The effect of superspreading on epidemic outbreak size distributions

Computation of random time-shift distributions for stochastic population models

Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the initial conditions. We present a efficient numerical method to compute this time-shift distribution for a large class of stochastic models. The method relies on differentiation of certain functional equations, which we show can be effectively automated by deriving rules for different types of model rates that arise commonly when mass-action mixing is assumed. Explicit computation of the time-shift distribution can be used to build a practical tool for the efficient generation of macroscopic trajectories of stochastic population models, without the need for costly stochastic simulations. Full code is provided to implement the calculations and we demonstrate the method on an epidemic model and a model of within-host viral dynamics.

Host behaviour driven by awareness of infection risk amplifies the chance of superspreading events

We demonstrate that heterogeneity in the perceived risks associated with infection within host populations amplifies chances of superspreading during the crucial early stages of epidemics. Under this behavioural model, individuals less concerned about dangers from infection are more likely to be infected and attend larger sized (riskier) events, where we assume event sizes remain unchanged. For directly transmitted diseases such as COVID-19, this leads to infections being introduced at rates above the population prevalence to those events most conducive to superspreading. We develop an interpretable, computational framework for evaluating within-event risks and derive a small-scale reproduction number measuring how the infections generated at an event depend on transmission heterogeneities and numbers of introductions. This generalizes previous frameworks and quantifies how event-scale patterns and population-level characteristics relate. As event duration and size grow, our reproduction number converges to the basic reproduction number. We illustrate that even moderate levels of heterogeneity in the perceived risks of infection substantially increase the likelihood of disproportionately large clusters of infections occurring at larger events, despite fixed overall disease prevalence. We show why collecting data linking host behaviour and event attendance is essential for accurately assessing the risks posed by invading pathogens in emerging stages of outbreaks.

Infectious Disease in the Workplace: Quantifying Uncertainty in Transmission

Understanding disease transmission in the workplace is essential for protecting workers. To model disease outbreaks, the small populations in many workplaces require that stochastic effects are considered, which results in higher uncertainty. The aim of this study was to quantify and interpret the uncertainty inherent in such circumstances. We assessed how uncertainty of an outbreak in workplaces depends on i) the infection dynamics in the community, ii) the workforce size, iii) spatial structure in the workplace, iv) heterogeneity in susceptibility of workers, and v) heterogeneity in infectiousness of workers. To address these questions, we developed a multiscale model: A deterministic model to predict community transmission, and a stochastic model to predict workplace transmission. We extended this basic workplace model to allow for spatial structure, and heterogeneity in susceptibility and infectiousness in workers. We found a non-monotonic relationship between the workplace transmission rate and the coefficient of variation (CV), which we use as a measure of uncertainty. Increasing community transmission, workforce size and heterogeneity in susceptibility decreased the CV. Conversely, increasing the level of spatial structure and heterogeneity in infectiousness increased the CV. However, when the model predicts bimodal distributions, for example when community transmission is low and workplace transmission is high, the CV fails to capture this uncertainty. Overall, our work informs modellers and policy makers on how model complexity impacts outbreak uncertainty. In particular: workforce size, community and workplace transmission, spatial structure and individual heterogeneity contribute in a specific and individual manner to the predicted workplace outbreak size distribution.

The aquaculture disease network model (AquaNet-Mod): A simulation model to evaluate disease spread and controls for the salmonid industry in England and Wales

Infectious disease causes significant mortality in wild and farmed systems, threatening biodiversity, conservation and animal welfare, as well as food security. To mitigate impacts and inform policy, tools such as mathematical models and computer simulations are valuable for predicting the potential spread and impact of disease. This paper describes the development of the Aquaculture Disease Network Model, AquaNet-Mod, and demonstrates its application to evaluating disease epidemics and the efficacy of control, using a Viral Haemorrhagic Septicaemia (VHS) case study. AquaNet-Mod is a data-driven, stochastic, state-transition model. Disease spread can occur via four different mechanisms, i) live fish movement, ii) river based, iii) short distance mechanical and iv) distance independent mechanical. Sites transit between three disease states: susceptible, clinically infected and subclinically infected. Disease spread can be interrupted by the application of disease mitigation measures and controls such as contact tracing, culling, fallowing and surveillance. Results from a VHS case study highlight the potential for VHS to spread to 96% of sites over a 10 year time horizon if no disease controls are applied. Epidemiological impact is significantly reduced when live fish movement restrictions are placed on the most connected sites and further still, when disease controls, representative of current disease control policy in England and Wales, are applied. The importance of specific disease control measures, particularly contact tracing and disease detection rate, are also highlighted. The merit of this model for evaluation of disease spread and the efficacy of controls, in the context of policy, along with potential for further application and development of the model, for example to include economic parameters, is discussed.

The interplay of social constraints and individual variation in risk tolerance in the emergence of superspreaders

Individual host behaviours can drastically impact the spread of infection through a population. Differences in the value individuals place on both socializing with others and avoiding infection have been shown to yield emergent homophily in social networks and thereby shape epidemic outcomes. We build on this understanding to explore how individuals who do not conform to their social surroundings contribute to the propagation of infection during outbreaks. We show how non-conforming individuals, even if they do not directly expose a disproportionate number of other individuals themselves, can become functional superspreaders through an emergent social structure that positions them as the functional links by which infection jumps between otherwise separate communities. Our results can help estimate the potential success of real-world interventions that may be compromised by a small number of non-conformists if their impact is not anticipated, and plan for how best to mitigate their effects on intervention success.

COVID-19 outbreaks analysis in the Valencian Region of Spain in the prelude of the third wave

Introduction

The COVID-19 pandemic has led to unprecedented social and mobility restrictions on a global scale. Since its start in the spring of 2020, numerous scientific papers have been published on the characteristics of the virus, and the healthcare, economic and social consequences of the pandemic. However, in-depth analyses of the evolution of single coronavirus outbreaks have been rarely reported.

Methods

In this paper, we analyze the main properties of all the tracked COVID-19 outbreaks in the Valencian Region between September and December of 2020. Our analysis includes the evaluation of the origin, dynamic evolution, duration, and spatial distribution of the outbreaks.

Results

We find that the duration of the outbreaks follows a power-law distribution: most outbreaks are controlled within 2 weeks of their onset, and only a few last more than 2 months. We do not identify any significant differences in the outbreak properties with respect to the geographical location across the entire region. Finally, we also determine the cluster size distribution of each infection origin through a Bayesian statistical model.

Discussion

We hope that our work will assist in optimizing and planning the resource assignment for future pandemic tracking efforts.

A Hybrid Epidemic Model to Explore Stochasticity in COVID-19 Dynamics

The dynamic nature of the COVID-19 pandemic has demanded a public health response that is constantly evolving due to the novelty of the virus. Many jurisdictions in the USA, Canada, and across the world have adopted social distancing and recommended the use of face masks. Considering these measures, it is prudent to understand the contributions of subpopulations—such as “silent spreaders”—to disease transmission dynamics in order to inform public health strategies in a jurisdiction-dependent manner. Additionally, we and others have shown that demographic and environmental stochasticity in transmission rates can play an important role in shaping disease dynamics. Here, we create a model for the COVID-19 pandemic by including two classes of individuals: silent spreaders, who either never experience a symptomatic phase or remain undetected throughout their disease course; and symptomatic spreaders, who experience symptoms and are detected. We fit the model to real-time COVID-19 confirmed cases and deaths to derive the transmission rates, death rates, and other relevant parameters for multiple phases of outbreaks in British Columbia (BC), Canada. We determine the extent to which SilS contributed to BC’s early wave of disease transmission as well as the impact of public health interventions on reducing transmission from both SilS and SymS. To do this, we validate our model against an existing COVID-19 parameterized framework and then fit our model to clinical data to estimate key parameter values for different stages of BC’s disease dynamics. We then use these parameters to construct a hybrid stochastic model that leverages the strengths of both a time-nonhomogeneous discrete process and a stochastic differential equation model. By combining these previously established approaches, we explore the impact of demographic and environmental variability on disease dynamics by simulating various scenarios in which a COVID-19 outbreak is initiated. Our results demonstrate that variability in disease transmission rate impacts the probability and severity of COVID-19 outbreaks differently in high- versus low-transmission scenarios.

Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Superspreading is one of the key transmission features of many infectious diseases and is considered a consequence of the heterogeneity in infectiousness of individual cases. To characterize the superspreading potential, we divided individual infectiousness into two independent and additive components, including a fixed baseline and a variable part. Such decomposition produced an improvement in the fit of the model explaining the distribution of real-world datasets of COVID-19 and SARS that can be captured by the classic statistical tests. Disease control strategies may be developed by monitoring the characteristics of superspreading. For the COVID-19 pandemic, population-wide interventions are suggested first to limit the transmission at a scale of general population, and then high-risk-specific control strategies are recommended subsequently to lower the risk of superspreading.

The source of individual heterogeneity shapes infectious disease outbreaks

There is known heterogeneity between individuals in infectious disease transmission patterns. The source of this heterogeneity is thought to affect epidemiological dynamics but studies tend not to control for the overall heterogeneity in the number of secondary cases caused by an infection. To explore the role of individual variation in infection duration and transmission rate in parasite emergence and spread, while controlling for this potential bias, we simulate stochastic outbreaks with and without parasite evolution. As expected, heterogeneity in the number of secondary cases decreases the probability of outbreak emergence. Furthermore, for epidemics that do emerge, assuming more realistic infection duration distributions leads to faster outbreaks and higher epidemic peaks. When parasites require adaptive mutations to cause large epidemics, the impact of heterogeneity depends on the underlying evolutionary model. If emergence relies on within-host evolution, decreasing the infection duration variance decreases the probability of emergence. These results underline the importance of accounting for realistic distributions of transmission rates to anticipate the effect of individual heterogeneity on epidemiological dynamics.

Multi-scale modelling reveals that early super-spreader events are a likely contributor to novel variant predominance

The emergence of new SARS-CoV-2 variants of concern (VOC) has hampered international efforts to contain the COVID-19 pandemic. VOCs have been characterized to varying degrees by higher transmissibility, worse infection outcomes and evasion of vaccine and infection-induced immunologic memory. VOCs are hypothesized to have originated from animal reservoirs, communities in regions with low surveillance and/or single individuals with poor immunologic control of the virus. Yet, the factors dictating which variants ultimately predominate remain incompletely characterized. Here we present a multi-scale model of SARS-CoV-2 dynamics that describes population spread through individuals whose viral loads and numbers of contacts (drawn from an over-dispersed distribution) are both time-varying. This framework allows us to explore how super-spreader events (SSE) (defined as greater than five secondary infections per day) contribute to variant emergence. We find stochasticity remains a powerful determinant of predominance. Variants that predominate are more likely to be associated with higher infectiousness, an SSE early after variant emergence and ongoing decline of the current dominant variant. Additionally, our simulations reveal that most new highly infectious variants that infect one or a few individuals do not achieve permanence in the population. Consequently, interventions that reduce super-spreading may delay or mitigate emergence of VOCs.

Reconstruction of the transmission dynamics of the first COVID-19 epidemic wave in Thailand

Thailand was the first country reporting the first Coronavirus disease 2019 (COVID-19) infected individual outside mainland China. Here we delineated the course of the COVID-19 outbreak together with the timeline of the control measures and public health policies employed by the Thai government during the first wave of the COVID-19 outbreak in Thailand. Based on the comprehensive epidemiological data, we reconstructed the dynamics of COVID-19 transmission in Thailand using a stochastic modeling approach. Our stochastic model incorporated the effects of individual heterogeneity in infectiousness on disease transmission, which allows us to capture relevant features of superspreading events. We found that our model could accurately capture the transmission dynamics of the first COVID-19 epidemic wave in Thailand. The model predicted that at the end of the first wave, the number of cumulative confirmed cases was 3091 (95%CI: 2782-3400). We also estimated the time-varying reproduction number (R_t) during the first epidemic wave. We found that after implementing the nationwide interventions, the R_t in Thailand decreased from the peak value of 5.67 to a value below one in less than one month, indicating that the control measures employed by the Thai government during the first COVID-19 epidemic wave were effective. Finally, the effects of transmission heterogeneity and control measures on the likelihood of outbreak extinction were also investigated.

Sub-spreading events limit the reliable elimination of heterogeneous epidemics

We show that sub-spreading events, i.e. transmission events in which an infection propagates to few or no individuals, can be surprisingly important for defining the lifetime of an infectious disease epidemic and hence its waiting time to elimination or fade-out, measured from the time-point of its last observed case. While limiting super-spreading promotes more effective control when cases are growing, we find that when incidence is waning, curbing sub-spreading is more important for achieving reliable elimination of the epidemic. Controlling super-spreading in this low-transmissibility phase offers diminishing returns over non-selective, population-wide measures. By restricting sub-spreading, we efficiently dampen remaining variations among the reproduction numbers of infectious events, which minimizes the risk of premature and late end-of-epidemic declarations. Because case-ascertainment or reporting rates can be modelled in exactly the same way as control policies, we concurrently show that the under-reporting of sub-spreading events during waning phases will engender overconfident assessments of epidemic elimination. While controlling sub-spreading may not be easily realized, the likely neglecting of these events by surveillance systems could result in unexpectedly risky end-of-epidemic declarations. Super-spreading controls the size of the epidemic peak but sub-spreading mediates the variability of its tail.

The devil in the details: Herd immunity and pandemic response

If enough individuals in a population are immune to a pathogen, it cannot cause an outbreak. Deliberately seeking such herd immunity through infection during a potentially lethal pandemic is contrary to all principles of public health, given the potential for uncontrolled outbreaks and risks to vulnerable populations.

Impact of mobility restriction in COVID-19 superspreading events using agent-based model

COVID-19 pandemic is an immediate major public health concern. The search for the understanding of the disease spreading made scientists around the world turn their attention to epidemiological studies. An interesting approach in epidemiological modeling nowadays is to use agent-based models, which allow to consider a heterogeneous population and to evaluate the role of superspreaders in this population. In this work, we implemented an agent-based model using probabilistic cellular automata to simulate SIR (Susceptible-Infected-Recovered) dynamics using COVID-19 infection parameters. Differently to the usual studies, we did not define the superspreaders individuals a priori, we only left the agents to execute a random walk along the sites. When two or more agents share the same site, there is a probability to spread the infection if one of them is infected. To evaluate the spreading, we built the transmission network and measured the degree distribution, betweenness, and closeness centrality. The results displayed for different levels of mobility restriction show that the degree reduces as the mobility reduces, but there is an increase of betweenness and closeness for some network nodes. We identified the superspreaders at the end of the simulation, showing the emerging behavior of the model since these individuals were not initially defined. Simulations also showed that the superspreaders are responsible for most of the infection propagation and the impact of personal protective equipment in the spreading of the infection. We believe that this study can bring important insights for the analysis of the disease dynamics and the role of superspreaders, contributing to the understanding of how to manage mobility during a highly infectious pandemic as COVID-19.

The role of social structure and dynamics in the maintenance of endemic disease

Social interactions are required for the direct transmission of infectious diseases. Consequently, the social network structure of populations plays a key role in shaping infectious disease dynamics. A huge research effort has examined how specific social network structures make populations more (or less) vulnerable to damaging epidemics. However, it can be just as important to understand how social networks can contribute to endemic disease dynamics, in which pathogens are maintained at stable levels for prolonged periods of time. Hosts that can maintain endemic disease may serve as keystone hosts for multi-host pathogens within an ecological community, and also have greater potential to act as key wildlife reservoirs of agricultural and zoonotic diseases. Here, we examine combinations of social and demographic processes that can foster endemic disease in hosts. We synthesise theoretical and empirical work to demonstrate the importance of both social structure and social dynamics in maintaining endemic disease. We also highlight the importance of distinguishing between the local and global persistence of infection and reveal how different social processes drive variation in the scale at which infectious diseases appear endemic. Our synthesis provides a framework by which to understand how sociality contributes to the long-term maintenance of infectious disease in wildlife hosts and provides a set of tools to unpick the social and demographic mechanisms involved in any given host-pathogen system.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00265-021-03055-8.

Single infection with Batrachochytrium dendrobatidis or Ranavirus does not increase probability of co-infection in a montane community of amphibians

Understanding the occurrence and consequence of co-infections can be useful in designing disease management interventions. Amphibians are the most highly threatened vertebrates, and emerging pathogens are a serious threat to their conservation. The amphibian chytrid fungus and the viruses of the Ranavirus genus are already widely distributed, causing disease outbreaks and population declines worldwide. However, we lack information about the occurrence and consequences of coinfection with these pathogens across age-classes of amphibian hosts. Here, we analyze the occurrence of infection of the amphibian chytrid fungus and ranaviruses during one season in two susceptible amphibian species at two different locations at which outbreaks have occurred. We found that the co-occurrence of both pathogens in a particular host is not common except in highly susceptible life-stages, and that single infections are the most common situation. Moreover, we found that the occurrence of one pathogen in a particular host did not predict the occurrence of the other. We attribute these results to the niches in which both pathogens proliferate in amphibian hosts.

Spatial super-spreaders and super-susceptibles in human movement networks

As lockdowns and stay-at-home orders start to be lifted across the globe, governments are struggling to establish effective and practical guidelines to reopen their economies. In dense urban environments with people returning to work and public transportation resuming full capacity, enforcing strict social distancing measures will be extremely challenging, if not practically impossible. Governments are thus paying close attention to particular locations that may become the next cluster of disease spreading. Indeed, certain places, like some people, can be “super-spreaders”. Is a bustling train station in a central business district more or less susceptible and vulnerable as compared to teeming bus interchanges in the suburbs? Here, we propose a quantitative and systematic framework to identify spatial super-spreaders and the novel concept of super-susceptibles, i.e. respectively, places most likely to contribute to disease spread or to people contracting it. Our proposed data-analytic framework is based on the daily-aggregated ridership data of public transport in Singapore. By constructing the directed and weighted human movement networks and integrating human flow intensity with two neighborhood diversity metrics, we are able to pinpoint super-spreader and super-susceptible locations. Our results reveal that most super-spreaders are also super-susceptibles and that counterintuitively, busy peripheral bus interchanges are riskier places than crowded central train stations. Our analysis is based on data from Singapore, but can be readily adapted and extended for any other major urban center. It therefore serves as a useful framework for devising targeted and cost-effective preventive measures for urban planning and epidemiological preparedness.

Characterization of potential superspreader farms for bovine tuberculosis: A review

Background

Variation in host attributes that influence their contact rates and infectiousness can lead some individuals to make disproportionate contributions to the spread of infections. Understanding the roles of such ‘superspreaders’ can be crucial in deciding where to direct disease surveillance and controls to greatest effect. In the epidemiology of bovine tuberculosis (bTB) in Great Britain, it has been suggested that a minority of cattle farms or herds might make disproportionate contributions to the spread of Mycobacterium bovis, and hence might be considered ‘superspreader farms’.

Objectives and Methods

We review the literature to identify the characteristics of farms that have the potential to contribute to exceptional values in the three main components of the farm reproductive number ‐ R_f: contact rate, infectiousness and duration of infectiousness, and therefore might characterize potential superspreader farms for bovine tuberculosis in Great Britain.

Results

Farms exhibit marked heterogeneity in contact rates arising from between‐farm trading of cattle. A minority of farms act as trading hubs that greatly augment connections within cattle trading networks. Herd infectiousness might be increased by high within‐herd transmission or the presence of supershedding individuals, or infectiousness might be prolonged due to undetected infections or by repeated local transmission, via wildlife or fomites.

Conclusions

Targeting control methods on putative superspreader farms might yield disproportionate benefits in controlling endemic bovine tuberculosis in Great Britain. However, real‐time identification of any such farms, and integration of controls with industry practices, present analytical, operational and policy challenges.

Inferring transmission heterogeneity using virus genealogies: Estimation and targeted prevention

Spread of HIV typically involves uneven transmission patterns where some individuals spread to a large number of individuals while others to only a few or none. Such transmission heterogeneity can impact how fast and how much an epidemic spreads. Further, more efficient interventions may be achieved by taking such transmission heterogeneity into account. To address these issues, we developed two phylogenetic methods based on virus sequence data: 1) to generally detect if significant transmission heterogeneity is present, and 2) to pinpoint where in a phylogeny high-level spread is occurring. We derive inference procedures to estimate model parameters, including the amount of transmission heterogeneity, in a sampled epidemic. We show that it is possible to detect transmission heterogeneity under a wide range of simulated situations, including incomplete sampling, varying levels of heterogeneity, and including within-host genetic diversity. When evaluating real HIV-1 data from different epidemic scenarios, we found a lower level of transmission heterogeneity in slowly spreading situations and a higher level of heterogeneity in data that included a rapid outbreak, while R0 and Sackin's index (overall tree shape statistic) were similar in the two scenarios, suggesting that our new method is able to detect transmission heterogeneity in real data. We then show by simulations that targeted prevention, where we pinpoint high-level spread using a coalescence measurement, is efficient when sequence data are collected in an ongoing surveillance system. Such phylogeny-guided prevention is efficient under both single-step contact tracing as well as iterative contact tracing as compared to random intervention.

Sub- or supercritical transmissibilities in a finite disease outbreak: Symmetry in outbreak properties of a disease conditioned on extinction

This work is concerned with the transmissibility of a disease, on observation of an outbreak of limited size. When such an outbreak occurs, an accurate estimate of the transmissibility of the responsible pathogen is essential for an appropriate response to future outbreaks. Transmissibility is usually characterised in terms of the reproduction number, R, which is the mean number of new cases of infection produced by a single infectious individual. A subcritical reproduction number (R < 1) guarantees that an outbreak will eventually die out of its own accord. By contrast, a supercritical reproduction number (R > 1) does not guarantee spread of the disease, since even with appreciable transmissibility, an outbreak may become extinct due to stochastic effects associated with a small number of infected individuals. Once the number of infectious individuals is conditioned on extinction, we show that an exact symmetry of the underlying theory ensures two distinct values of R, one larger than unity, the other smaller than unity, for which all outbreak properties are identical, with no signature of difference. Therefore a disease with a subcritical R, or its supercritical counterpart, when conditioned on extinction, have, for a given outbreak, identical individual likelihoods. In the full likelihood, this symmetry is lost, since the individual likelihood for a subcritical R is weighted by an extinction probability of unity, but the individual likelihood of a supercritical R is weighted by a sub-unity extinction probability. However, the inference can still benefit from the underlying symmetry, since it yields a mapping of all supercritical reproduction numbers onto the subcritical domain (R < 1), thereby speeding up evaluation of the likelihood profile. The symmetry holds in the standard situation, where the distribution of secondary cases is Poisson, as well as where this distribution has a negative binomial form and super-spreading can occur.

A dynamic power-law sexual network model of gonorrhoea outbreaks

Human networks of sexual contacts are dynamic by nature, with partnerships forming and breaking continuously over time. Sexual behaviours are also highly heterogeneous, so that the number of partners reported by individuals over a given period of time is typically distributed as a power-law. Both the dynamism and heterogeneity of sexual partnerships are likely to have an effect in the patterns of spread of sexually transmitted diseases. To represent these two fundamental properties of sexual networks, we developed a stochastic process of dynamic partnership formation and dissolution, which results in power-law numbers of partners over time. Model parameters can be set to produce realistic conditions in terms of the exponent of the power-law distribution, of the number of individuals without relationships and of the average duration of relationships. Using an outbreak of antibiotic resistant gonorrhoea amongst men have sex with men as a case study, we show that our realistic dynamic network exhibits different properties compared to the frequently used static networks or homogeneous mixing models. We also consider an approximation to our dynamic network model in terms of a much simpler branching process. We estimate the parameters of the generation time distribution and offspring distribution which can be used for example in the context of outbreak reconstruction based on genomic data. Finally, we investigate the impact of a range of interventions against gonorrhoea, including increased condom use, more frequent screening and immunisation, concluding that the latter shows great promise to reduce the burden of gonorrhoea, even if the vaccine was only partially effective or applied to only a random subset of the population.

Agent-Based Modeling for Super-Spreading Events: A Case Study of MERS-CoV Transmission Dynamics in the Republic of Korea

Super-spreading events have been observed in the transmission dynamics of many infectious diseases. The 2015 MERS-CoV outbreak in the Republic of Korea has also shown super-spreading events with a significantly high level of heterogeneity in generating secondary cases. It becomes critical to understand the mechanism for this high level of heterogeneity to develop effective intervention strategies and preventive plans for future emerging infectious diseases. In this regard, agent-based modeling is a useful tool for incorporating individual heterogeneity into the epidemic model. In the present work, a stochastic agent-based framework is developed in order to understand the underlying mechanism of heterogeneity. Clinical (i.e., an infectivity level) and social or environmental (i.e., a contact level) heterogeneity are modeled. These factors are incorporated in the transmission rate functions under assumptions that super-spreaders have stronger transmission and/or higher links. Our agent-based model has employed real MERS-CoV epidemic features based on the 2015 MERS-CoV epidemiological data. Monte Carlo simulations are carried out under various epidemic scenarios. Our findings highlight the roles of super-spreaders in a high level of heterogeneity, underscoring that the number of contacts combined with a higher level of infectivity are the most critical factors for substantial heterogeneity in generating secondary cases of the 2015 MERS-CoV transmission.

Quantifying Transmission Heterogeneity Using Both Pathogen Phylogenies and Incidence Time Series

Heterogeneity in individual-level transmissibility can be quantified by the dispersion parameter k of the offspring distribution. Quantifying heterogeneity is important as it affects other parameter estimates, it modulates the degree of unpredictability of an epidemic, and it needs to be accounted for in models of infection control. Aggregated data such as incidence time series are often not sufficiently informative to estimate k. Incorporating phylogenetic analysis can help to estimate k concurrently with other epidemiological parameters. We have developed an inference framework that uses particle Markov Chain Monte Carlo to estimate k and other epidemiological parameters using both incidence time series and the pathogen phylogeny. Using the framework to fit a modified compartmental transmission model that includes the parameter k to simulated data, we found that more accurate and less biased estimates of the reproductive number were obtained by combining epidemiological and phylogenetic analyses. However, k was most accurately estimated using pathogen phylogeny alone. Accurately estimating k was necessary for unbiased estimates of the reproductive number, but it did not affect the accuracy of reporting probability and epidemic start date estimates. We further demonstrated that inference was possible in the presence of phylogenetic uncertainty by sampling from the posterior distribution of phylogenies. Finally, we used the inference framework to estimate transmission parameters from epidemiological and genetic data collected during a poliovirus outbreak. Despite the large degree of phylogenetic uncertainty, we demonstrated that incorporating phylogenetic data in parameter inference improved the accuracy and precision of estimates.

Routes of Transmission in the Food Chain

More than 250 different foodborne diseases have been described to date, annually affecting about one-third of the world's population. The incidence of foodborne diseases has been underreported and underestimated, and the asymptomatic presentation of some of the illnesses, worldwide heterogeneities in reporting, and the alternative transmission routes of certain pathogens are among the factors that contribute to this. Globalization, centralization of the food supply, transportation of food products progressively farther from their places of origin, and the multitude of steps where contamination may occur have made it increasingly challenging to investigate foodborne and waterborne outbreaks. Certain foodborne pathogens may be transmitted directly from animals to humans, while others are transmitted through vectors, such as insects, or through food handlers, contaminated food products or food-processing surfaces, or transfer from sponges, cloths, or utensils. Additionally, the airborne route may contribute to the transmission of certain foodborne pathogens. Complicating epidemiological investigations, multiple transmission routes have been described for some foodborne pathogens. Two types of transmission barriers, primary and secondary, have been described for foodborne pathogens, each of them providing opportunities for preventing and controlling outbreaks. Primary barriers, the most effective sites of prophylactic intervention, prevent pathogen entry into the environment, while secondary barriers prevent the multiplication and dissemination of pathogens that have already entered the environment. Understanding pathogen dynamics, monitoring transmission, and implementing preventive measures are complicated by the phenomenon of superspreading, which refers to the concept that, at the level of populations, a minority of hosts is responsible for the majority of transmission events.

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

Revealing the Micro-scale Signature of Endemic Zoonotic Disease Transmission in an African Urban Setting

The development of novel approaches that combine epidemiological and genomic data provides new opportunities to reveal the spatiotemporal dynamics of infectious diseases and determine the processes responsible for their spread and maintenance. Taking advantage of detailed epidemiological time series and viral sequence data from more than 20 years reported by the National Reference Centre for Rabies of Bangui, the capital city of Central African Republic, we used a combination of mathematical modeling and phylogenetic analysis to determine the spatiotemporal dynamics of rabies in domestic dogs as well as the frequency of extinction and introduction events in an African city. We show that although dog rabies virus (RABV) appears to be endemic in Bangui, its epidemiology is in fact shaped by the regular extinction of local chains of transmission coupled with the introduction of new lineages, generating successive waves of spread. Notably, the effective reproduction number during each wave was rarely above the critical value of 1, such that rabies is not self-sustaining in Bangui. In turn, this suggests that rabies at local geographic scales is driven by human-mediated dispersal of RABV among sparsely connected peri-urban and rural areas as opposed to dispersion in a relatively large homogenous urban dog population. This combined epidemiological and genomic approach enables development of a comprehensive framework for understanding disease persistence and informing control measures, indicating that control measures are probably best targeted towards areas neighbouring the city that appear as the source of frequent incursions seeding outbreaks in Bangui.

Increasing influenza vaccination in New York City taxi drivers: A community driven approach

The Healthy People 2020 influenza immunization goal is 80% for non-institutionalized adults 18-64. However, vaccination rates remain stubbornly low. Culturally tailored approaches to communities with poor vaccine uptake are necessary. Taxi drivers are at risk for influenza and its complications, could serve as vectors for influenza infection, and could be an effective vaccination target to enhance herd immunity of the urban population. To the best of our knowledge, this is the first study related to influenza vaccination among taxi drivers. The NYC Taxi Network surveyed a convenience sample of 53 taxi drivers to understand vaccination barriers. Only 17% had been vaccinated. Results informed a pilot tailored workplace intervention, which resulted in vaccinations for 44% of unvaccinated drivers. The study revealed that older drivers were more likely to be vaccinated than younger drivers, while the most common barrier to immunization was that drivers thought vaccination was 'not necessary'.

A marginal benefit approach for vaccinating influenza "superspreaders"

BACKGROUND

There is widespread recognition that interventions targeting "superspreaders" are more effective at containing epidemics than strategies aimed at the broader

POPULATION

However, little attention has been devoted to determining optimal levels of coverage for targeted vaccination strategies, given the nonlinear relationship between program scale and the costs and benefits of identifying and successfully administering vaccination to potential superspreaders.

METHODS

We developed a framework for such an assessment derived from a transmission model of seasonal influenza parameterized to emulate typical seasonal influenza epidemics in the US. We used this framework to estimate how the marginal benefit of expanded targeted vaccination changes with the proportion of the target population already vaccinated.

RESULTS

The benefit of targeting additional superspreaders varies considerably as a function of both the baseline vaccination coverage and proximity to the herd immunity threshold. The general form of the marginal benefit function starts low, particularly for severe epidemics, increases monotonically until its peak at the point of herd immunity, and then plummets rapidly. We present a simplified transmission model, primarily designed to convey qualitative insight rather than quantitative precision. With appropriate contact data, future work could address more complex population structures, such as age structure and assortative mixing patterns. Our illustrative example highlights the general economic and epidemiological findings of our method but does not address intervention design, policy, and resource allocation issues related to practical implementation of this particular scenario.

CONCLUSIONS

Our approach offers a means of estimating willingness to pay for search costs associated with targeted vaccination of superspreaders, which can inform policies regarding whether a targeted intervention should be implemented and, if so, up to what levels.

Infections do not predict shedding in co-infections with two helminths from a natural system

Given the health and economic burden associated with the widespread occurrence of co-infections in humans and agricultural animals, understanding how coinfections contribute to host heterogeneity to infection and transmission is critical if we are to assess risk of infection based on host characteristics. Here, we examine whether host heterogeneity to infection leads to similar heterogeneity in transmission in a population of rabbits single and co-infected with two helminths and monitored monthly for eight years. Compared to single infections, co-infected rabbits carried higher Trichostrongylus retortaeformis intensities, shorter worms with fewer eggs in utero, and shed similar numbers of parasite eggs. In contrast, the same co-infected rabbits harbored fewer Graphidium strigosum with longer bodies and more eggs in utero, and shed more eggs of this helminth. A positive density-dependent relationship between fecundity and intensity was found for T. retortaeformis but not G. strigosum in co-infected rabbits. Juvenile rabbits contributed to most of the infection and shedding of T. retortaeformis, while adult hosts were more important for G. strigosum dynamics of infection and transmission, and this pattern was consistent in single and co-infected individuals. This host-parasite system suggests that we cannot predict the pattern of parasite shedding during co-infections based on intensity of infection alone. We suggest that a mismatching between susceptibility and infectiousness should be expected in helminth coinfections and should not be overlooked.

Field-isolated genotypes of Mycobacterium bovis vary in virulence and influence case pathology but do not affect outbreak size

Strains of many infectious agents differ in fundamental epidemiological parameters including transmissibility, virulence and pathology. We investigated whether genotypes of Mycobacterium bovis (the causative agent of bovine tuberculosis, bTB) differ significantly in transmissibility and virulence, combining data from a nine-year survey of the genetic structure of the M. bovis population in Northern Ireland with detailed records of the cattle population during the same period. We used the size of herd breakdowns as a proxy measure of transmissibility and the proportion of skin test positive animals (reactors) that were visibly lesioned as a measure of virulence. Average breakdown size increased with herd size and varied depending on the manner of detection (routine herd testing or tracing of infectious contacts) but we found no significant variation among M. bovis genotypes in breakdown size once these factors had been accounted for. However breakdowns due to some genotypes had a greater proportion of lesioned reactors than others, indicating that there may be variation in virulence among genotypes. These findings indicate that the current bTB control programme may be detecting infected herds sufficiently quickly so that differences in virulence are not manifested in terms of outbreak sizes. We also investigated whether pathology of infected cattle varied according to M. bovis genotype, analysing the distribution of lesions recorded at post mortem inspection. We concentrated on the proportion of cases lesioned in the lower respiratory tract, which can indicate the relative importance of the respiratory and alimentary routes of infection. The distribution of lesions varied among genotypes and with cattle age and there were also subtle differences among breeds. Age and breed differences may be related to differences in susceptibility and husbandry, but reasons for variation in lesion distribution among genotypes require further investigation.

Nipah virus infection outbreak with nosocomial and corpse-to-human transmission, Bangladesh

Particularly vulnerable are health care workers who do not use personal protective equipment and persons who do not wash hands after traditional burial practices.

Active Nipah virus encephalitis surveillance identified an encephalitis cluster and sporadic cases in Faridpur, Bangladesh, in January 2010. We identified 16 case-patients; 14 of these patients died. For 1 case-patient, the only known exposure was hugging a deceased patient with a probable case, while another case-patient’s exposure involved preparing the same corpse for burial by removing oral secretions and anogenital excreta with a cloth and bare hands. Among 7 persons with confirmed sporadic cases, 6 died, including a physician who had physically examined encephalitis patients without gloves or a mask. Nipah virus–infected patients were more likely than community-based controls to report drinking raw date palm sap and to have had physical contact with an encephalitis patient (29% vs. 4%, matched odds ratio undefined). Efforts to prevent transmission should focus on reducing caregivers’ exposure to infected patients’ bodily secretions during care and traditional burial practices.

Comparing methods for estimating R0 from the size distribution of subcritical transmission chains

Many diseases exhibit subcritical transmission (i.e. 0<R0<1) so that infections occur as self-limited 'stuttering chains'. Given an ensemble of stuttering chains, information about the number of cases in each chain can be used to infer R0, which is of crucial importance for monitoring the risk that a disease will emerge to establish endemic circulation. However, the challenge of imperfect case detection has led authors to adopt a variety of work-around measures when inferring R0, such as discarding data on isolated cases or aggregating intermediate-sized chains together. Each of these methods has the potential to introduce bias, but a quantitative comparison of these approaches has not been reported. By adapting a model based on a negative binomial offspring distribution that permits a variable degree of transmission heterogeneity, we present a unified analysis of existing R0 estimation methods. Simulation studies show that the degree of transmission heterogeneity, when improperly modeled, can significantly impact the bias of R0 estimation methods designed for imperfect observation. These studies also highlight the importance of isolated cases in assessing whether an estimation technique is consistent with observed data. Analysis of data from measles outbreaks shows that likelihood scores are highest for models that allow a flexible degree of transmission heterogeneity. Aggregating intermediate sized chains often has similar performance to analyzing a complete chain size distribution. However, truncating isolated cases is beneficial only when surveillance systems clearly favor full observation of large chains but not small chains. Meanwhile, if data on the type and proportion of cases that are unobserved were known, we demonstrate that maximum likelihood inference of R0 could be adjusted accordingly. This motivates the need for future empirical and theoretical work to quantify observation error and incorporate relevant mechanisms into stuttering chain models used to estimate transmission parameters.

Inference of R(0) and transmission heterogeneity from the size distribution of stuttering chains

For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, [Formula: see text] and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring [Formula: see text] and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer [Formula: see text], but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, [Formula: see text]) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both [Formula: see text] and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for [Formula: see text] is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in [Formula: see text] is detectable. In addition, by allowing for superspreading events, inference of [Formula: see text] shifts the threshold above which a transmission chain should be considered anomalously large for a given value of [Formula: see text] (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.

Integrating phylodynamics and epidemiology to estimate transmission diversity in viral epidemics

The epidemiology of chronic viral infections, such as those caused by Hepatitis C Virus (HCV) and Human Immunodeficiency Virus (HIV), is affected by the risk group structure of the infected population. Risk groups are defined by each of their members having acquired infection through a specific behavior. However, risk group definitions say little about the transmission potential of each infected individual. Variation in the number of secondary infections is extremely difficult to estimate for HCV and HIV but crucial in the design of efficient control interventions. Here we describe a novel method that combines epidemiological and population genetic approaches to estimate the variation in transmissibility of rapidly-evolving viral epidemics. We evaluate this method using a nationwide HCV epidemic and for the first time co-estimate viral generation times and superspreading events from a combination of molecular and epidemiological data. We anticipate that this integrated approach will form the basis of powerful tools for describing the transmission dynamics of chronic viral diseases, and for evaluating control strategies directed against them.

To design strategies that efficiently mitigate an epidemic requires estimates of how many people each carrier is likely to infect, what is the variation of this number among infections, and what is the time needed for these transmissions to take place. The disciplines of epidemiology and population genetics independently provide partial answers to these questions by analysing surveillance data and molecular sequences, respectively. Here we propose a novel integration of the two fields that can reveal the underlying transmission dynamics of rapidly-evolving viruses such as HIV or HCV. We explore a well-described nationwide HCV epidemic and show that our method provides new insights into the nature and variation of HCV transmission among infected individuals. We suggest that this approach could form the basis of new tools that can help in the design of effective public health interventions targeting the spread of viral pathogens.

Characteristics of exhaled particle production in healthy volunteers: possible implications for infectious disease transmission

The size and concentration of exhaled particles may influence respiratory infection transmission risk. We assessed variation in exhaled particle production between individuals, factors associated with high production and stability over time.

We measured exhaled particle production during tidal breathing in a sample of 79 healthy volunteers, using optical particle counter technology. Repeat measurements (several months after baseline) were obtained for 37 of the 79 participants.   Multilevel linear regression models of log transformed particle production measures were used to assess risk factors for high production.  Stability between measurements over time was assessed using Lin’s correlation coefficients.

Ninety-nine percent of expired particles were <1μm in diameter. Considerable variation in exhaled particle production was observed between individuals and within individuals over time. Distribution of particle production was right skewed.  Approximately 90% of individuals produce <150 particles per litre in normal breathing.  A few individuals had measurements of over 1000 particles per litre (maximum 1456). Particle production increased with age (p<0.001) and was associated with high tree pollen counts. Particle production levels did not remain stable over time [rho 0.14 (95%CI -0.10, 0.38, p=0.238)].

Sub-micron particles conducive to airborne rather than droplet transmission form the great majority of exhaled particles in tidal breathing. There is a high level of variability between subjects but measurements are not stable over time. Production increases with age and may be influenced by airway inflammation caused by environmental irritants. Further research is needed to determine whether the observed variations in exhaled particle production affect transmission of respiratory infection.

Expectation-maximization algorithm for determining natural selection of Y-linked genes through two-sex branching processes

A two-dimensional bisexual branching process has recently been presented for the analysis of the generation-to-generation evolution of the number of carriers of a Y-linked gene. In this model, preference of females for males with a specific genetic characteristic is assumed to be determined by an allele of the gene. It has been shown that the behavior of this kind of Y-linked gene is strongly related to the reproduction law of each genotype. In practice, the corresponding offspring distributions are usually unknown, and it is necessary to develop their estimation theory in order to determine the natural selection of the gene. Here we deal with the estimation problem for the offspring distribution of each genotype of a Y-linked gene when the only observable data are each generation's total numbers of males of each genotype and of females. We set out the problem in a non parametric framework and obtain the maximum likelihood estimators of the offspring distributions using an expectation-maximization algorithm. From these estimators, we also derive the estimators for the reproduction mean of each genotype and forecast the distribution of the future population sizes. Finally, we check the accuracy of the algorithm by means of a simulation study.

Higher risk of measles when the first dose of a 2-dose schedule of measles vaccine is given at 12-14 months versus 15 months of age

BACKGROUND

In 2011, >750 cases of measles were reported in Quebec, Canada, where a routine 2-dose measles immunization schedule, in which measles vaccine is given at 12 and 18 months of age, had been in effect since 1996. Effectiveness of this schedule was assessed during a high school outbreak.

METHODS

Cases were identified by passive followed by active surveillance. Classical cases met the national surveillance definition; attenuated cases showed clinical signs and high measles-specific immunoglobulin G but did not fulfill all classical criteria. Immunization status was ascertained from written records, and vaccine effectiveness (VE) was calculated as 1 - [(risk of measles in vaccinated individuals)/(risk in unvaccinated individuals)] × 100%.

RESULTS

Among 1306 students, 110 measles cases were identified; 98 were classical cases, and 12 were attenuated cases. The attack rates among unvaccinated and fully vaccinated students were 82% and 4.8%, respectively. The VE among 2-dose recipients was 95.5% against classical and 94.2% against all (classical + attenuated) measles. Among 2-dose recipients, attack rates with first immunization at 12 and ≥15 months of age were 5.8% and 2.0%, respectively, with corresponding VE values of 93.0% and 97.5%. The risk of measles in 2-dose recipients was significantly (3-4-fold) higher when vaccine was first administered at 12 months of age, compared with ≥15 months of age (P = .04).

CONCLUSIONS

Despite compliance with the recommended 2-dose measles immunization schedule, 6% of high school students were susceptible during this outbreak. Residual susceptibility was 2-4-fold higher among 2-dose recipients who had received the first dose of vaccine prior to 15 months of age. If confirmed in other settings, these results suggest that administration of the first dose of measles vaccine before 15 months of age may not be optimal for measles elimination efforts.

Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks

Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k=1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97–1.38). When less dispersed with k=2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.

Modelling the effect of heterogeneity of shedding on the within herd Coxiella burnetii spread and identification of key parameters by sensitivity analysis

Coxiella burnetii is the bacterium responsible for Q fever, a worldwide zoonosis. Ruminants, especially cattle, are recognized as the most important source of human infections. Although a great heterogeneity between shedder cows has been described, no previous studies have determined which features such as shedding route and duration or the quantity of bacteria shed have the strongest impact on the environmental contamination and thus on the zoonotic risk. Our objective was to identify key parameters whose variation highly influences C. burnetii spread within a dairy cattle herd, especially those related to the heterogeneity of shedding. To compare the impact of epidemiological parameters on different dynamical aspects of C. burnetii infection, we performed a sensitivity analysis on an original stochastic model describing the bacterium spread and representing the individual variability of the shedding duration, routes and intensity as well as herd demography. This sensitivity analysis consisted of a principal component analysis followed by an ANOVA. Our findings show that the most influential parameters are the probability distribution governing the levels of shedding, especially in vaginal mucus and faeces, the characteristics of the bacterium in the environment (i.e. its survival and the fraction of bacteria shed reaching the environment), and some physiological parameters related to the intermittency of shedding (transition probability from a non-shedding infected state to a shedding state) or to the transition from one type of shedder to another one (transition probability from a seronegative shedding state to a seropositive shedding state). Our study is crucial for the understanding of the dynamics of C. burnetii infection and optimization of control measures. Indeed, as control measures should impact the parameters influencing the bacterium spread most, our model can now be used to assess the effectiveness of different control strategies of Q fever within dairy cattle herds.

Assortativity and the Probability of Epidemic Extinction: A Case Study of Pandemic Influenza A (H1N1-2009)

Unlike local transmission of pandemic influenza A (H1N1-2009), which was frequently driven by school children, most cases identified in long-distance intranational and international travelers have been adults. The present study examines the relationship between the probability of temporary extinction and the age-dependent next-generation matrix, focusing on the impact of assortativity. Preferred mixing captures as a good approximation the assortativity of a heterogeneously mixing population. We show that the contribution of a nonmaintenance host (i.e., a host type which cannot sustain transmission on its own) to the risk of a major epidemic is greatly diminished as mixing patterns become more assortative, and in such a scenario, a higher proportion of non-maintenance hosts among index cases elevates the probability of extinction. Despite the presence of various other epidemiological factors that undoubtedly influenced the delay between first importations and the subsequent epidemic, these results suggest that the dominance of adults among imported cases represents one of the possible factors explaining the delays in geographic spread observed during the recent pandemic.

Prevalent high-risk respiratory hygiene practices in urban and rural Bangladesh

OBJECTIVES

To identify existing respiratory hygiene risk practices, and guide the development of interventions for improving respiratory hygiene.

METHODS

We selected a convenience sample of 80 households and 20 schools in two densely populated communities in Bangladesh, one urban and one rural. We observed and recorded respiratory hygiene events with potential to spread viruses such as coughing, sneezing, spitting and nasal cleaning using a standardized assessment tool.

RESULTS

In 907 (81%) of 1122 observed events, households' participants coughed or sneezed into the air (i.e. uncovered), 119 (11%) into their hands and 83 (7%) into their clothing. Twenty-two per cent of women covered their coughs and sneezes compared to 13% of men (OR 2.6, 95% CI 1.6-4.3). Twenty-seven per cent of persons living in households with a reported monthly income of >72.6 US$ covered their coughs or sneezes compared to 13% of persons living in households with lower income (OR 3.2, 95% CI 1.6-6.2). In 956 (85%) of 1126 events, school participants coughed or sneezed into the air and 142 (13%) into their hands. Twenty-seven per cent of coughs/sneezes in rural schools were covered compared to 10% of coughs/sneezes in urban schools (OR 2.3, 95% CI 1.5-3.6). Hand washing was never observed after participants coughed or sneezed into their hands.

CONCLUSION

There is an urgent need to develop culturally appropriate, cost-effective and scalable interventions to improve respiratory hygiene practices and to assess their effectiveness in reducing respiratory pathogen transmission.

Bisexual branching processes to model extinction conditions for Y-linked genes

In a two-sex monogamic population, the evolution of the number of carriers of the two alleles of a Y-linked gene is considered. To this end, a multitype bisexual branching model is presented in which it is assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit constitute the key to determining the extinction or survival of each allele. Moreover, the destiny of each allele in the population is found not to depend on the behavior of the other.