A simulation-based approach for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data.

Tracking pathogen transmissibility during infectious disease outbreaks is essential for assessing the effectiveness of public health measures and planning future control strategies. A key measure of transmissibility is the time-dependent reproduction number, which has been estimated in real-time during outbreaks of a range of pathogens from disease incidence time series data. While commonly used approaches for estimating the time-dependent reproduction number can be reliable when disease incidence is recorded frequently, such incidence data are often aggregated temporally (for example, numbers of cases may be reported weekly rather than daily). As we show, commonly used methods for estimating transmissibility can be unreliable when the timescale of transmission is shorter than the timescale of data recording. To address this, here we develop a simulation-based approach involving Approximate Bayesian Computation for estimating the time-dependent reproduction number from temporally aggregated disease incidence time series data. We first use a simulated dataset representative of a situation in which daily disease incidence data are unavailable and only weekly summary values are reported, demonstrating that our method provides accurate estimates of the time-dependent reproduction number under such circumstances. We then apply our method to two outbreak datasets consisting of weekly influenza case numbers in 2019-20 and 2022-23 in Wales (in the United Kingdom). Our simple-to-use approach will allow accurate estimates of time-dependent reproduction numbers to be obtained from temporally aggregated data during future infectious disease outbreaks.

Exact calculation of end-of-outbreak probabilities using contact tracing data.

A key challenge for public health policymakers is determining when an infectious disease outbreak has finished. Following a period without cases, an estimate of the probability that no further cases will occur in future (the end-of-outbreak probability) can be used to inform whether or not to declare an outbreak over. An existing quantitative approach (the Nishiura method), based on a branching process transmission model, allows the end-of-outbreak probability to be approximated from disease incidence time series, the offspring distribution and the serial interval distribution. Here, we show how the end-of-outbreak probability under the same transmission model can be calculated exactly if data describing who-infected-whom (the transmission tree) are also available (e.g. from contact tracing studies). In that scenario, our novel approach (the traced transmission method) is straightforward to use. We demonstrate this by applying the method to data from previous outbreaks of Ebola virus disease and Nipah virus infection. For both outbreaks, the traced transmission method would have determined that the outbreak was over earlier than the Nishiura method. This highlights that collection of contact tracing data and application of the traced transmission method may allow stringent control interventions to be relaxed quickly at the end of an outbreak, with only a limited risk of outbreak resurgence.

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

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

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

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

A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments.

Seasonal variations in environmental conditions lead to changing infectious disease epidemic risks at different times of year. The probability that early cases initiate a major epidemic depends on the season in which the pathogen enters the population. The instantaneous epidemic risk (IER) can be tracked. This quantity is straightforward to calculate, and corresponds to the probability of a major epidemic starting from a single case introduced at time t=t0, assuming that environmental conditions remain identical from that time onwards (i.e. for all t≥t0). However, the threat when a pathogen enters the population in fact depends on changes in environmental conditions occurring within the timescale of the initial phase of the outbreak. For that reason, we compare the IER with a different metric: the case epidemic risk (CER). The CER corresponds to the probability of a major epidemic starting from a single case entering the population at time t=t0, accounting for changes in environmental conditions after that time. We show how the IER and CER can be calculated using different epidemiological models (the stochastic Susceptible-Infectious-Removed model and a stochastic host-vector model that is parameterised using temperature data for Miami) in which transmission parameter values vary temporally. While the IER is always easy to calculate numerically, the adaptable method we provide for calculating the CER for the host-vector model can also be applied easily and solved using widely available software tools. In line with previous research, we demonstrate that, if a pathogen is likely to either invade the population or fade out on a fast timescale compared to changes in environmental conditions, the IER closely matches the CER. However, if this is not the case, the IER and the CER can be significantly different, and so the CER should be used. This demonstrates the need to consider future changes in environmental conditions carefully when assessing the risk posed by emerging pathogens.

Will an outbreak exceed available resources for control? Estimating the risk from invading pathogens using practical definitions of a severe epidemic.

Forecasting whether or not initial reports of disease will be followed by a severe epidemic is an important component of disease management. Standard epidemic risk estimates involve assuming that infections occur according to a branching process and correspond to the probability that the outbreak persists beyond the initial stochastic phase. However, an alternative assessment is to predict whether or not initial cases will lead to a severe epidemic in which available control resources are exceeded. We show how this risk can be estimated by considering three practically relevant potential definitions of a severe epidemic; namely, an outbreak in which: (i) a large number of hosts are infected simultaneously; (ii) a large total number of infections occur; and (iii) the pathogen remains in the population for a long period. We show that the probability of a severe epidemic under these definitions often coincides with the standard branching process estimate for the major epidemic probability. However, these practically relevant risk assessments can also be different from the major epidemic probability, as well as from each other. This holds in different epidemiological systems, highlighting that careful consideration of how to classify a severe epidemic is vital for accurate epidemic risk quantification.

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study.

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models.

Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection.

Epidemiological models are routinely used to predict the effects of interventions aimed at reducing the impacts of Ebola epidemics. Most models of interventions targeting symptomatic hosts, such as isolation or treatment, assume that all symptomatic hosts are equally likely to be detected. In other words, following an incubation period, the level of symptoms displayed by an individual host is assumed to remain constant throughout an infection. In reality, however, symptoms vary between different stages of infection. During an Ebola infection, individuals progress from initial non-specific symptoms through to more severe phases of infection. Here we compare predictions of a model in which a constant symptoms level is assumed to those generated by a more epidemiologically realistic model that accounts for varying symptoms during infection. Both models can reproduce observed epidemic data, as we show by fitting the models to data from the ongoing epidemic in the Democratic Republic of the Congo and the 2014-16 epidemic in Liberia. However, for both of these epidemics, when interventions are altered identically in the models with and without levels of symptoms that depend on the time since first infection, predictions from the models differ. Our work highlights the need to consider whether or not varying symptoms should be accounted for in models used by decision makers to assess the likely efficacy of Ebola interventions.

Improved inference of time-varying reproduction numbers during infectious disease outbreaks.

Accurate estimation of the parameters characterising infectious disease transmission is vital for optimising control interventions during epidemics. A valuable metric for assessing the current threat posed by an outbreak is the time-dependent reproduction number, i.e. the expected number of secondary cases caused by each infected individual. This quantity can be estimated using data on the numbers of observed new cases at successive times during an epidemic and the distribution of the serial interval (the time between symptomatic cases in a transmission chain). Some methods for estimating the reproduction number rely on pre-existing estimates of the serial interval distribution and assume that the entire outbreak is driven by local transmission. Here we show that accurate inference of current transmissibility, and the uncertainty associated with this estimate, requires: (i) up-to-date observations of the serial interval to be included, and; (ii) cases arising from local transmission to be distinguished from those imported from elsewhere. We demonstrate how pathogen transmissibility can be inferred appropriately using datasets from outbreaks of H1N1 influenza, Ebola virus disease and Middle-East Respiratory Syndrome. We present a tool for estimating the reproduction number in real-time during infectious disease outbreaks accurately, which is available as an R software package (EpiEstim 2.2). It is also accessible as an interactive, user-friendly online interface (EpiEstim App), permitting its use by non-specialists. Our tool is easy to apply for assessing the transmission potential, and hence informing control, during future outbreaks of a wide range of invading pathogens.

Increased frequency of travel in the presence of cross-immunity may act to decrease the chance of a global pandemic.

The high frequency of modern travel has led to concerns about a devastating pandemic since a lethal pathogen strain could spread worldwide quickly. Many historical pandemics have arisen following pathogen evolution to a more virulent form. However, some pathogen strains invoke immune responses that provide partial cross-immunity against infection with related strains. Here, we consider a mathematical model of successive outbreaks of two strains-a low virulence (LV) strain outbreak followed by a high virulence (HV) strain outbreak. Under these circumstances, we investigate the impacts of varying travel rates and cross-immunity on the probability that a major epidemic of the HV strain occurs, and the size of that outbreak. Frequent travel between subpopulations can lead to widespread immunity to the HV strain, driven by exposure to the LV strain. As a result, major epidemics of the HV strain are less likely, and can potentially be smaller, with more connected subpopulations. Cross-immunity may be a factor contributing to the absence of a global pandemic as severe as the 1918 influenza pandemic in the century since. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Preface to theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

This preface forms part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Atypical femoral fractures and bisphosphonate treatment: experience in two large United Kingdom teaching hospitals.

We performed a retrospective review of all patients admitted to two large University Hospitals in the United Kingdom over a 24-month period from January 2008 to January 2010 to identify the incidence of atypical subtrochanteric and femoral shaft fractures and their relationship to bisphosphonate treatment. Of the 3515 patients with a fracture of the proximal femur, 156 fractures were in the subtrochanteric region. There were 251 femoral shaft fractures. The atypical fracture pattern was seen in 27 patients (7%) with 29 femoral shaft or subtrochanteric fractures. A total of 22 patients with 24 atypical fractures were receiving bisphosphonate treatment at the time of fracture. Prodromal pain was present in nine patients (11 fractures); 11 (50%) of the patients on bisphosphonates suffered 12 spontaneous fractures, and healing of these fractures was delayed in a number of patients. This large dual-centre review has established the incidence of atypical femoral fractures at 7% of the study population, 81% of whom had been on bisphosphonate treatment for a mean of 4.6 years (0.04 to 12.1). This study does not advocate any change in the use of bisphosphonates to prevent fragility fractures but attempts to raise awareness of this possible problem so symptomatic patients will be appropriately investigated. However, more work is required to identify the true extent of this new and possibly increasing problem.

Electrophysiological and behavioral phenotype of insulin receptor defective mice.

The olfactory bulb expresses one of the highest levels of insulin found in the brain. A high level of expression of the concomitant insulin receptor (IR) kinase is also retained in this brain region, even in the adult. We have previously demonstrated in a heterologous system that insulin modulates the voltage-dependent potassium channel, Kv1.3, through tyrosine phosphorylation of three key residues in the amino and carboxyl terminus of the channel protein. Phosphorylation also induces current suppression of the Kv1.3-contributed current in cultured olfactory bulb neurons (OBNs) of rodents. In order to explore the behavioral importance of this kinase-induced modulation of the channel for the olfactory ability of the animal, mice with a targeted-gene deletion of the insulin receptor were electrophysiologically and behaviorally characterized. Mice heterozygous for the insulin receptor kinase (IR+/-) gene performed the same as wild-type (+/+) mice when challenged with a traditional, non-learning-based task to test gross anosmia. There was also no significant difference across the two genotypes in tests designed to measure exploratory behavior or in a battery of systems physiology experiments designed to assess metabolic energy usage (locomotion, ingestive behaviors, weight, oxygen consumption, and respiratory quotient). Object memory recognition tests suggest that IR+/- mice have an impairment in recognition of familiarized objects; IR+/- mice demonstrate poor performance for both short-term (1 h) and long-term (24 h) memory tests in comparison to that of wild-type mice. Electrophysiological experiments indicate that mitral cell neurons cultured from both heterozygous and homozygous-null mice (IR+/- and IR-/-) have an decreased peak current amplitude compared with that recorded for wild-type (+/+) animals matched for days in vitro (DIV). These data indicate that the loss of one allele of the IR kinase gene modifies the electrical phenotype of the mitral cell neurons in the olfactory bulb without a change in gross olfactory ability. Given our findings that there are no significant changes in metabolic balance of the IR (+/-) mice but some impairment in memory retention, future experiments testing for specific olfactory behaviors or functional deficits in IR-/+ mice models of diabetes will need to either be tasks that do not require learning or will require a different model (such as diet-induced diabetes) that may evoke a stronger phenotype.

Kv1.3 channel gene-targeted deletion produces "Super-Smeller Mice" with altered glomeruli, interacting scaffolding proteins, and biophysics.

Mice with gene-targeted deletion of the Kv1.3 channel were generated to study its role in olfactory function. Potassium currents in olfactory bulb mitral cells from Kv1.3 null mice have slow inactivation kinetics, a modified voltage dependence, and a dampened C-type inactivation and fail to be modulated by activators of receptor tyrosine signaling cascades. Kv1.3 deletion increases expression of scaffolding proteins that normally regulate the channel through protein-protein interactions. Kv1.3-/- mice have a 1,000- to 10,000-fold lower threshold for detection of odors and an increased ability to discriminate between odorants. In accordance with this heightened sense of smell, Kv1.3-/- mice have glomeruli or olfactory coding units that are smaller and more numerous than those of wild-type mice. These data suggest that Kv1.3 plays a far more reaching role in signal transduction, development, and olfactory coding than that of the classically defined role of a potassium channel-to shape excitability by influencing membrane potential.

Natural killer cells in the synovial fluid of rheumatoid arthritis patients exhibit a CD56bright,CD94bright,CD158negative phenotype.

BACKGROUND: Natural killer (NK) cells play an important role in several animal models of autoimmunity by modulating T-cell responses, but it is unclear whether human NK cells have similar functions. METHODS: We characterized the phenotype of NK cells in synovial fluid (SF) and peripheral blood (PB) of patients with rheumatoid arthritis (RA) and in healthy control subjects using flow cytometry and quantitative PCR. RESULTS: The proportions of NK cells in PB and SF of RA patients were not significantly different from those in healthy PB. However, the SF NK cell phenotype was strikingly different, with increased CD94 and CD56 densities and greatly reduced proportions of cells expressing CD158a/b. These cells also had reduced mRNAs coding for CD158a/b and low perforin levels compared with RA PB and healthy PB NK cells. CONCLUSIONS: We identified a novel phenotype of SF NK cells that is of potential significance in RA. Experiments are now under way to determine the function of these SF NK cells and their potential role in RA.

Bilateral distal fibular and tibial stress fractures associated with heavy smoking.

An unusual case of simultaneous bilateral stress fractures of the distal tibia and fibula in a 45 year old white woman is described. The onset of symptoms was not associated with a specific episode of trauma, sporting activity, or identifiable inflammatory predisposing cause. Her bone density scan, bone profile, and biochemistry were all normal. Although stress fractures are well recognised, bilateral distal tibial and fibular fractures are particularly rare. A high degree of awareness is required for early diagnosis.