a survey declaring any possible symptoms prior to admission to their destination country; while more thorough testing typically exists, these would generally prove more disruptive to deploy. In this paper, we describe a simple Monte Carlo based model that incorporates the epidemiology of coronavirus disease-2019 (COVID-19) to investigate the potential decrease in risk of disease importation that might be achieved by requiring travellers to undergo screening upon arrival during the current pandemic. This is a purely theoretical study to investigate the maximum impact that might be attained by deploying a test or testing programme simply at the point of entry, through which we may assess such action in the real world as a method of decreasing the risk of importation. We, therefore, assume ideal conditions such as 100% compliance among travellers and the use of a 'perfect' test. In addition to COVID-19, we also apply the presented model to simulated outbreaks of influenza, severe acute respiratory syndrome (SARS) and Ebola for comparison. Our model only considers screening implemented at airports, being the predominant method of international travel. Primary results showed that in the best-case scenario, screening at the point of entry may detect a maximum of 8.8% of travellers infected with COVID-19, compared to 34.8.%, 9.7% and 3.0% for travellers infected with influenza, SARS and Ebola respectively. While results appear to indicate that screening is more effective at preventing disease ingress when the disease in question has a shorter average incubation period, our results suggest that screening at the point of entry alone does not represent a sufficient method to adequately protect a nation from the importation of COVID-19 cases.

Symptom propagation in respiratory pathogens of public health concern: a review of the evidence.

Symptom propagation occurs when the symptom set an individual experiences is correlated with the symptom set of the individual who infected them. Symptom propagation may dramatically affect epidemiological outcomes, potentially causing clusters of severe disease. Conversely, it could result in chains of mild infection, generating widespread immunity with minimal cost to public health. Despite accumulating evidence that symptom propagation occurs for many respiratory pathogens, the underlying mechanisms are not well understood. Here, we conducted a scoping literature review for 14 respiratory pathogens to ascertain the extent of evidence for symptom propagation by two mechanisms: dose-severity relationships and route-severity relationships. We identify considerable heterogeneity between pathogens in the relative importance of the two mechanisms, highlighting the importance of pathogen-specific investigations. For almost all pathogens, including influenza and SARS-CoV-2, we found support for at least one of the two mechanisms. For some pathogens, including influenza, we found convincing evidence that both mechanisms contribute to symptom propagation. Furthermore, infectious disease models traditionally do not include symptom propagation. We summarize the present state of modelling advancements to address the methodological gap. We then investigate a simplified disease outbreak scenario, finding that under strong symptom propagation, isolating mildly infected individuals can have negative epidemiological implications.

Estimating the household secondary attack rate and serial interval of COVID-19 using social media.

We propose a method to estimate the household secondary attack rate (hSAR) of COVID-19 in the United Kingdom based on activity on the social media platform X, formerly known as Twitter. Conventional methods of hSAR estimation are resource intensive, requiring regular contact tracing of COVID-19 cases. Our proposed framework provides a complementary method that does not rely on conventional contact tracing or laboratory involvement, including the collection, processing, and analysis of biological samples. We use a text classifier to identify reports of people tweeting about themselves and/or members of their household having COVID-19 infections. A probabilistic analysis is then performed to estimate the hSAR based on the number of self or household, and self and household tweets of COVID-19 infection. The analysis includes adjustments for a reluctance of Twitter users to tweet about household members, and the possibility that the secondary infection was not acquired within the household. Experimental results for the UK, both monthly and weekly, are reported for the period from January 2020 to February 2022. Our results agree with previously reported hSAR estimates, varying with the primary variants of concern, e.g. delta and omicron. The serial interval (SI) is based on the time between the two tweets that indicate a primary and secondary infection. Experimental results, though larger than the consensus, are qualitatively similar. The estimation of hSAR and SI using social media data constitutes a new tool that may help in characterizing, forecasting and managing outbreaks and pandemics in a faster, affordable, and more efficient manner.

Combining models to generate consensus medium-term projections of hospital admissions, occupancy and deaths relating to COVID-19 in England.

Mathematical modelling has played an important role in offering informed advice during the COVID-19 pandemic. In England, a cross government and academia collaboration generated medium-term projections (MTPs) of possible epidemic trajectories over the future 4-6 weeks from a collection of epidemiological models. In this article, we outline this collaborative modelling approach and evaluate the accuracy of the combined and individual model projections against the data over the period November 2021-December 2022 when various Omicron subvariants were spreading across England. Using a number of statistical methods, we quantify the predictive performance of the model projections for both the combined and individual MTPs, by evaluating the point and probabilistic accuracy. Our results illustrate that the combined MTPs, produced from an ensemble of heterogeneous epidemiological models, were a closer fit to the data than the individual models during the periods of epidemic growth or decline, with the 90% confidence intervals widest around the epidemic peaks. We also show that the combined MTPs increase the robustness and reduce the biases associated with a single model projection. Learning from our experience of ensemble modelling during the COVID-19 epidemic, our findings highlight the importance of developing cross-institutional multi-model infectious disease hubs for future outbreak control.

Understanding the immunological landscape of England during SARS-CoV2 Omicron variant wave.

Understanding the scale of the threat posed by SARS-CoV2 B.1.1.529, or Omicron, variant formed a key problem in public health in the early part of 2022. Early evidence indicated that the variant was more transmissible and less severe than previous variants. As the virus was expected to spread quickly through the population of England, it was important that some understanding of the immunological landscape of the country was developed. This paper attempts to estimate the number of people with good immunity to the Omicron variant, defined as either recent infection with two doses of vaccine, or two doses of vaccine with a recent booster dose. To achieve this, we use a process of iterative proportional fitting to estimate the cell values of a contingency table, using national immunisation records and real-time model infection estimates as marginal values. Our results indicate that, despite the increased risk of immune evasion with the Omicron variant, a high proportion of England's population had good immunity to the virus, particularly in older age groups. However, low rates of immunity in younger populations may allow endemic infection to persist for some time.

Risk of paediatric multisystem inflammatory syndrome (PIMS-TS) during the SARS-CoV-2 alpha and delta variant waves: National observational and modelling study, 2020-21, England.

Objectives: Paediatric Multisystem Inflammatory Syndrome (PIMS-TS) is a rare life-threatening complication that typically occurs several weeks after SARS-CoV-2 infection in children and young people (CYP). We used national and regional-level data from the COVID-19 pandemic waves in England to develop a model to predict PIMS-TS cases. Methods: SARS-CoV-2 infections in CYP aged 0-15 years in England were estimated using the PHE-Cambridge real-time model. PIMS-TS cases were identified through the British Paediatric Surveillance Unit during (March-June 2020) and through Secondary Uses Services (SUS) from November 2020. A predictive model was developed to estimate PIMS-TS risk and lag times after SARS-CoV-2 infections. Results: During the Alpha wave, the model accurately predicted PIMS-TS cases (506 vs. 502 observed cases), with a median estimated risk of 0.038% (IQR, 0.037-0.041%) of paediatric SARS-CoV-2 infections. For the Delta wave, the median risk of PIMS-TS was significantly lower at 0.026% (IQR, 0.025-0.029%), with 212 observed PIMS-TS cases compared to 450 predicted by the model. Conclusions: The model accurately predicted national and regional PIMS-TS cases in CYP during the Alpha wave. PIMS-TS cases were 53% lower than predicted during the Delta wave. Further studies are needed to understand the mechanisms of the observed lower risk with the Delta variant.

Shut and re-open: the role of schools in the spread of COVID-19 in Europe.

We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases under different interventions, we provide evidence that school closures contribute to a reduction in the growth rate approximately 7 days after implementation. Limited school attendance, such as older students sitting exams or the partial return of younger year groups, does not appear to significantly affect community transmission. In countries where community transmission is generally low, such as Denmark or Norway, a large-scale reopening of schools while controlling or suppressing the epidemic appears feasible. However, school reopening can contribute to statistically significant increases in the growth rate in countries like Germany, where community transmission is relatively high. In all regions, a combination of low classroom occupancy and robust test-and-trace measures were in place. Our findings underscore the need for a cautious evaluation of reopening strategies. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

Insights gained from early modelling of COVID-19 to inform the management of outbreaks in UK prisons.

PURPOSE: In this work, the authors present some of the key results found during early efforts to model the COVID-19 outbreak inside a UK prison. In particular, this study describes outputs from an idealised disease model that simulates the dynamics of a COVID-19 outbreak in a prison setting when varying levels of social interventions are in place, and a Monte Carlo-based model that assesses the reduction in risk of case importation, resulting from a process that requires incoming prisoners to undergo a period of self-isolation prior to admission into the general prison population. DESIGN/METHODOLOGY/APPROACH: Prisons, typically containing large populations confined in a small space with high degrees of mixing, have long been known to be especially susceptible to disease outbreaks. In an attempt to meet rising pressures from the emerging COVID-19 situation in early 2020, modellers for Public Health England's Joint Modelling Cell were asked to produce some rapid response work that sought to inform the approaches that Her Majesty's Prison and Probation Service (HMPPS) might take to reduce the risk of case importation and sustained transmission in prison environments. FINDINGS: Key results show that deploying social interventions has the potential to considerably reduce the total number of infections, while such actions could also reduce the probability that an initial infection will propagate into a prison-wide outbreak. For example, modelling showed that a 50% reduction in the risk of transmission (compared to an unmitigated outbreak) could deliver a 98% decrease in total number of cases, while this reduction could also result in 86.8% of outbreaks subsiding before more than five persons have become infected. Furthermore, this study also found that requiring new arrivals to self-isolate for 10 and 14 days prior to admission could detect up to 98% and 99% of incoming infections, respectively. RESEARCH LIMITATIONS/IMPLICATIONS: In this paper we have presented models which allow for the studying of COVID-19 in a prison scenario, while also allowing for the assessment of proposed social interventions. By publishing these works, the authors hope these methods might aid in the management of prisoners across additional scenarios and even during subsequent disease outbreaks. Such methods as described may also be readily applied use in other closed community settings. ORIGINALITY/VALUE: These works went towards informing HMPPS on the impacts that the described strategies might have during COVID-19 outbreaks inside UK prisons. The works described herein are readily amendable to the study of a range of addition outbreak scenarios. There is also room for these methods to be further developed and built upon which the timeliness of the original project did not permit.

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity.

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis. The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis. The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

A controlled cross-over study to evaluate the efficacy of improvised dry and wet emergency decontamination protocols for chemical incidents.

The UK Initial Operational Response (IOR) to chemical incidents includes improvised decontamination procedures, which use readily available materials to rapidly reduce risk to potentially exposed persons. A controlled, cross-over human volunteer study was conducted to investigate the effectiveness of improvised dry and wet decontamination procedures on skin, both alone, and in sequence. A simulant contaminant, methyl salicylate (MeS) in vegetable oil with a fluorophore was applied to three locations (shoulder, leg, arm). Participants then received no decontamination (control) or attempted to remove the simulant using one of three improvised protocols (dry decontamination; wet decontamination; combined dry and wet decontamination). Simulant remaining on the skin following decontamination was quantified using both Gas Chromatography Tandem Mass Spectrometry (GC-MSMS) for analysis of MeS and UV imaging to detect fluorophores. Additionally, urine samples were collected for 24 hours following application for analysis of MeS. Significantly less simulant was recovered from skin following each improvised decontamination protocol, compared to the no decontamination control. Further, combined dry and wet decontamination resulted in lower recovery of simulant when compared to either dry or wet decontamination alone. Irrespective of decontamination protocol, significantly more simulant remained on the shoulders compared to either the arms or legs, suggesting that improvised decontamination procedures are less effective for difficult to reach areas of the body. There was no effect of decontamination on excreted MeS in urine over 24 hours. Overall, findings indicate that improvised decontamination is an effective means of rapidly removing contaminants from skin, and combinations of improvised approaches can increase effectiveness in the early stages of decontamination and in the absence of specialist resources at an incident scene. However, the variable control and consistency of improvised decontamination techniques means that further intervention is likely to be needed, particularly for less accessible areas of the body.

Methods for calculating credible intervals for ratios of beta distributions with application to relative risks of death during the second plague pandemic.

Employing historical records we are able to estimate the risk of premature death during the second plague pandemic, and identify the Black Death and pestis secunda epidemics. We show a novel method of calculating Bayesian credible intervals for a ratio of beta distributed random variables and use this to quantify uncertainty of relative risk estimates for these two epidemics which we consider in a 2 × 2 contingency table framework.

EpiJSON: A unified data-format for epidemiology.

Epidemiology relies on data but the divergent ways data are recorded and transferred, both within and between outbreaks, and the expanding range of data-types are creating an increasingly complex problem for the discipline. There is a need for a consistent, interpretable and precise way to transfer data while maintaining its fidelity. We introduce 'EpiJSON', a new, flexible, and standards-compliant format for the interchange of epidemiological data using JavaScript Object Notation. This format is designed to enable the widest range of epidemiological data to be unambiguously held and transferred between people, software and institutions. In this paper, we provide a full description of the format and a discussion of the design decisions made. We introduce a schema enabling automatic checks of the validity of data stored as EpiJSON, which can serve as a basis for the development of additional tools. In addition, we also present the R package 'repijson' which provides conversion tools between this format, line-list data and pre-existing analysis tools. An example is given to illustrate how EpiJSON can be used to store line list data. EpiJSON, designed around modern standards for interchange of information on the internet, is simple to implement, read and check. As such, it provides an ideal new standard for epidemiological, and other, data transfer to the fast-growing open-source platform for the analysis of disease outbreaks.

Behaviour and control of influenza in institutions and small societies.

A literature review was undertaken to assess the impact of influenza in enclosed societies. The literature spanned 120 years and included both readily accessible material from online keyword searches, as well as more obscure paper documents found through in-depth library research. Enclosed societies have been predominantly found in some type of institution through this period although noticeable similarities exist in communities isolated by distance and geography. We observe that no matter how isolated a community is, it is not necessarily insulated from infection by influenza and that even where there are no complicating factors, such as the age distribution or the presence of individuals with greater susceptibility in the enclosed population, their organization tends to increase influenza transmission and the risk of secondary infection. The collected accounts demonstrate important features of outbreaks in such societies and the necessity of considering them in pandemic planning: in particular, rapid intervention is essential for the control of influenza spread in such circumstances. Recent experience has shown that administration of modern antiviral drugs, such as neuraminidase inhibitors are effective at moderating outbreaks of influenza, but only in combination with other methods of control. In more remote communities where such drugs are not, or less, readily available, and medical care is limited, such outbreaks can still pose particular difficulties. In all cases delay in correct diagnosis, detection of an outbreak or the implementation of control measures can result in the majority of the enclosed population succumbing to the disease.