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CSF-venous fistulas (CVFs) are increasingly recognised as a cause of spontaneous intracranial hypotension. They may present atypically including with brain sagging pseudo-dementia. Cervical CVFs are rare and their management can be difficult due to associated eloquent nerve roots. We report the case of a 49-year-old woman who presented with cognitive decline progressing to coma. Brain imaging showed features of spontaneous intracranial hypotension and a right C7 CVF was identified at digital subtraction and CT myelography. Initial treatment with CT-guided injection of fibrin sealant produced temporary improvement in symptoms before surgical treatment resulted in total clinical remission and radiological resolution. [ABSTRACT FROM AUTHOR]

CSF-venous fistulas (CVFs) are increasingly recognised as a cause of spontaneous intracranial hypotension. They may present atypically including with brain sagging pseudo-dementia. Cervical CVFs are rare and their management can be difficult due to associated eloquent nerve roots. We report the case of a 49-year-old woman who presented with cognitive decline progressing to coma. Brain imaging showed features of spontaneous intracranial hypotension and a right C7 CVF was identified at digital subtraction and CT myelography. Initial treatment with CT-guided injection of fibrin sealant produced temporary improvement in symptoms before surgical treatment resulted in total clinical remission and radiological resolution. [ABSTRACT FROM AUTHOR]

This article considers the minimization of the total number of infected individuals over the course of an epidemic in which the rate of infectious contacts can be reduced by timedependent nonpharmaceutical interventions. The societal and economic costs of interventions are taken into account using a linear budget constraint which imposes a trade-off between short-term heavy interventions and long-term light interventions. We search for an optimal intervention strategy in an infinite-dimensional space of controls containing multiple consecutive lockdowns, gradually imposed and lifted restrictions, and various heuristic controls based, for example, on tracking the effective reproduction number. Mathematical analysis shows that among all such strategies, the global optimum is achieved by a single constant-level lockdown of maximum possible magnitude. Numerical simulations highlight the need for careful timing of such interventions and illustrate their benefits and disadvantages compared to strategies designed for minimizing peak prevalence. Rather counterintuitively, adding restrictions prior to the start of a well-planned intervention strategy may even increase the total incidence. [ABSTRACT FROM AUTHOR]

The real-time analysis of infectious disease surveillance data is essential in obtaining situational awareness about the current dynamics of a major public health event such as the COVID-19 pandemic. This analysis of e.g., time-series of reported cases or fatalities is complicated by reporting delays that lead to under-reporting of the complete number of events for the most recent time points. This can lead to misconceptions by the interpreter, for instance the media or the public, as was the case with the time-series of reported fatalities during the COVID-19 pandemic in Sweden. Nowcasting methods provide real-time estimates of the complete number of events using the incomplete time-series of currently reported events and information about the reporting delays from the past. In this paper we propose a novel Bayesian nowcasting approach applied to COVID-19-related fatalities in Sweden. We incorporate additional information in the form of time-series of number of reported cases and ICU admissions as leading signals. We demonstrate with a retrospective evaluation that the inclusion of ICU admissions as a leading signal improved the nowcasting performance of case fatalities for COVID-19 in Sweden compared to existing methods. Author summary: Nowcasting methods are an essential tool to provide situational awareness in a pandemic. The methods aim to provide real-time estimates of the complete number of events using the incomplete time-series of currently reported events and the information about the reporting delays from the past. In this paper, we propose a Bayesian approach applied to COVID-19 fatalities in Sweden. We incorporate regression components into the Bayesian hierarchical model to accommodate additional information provided by leading indicators such as time-series of the number of reported cases and ICU admissions. We use a retrospective evaluation covering the second (alpha) and third (delta) wave of COVID-19 in Sweden to assess the performance of the proposed method. We demonstrate that the inclusion of ICU admissions as a regression component improved the nowcasting performance (measured by the CRPS score) of case fatalities for COVID-19 in Sweden by 3.9% compared to when this information was not incorporated into the model. [ABSTRACT FROM AUTHOR]

The transmission heterogeneity of an epidemic is associated with a complex mixture of host, pathogen and environmental factors. And it may indicate superspreading events to reduce the efficiency of population-level control measures and to sustain the epidemic over a larger scale and a longer duration. Methods have been proposed to identify significant transmission heterogeneity in historic epidemics based on several data sources, such as contact history, viral genomes and spatial information, which may not be available, and more importantly ignore the temporal trend of transmission heterogeneity. Here we attempted to establish a convenient method to estimate real-time heterogeneity over an epidemic. Within the branching process framework, we introduced an instant-individualheterogenous infectiousness model to jointly characterize the variation in infectiousness both between individuals and among different times. With this model, we could simultaneously estimate the transmission heterogeneity and the reproduction number from incidence time series. We validated the model with data of both simulated and real outbreaks. Our estimates of the overall and real-time heterogeneities of the six epidemics were consistent with those presented in the literature. Additionally, our model is robust to the ubiquitous bias of under-reporting and misspecification of serial interval. By analyzing recent data from South Africa, we found evidence that the Omicron might be of more significant transmission heterogeneity than Delta. Our model based on incidence data was proved to be reliable in estimating the real-time transmission heterogeneity. Author Summary: The transmission of many infectious diseases is usually heterogeneous in time and space. Such transmission heterogeneity may indicate superspreading events (where some infected individuals transmit to disproportionately more susceptibles than others), reduce the efficiency of the population-level control measures, and sustain the epidemic over a larger scale and a longer duration. Classical methods of monitoring epidemic spread centered on the reproduction number which represent the average transmission potential of the epidemic at the population level, but failed to reflect the systematic variation in transmission. Several recent methods have been proposed to identify significant transmission heterogeneity in the epidemics such as Ebola, MERS, COVID-19. However, these methods are developed based on some sophisticated information such as contact history, viral genome and spatial information, of the confirmed cases, which are typically field-specific and not easy to generalize. In this study, we proposed a simple and generic method of estimating transmission heterogeneity from incidence time series, which provided consistent estimation of heterogeneity with those records with detailed data. It also helps in exploring the transmission heterogeneity of the newly emerging variant of Omicron. Our model enhances current understanding of epidemic dynamics, and highlight the potential importance of targeted control measures. [ABSTRACT FROM AUTHOR]

Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and tested independently with some fixed probability. If such a traced individual tests positive it is isolated, and the contact tracing is iterated. This model is analysed using large population approximations, both for the early stage of the epidemic when the “to-be-traced components” of the epidemic behaves like a branching process, and for the main stage of the epidemic where the process of to-be-traced components converges to a deterministic process defined by a system of differential equations. These approximations are used to quantify the effect of testing and of contact tracing on the effective reproduction numbers (for the components as well as for the individuals), the probability of a major outbreak, and the final fraction getting infected. Using numerical illustrations when rates of infection and natural recovery are fixed, it is shown that Test-and-Trace strategy is effective in reducing the reproduction number. Surprisingly, the reproduction number for the branching process of components is not monotonically decreasing in the tracing probability, but the individual reproduction number is conjectured to be monotonic as expected. Further, in the situation where individuals also self-report for testing, the tracing probability is more influential than the screening rate (measured by the fraction infected being screened). [ABSTRACT FROM AUTHOR]

A stochastic SIR (susceptible → infective → recovered) model is considered for the spread of an epidemic on a network, described initially by an Erdős–Rényi random graph, in which susceptible individuals connected to infectious neighbors may drop or rewire such connections. A novel construction of the model is used to derive a deterministic model for epidemics started with a positive fraction initially infected and prove convergence of the scaled stochastic model to that deterministic model as the population size n→∞. For epidemics initiated by a single infective that take off, we prove that for part of the parameter space, in the limit as n→∞, the final fraction infected τ(λ) is discontinuous in the infection rate λ at its threshold λc, thus not converging to 0 as λ↓λc. The discontinuity is particularly striking when rewiring is necessarily to susceptible individuals in that τ(λ) jumps from 0 to 1 as λ passes through λc. [ABSTRACT FROM AUTHOR]

An important task in combating the current Covid-19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, often using different measures such as: the relative attack rate in case-control studies, the effect on incidence growth/decline in a specific time frame and the effect on the number of infected in a given time frame. These measures all depend on community-specific features and are hence not easily transferred to other community settings. We argue that a more universal measure is the relative reduction in the reproduction number, which we call the face mask effect, EFM. It is shown how to convert the other measures to EFM. We also apply the methodology to four empirical studies using different effect-measures. When converted to estimates of EFM, all estimates lie between 15 and 40%, suggesting that mandatory face masks reduce the reproduction number by an amount in this range, when compared with no individuals wearing face masks. [ABSTRACT FROM AUTHOR]

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. Author summary: Detecting and preventing pathogen outbreaks in the background of steady and slow spread is difficult, yet highly desirable, because such transmission heterogeneity can be a main driver of an epidemic. Hence, detection of transmission heterogeneity may direct prevention efforts and reduce future infections. While incidence and prevalence estimates may give overall indications of an epidemic's progression, they typically cannot indicate episodic outbreaks or rapid spreads in subpopulations. Likewise, detailed and reliable information about dynamic social networks is rare and not generalizable to detect local outbreaks. HIV sequence data can be used to reconstruct HIV phylogenies, which due to HIV's high evolutionary rate contain information about both transmission networks and rates of spread. Here, we use HIV phylogenies to first design a general heterogeneity detection method that can signal that there is high-level spreading present. Secondly, we develop a phylogenetic method to pinpoint which individuals that may have been infected by a super-spreader or have been involved in an outbreak. We show that using such phylogeny-guided information to prevent future HIV spread is highly efficient under many epidemiological situations, especially in typical public health situations where samples are collected through time. [ABSTRACT FROM AUTHOR]

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11–15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health. [ABSTRACT FROM AUTHOR]

This article considers stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large population properties of them are presented. The focus is then shifted to statistical methodology: what can be estimated and how, depending on the underlying network, transmission model, and the available data? This survey article discusses several different scenarios, giving references to publications where more details can be found, and identifies important open problems. [ABSTRACT FROM AUTHOR]

Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software69, 1-43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number $R_0$ using these data. [ABSTRACT FROM AUTHOR]

Despite more than 250 years of taxonomic research, we still have only a vague idea about the true size and composition of the faunas and floras of the planet. Many biodiversity inventories provide limited insight because they focus on a small taxonomic subsample or a tiny geographic area. Here, we report on the size and composition of the Swedish insect fauna, thought to represent roughly half of the diversity of multicellular life in one of the largest European countries. Our results are based on more than a decade of data from the Swedish Taxonomy Initiative and its massive inventory of the country's insect fauna, the Swedish Malaise Trap Project The fauna is considered one of the best known in the world, but the initiative has nevertheless revealed a surprising amount of hidden diversity: more than 3,000 new species (301 new to science) have been documented so far. Here, we use three independent methods to analyze the true size and composition of the fauna at the family or subfamily level: (1) assessments by experts who have been working on the most poorly known groups in the fauna; (2) estimates based on the proportion of new species discovered in the Malaise trap inventory; and (3) extrapolations based on species abundance and incidence data from the inventory. For the last method, we develop a new estimator, the combined non-parametric estimator, which we show is less sensitive to poor coverage of the species pool than other popular estimators. The three methods converge on similar estimates of the size and composition of the fauna, suggesting that it comprises around 33,000 species. Of those, 8,600 (26%) were unknown at the start of the inventory and 5,000 (15%) still await discovery. We analyze the taxonomic and ecological composition of the estimated fauna, and show that most of the new species belong to Hymenoptera and Diptera groups that are decomposers or parasitoids. Thus, current knowledge of the Swedish insect fauna is strongly biased taxonomically and ecologically, and we show that similar but even stronger biases have distorted our understanding of the fauna in the past. We analyze latitudinal gradients in the size and composition of known European insect faunas and show that several of the patterns contradict the Swedish data, presumably due to similar knowledge biases. Addressing these biases is critical in understanding insect biomes and the ecosystem services they provide. Our results emphasize the need to broaden the taxonomic scope of current insect monitoring efforts, a task that is all the more urgent as recent studies indicate a possible worldwide decline in insect faunas. [ABSTRACT FROM AUTHOR]

The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node. [ABSTRACT FROM AUTHOR]

Objectives Since 2017, the Public Health Agency of Sweden recommends that pre-exposure prophylaxis (PrEP) for HIV should be offered to high-risk individuals, in particular to men who have sex with men (MSM). The objective of this study is to develop a mathematical model investigating the effect of introducing PrEP to MSM in Sweden. Design A pair formation model, including steady and casual sex partners, is developed to study the impact of introducing PrEP. Two groups are included in the model: sexually high active MSM and sexually low active MSM. Three mixing assumptions between the groups are considered. Setting A gay-friendly MSM HIV/sexually transmitted infection testing clinic in Stockholm, Sweden. This clinic started offering PrEP to MSM in October 2018. Participants The model is calibrated according to detailed sexual behaviour data gathered in 2015 among 403 MSM. Results By targeting sexually high active MSM, a PrEP coverage of 3.5% of the MSM population (10% of all high actives) would result in the long-term HIV prevalence to drop considerably (close to 0%). While targeting only low actives would require a PrEP coverage of 35% for a similar reduction. The main effect of PrEP is the reduced susceptibility, whereas the increased HIV testing rate (every third month) among PrEP users plays a lesser role. Conclusions To create a multifaceted picture of the effects of interventions against HIV, we need models that include the different stages of HIV infection and real-world data on detailed sexual behaviour to calibrate the mathematical models. Our findings conclude that targeting HIV high-risk individuals, within HIV risk populations such as MSM, with PrEP programmes could greatly decrease the long-term HIV prevalence in Sweden. Therefore, risk stratification of individuals is of importance in PrEP implementation programmes, to ensure optimising the effect and cost-effectiveness of such programmes. [ABSTRACT FROM AUTHOR]

Background: Most HIV infections originate from individuals who are undiagnosed and unaware of their infection. Estimation of this quantity from surveillance data is hard because there is incomplete knowledge about (i) the time between infection and diagnosis (TI) for the general population, and (ii) the time between immigration and diagnosis for foreign-born persons.Methods: We developed a new statistical method for estimating the incidence of HIV-1 and the number of undiagnosed people living with HIV (PLHIV), based on dynamic modelling of heterogeneous HIV-1 surveillance data. The methods consist of a Bayesian non-linear mixed effects model using multiple biomarkers to estimate TI of HIV-1-positive individuals, and a novel incidence estimator which distinguishes between endogenous and exogenous infections by modelling explicitly the probability that a foreign-born person was infected either before or after immigration. The incidence estimator allows for direct calculation of the number of undiagnosed persons. The new methodology is illustrated combining heterogeneous surveillance data from Sweden between 2003 and 2015.Results: A leave-one-out cross-validation study showed that the multiple-biomarker model was more accurate than single biomarkers (mean absolute error 1.01 vs ≥1.95). We estimate that 816 [95% credible interval (CI) 775-865] PLHIV were undiagnosed in 2015, representing a proportion of 10.8% (95% CI 10.3-11.4%) of all PLHIV.Conclusions: The proposed methodology will enhance the utility of standard surveillance data streams and will be useful to monitor progress towards and compliance with the 90-90-90 UNAIDS target. [ABSTRACT FROM AUTHOR]

We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random weights (traversal times). This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation, we rely on the theory of multi-type real-time branching processes. We identify a special case of the two-type model in which the fraction of individuals of a certain type infected by individuals of the same type is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix. [ABSTRACT FROM AUTHOR]

A Markovian Susceptible → Infectious → Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size N → ∞ , assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy–Reed (in which the degrees of individuals are deterministic) and Newman–Strogatz–Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman–Strogatz–Watts version. The basic reproduction number R 0 and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when R 0 > 1 , the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N. [ABSTRACT FROM AUTHOR]

In this paper we present a family of models that allows us to estimate egos’ unobserved action dispositions from a joint behavioural outcome of a dyadic social interaction process of both egos’ and alters’ action dispositions. The method is put to test on a data set containing two different types of dyadic activities of high relevance for the spread of sexually transmitted infections (STI), condom use and anal sex. The data consists of individuals older than 15 years old who visited one of the nine youth clinics in the Vastra Gotaland region of Sweden between February 2010 and March 2011 for STI testing. This is hence a group of special interest for STI interventions. We cannot find any difference in condom disposition between women and men. Condoms are initially used more often in less risky types of relationships, especially if the partner ends up as a main partner. When studying the disposition towards anal sex we do however find a difference between men and women. Women are more against practising anal sex than men while the majority of men are neutral towards anal sex. [ABSTRACT FROM AUTHOR]

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic. Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic. [ABSTRACT FROM AUTHOR]

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $$\omega $$ (and reconnect to non-infectious individuals with probability $$\alpha $$ or else simply drop the edge if $$\alpha =0$$ ), so-called preventive rewiring. The models are denoted SIR- $$\omega $$ and SEIR- $$\omega $$ , and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number $$R_0$$ and the expected degree of the infectious nodes $$E(D_I)$$ using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR- $$\omega $$ and SEIR- $$\omega $$ epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same $$E(D_I)$$ for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of $$R_0$$ computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with $$\alpha > 0$$ (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations. [ABSTRACT FROM AUTHOR]

Respondent-driven sampling (RDS) is often used to estimate population properties (e.g., sexual risk behavior) in hard-to-reach populations. In RDS, already sampled individuals recruit population members to the sample from their social contacts in an efficient snowball-like sampling procedure. By assuming a Markov model for the recruitment of individuals, asymptotically unbiased estimates of population characteristics can be obtained. Current RDS estimation methodology assumes that the social network is undirected, that is, all edges are reciprocal. However, empirical social networks in general also include a substantial number of nonreciprocal edges. In this article, we develop an estimation method for RDS in populations connected by social networks that include reciprocal and nonreciprocal edges. We derive estimators of the selection probabilities of individuals as a function of the number of outgoing edges of sampled individuals. The proposed estimators are evaluated on artificial and empirical networks and are shown to generally perform better than existing estimators. This is the case in particular when the fraction of directed edges in the network is large. [ABSTRACT FROM AUTHOR]

Recent work has attempted to use whole-genome sequence data from pathogens to reconstruct the transmission trees linking infectors and infectees in outbreaks. However, transmission trees from one outbreak do not generalize to future outbreaks. Reconstruction of transmission trees is most useful to public health if it leads to generalizable scientific insights about disease transmission. In a survival analysis framework, estimation of transmission parameters is based on sums or averages over the possible transmission trees. A phylogeny can increase the precision of these estimates by providing partial information about who infected whom. The leaves of the phylogeny represent sampled pathogens, which have known hosts. The interior nodes represent common ancestors of sampled pathogens, which have unknown hosts. Starting from assumptions about disease biology and epidemiologic study design, we prove that there is a one-to-one correspondence between the possible assignments of interior node hosts and the transmission trees simultaneously consistent with the phylogeny and the epidemiologic data on person, place, and time. We develop algorithms to enumerate these transmission trees and show these can be used to calculate likelihoods that incorporate both epidemiologic data and a phylogeny. A simulation study confirms that this leads to more efficient estimates of hazard ratios for infectiousness and baseline hazards of infectious contact, and we use these methods to analyze data from a foot-and-mouth disease virus outbreak in the United Kingdom in 2001. These results demonstrate the importance of data on individuals who escape infection, which is often overlooked. The combination of survival analysis and algorithms linking phylogenies to transmission trees is a rigorous but flexible statistical foundation for molecular infectious disease epidemiology. [ABSTRACT FROM AUTHOR]

We study continuous-time birth-death type processes, where individuals have independent and identically distributed lifetimes, according to a random variable Q, with E[Q] = 1, and where the birth rate if the population is currently in state (has size) n is α(n). We focus on two important examples, namely α(n) = λn being a branching process, and α(n) = λn(N-n)/N which corresponds to an SIS (susceptible→infective →susceptible) epidemic model in a homogeneously mixing community of fixed size N. The processes are assumed to start with a single individual, i.e. in state 1. Let T , An, C, and S denote the (random) time to extinction, the total time spent in state n, the total number of individuals ever alive, and the sum of the lifetimes of all individuals in the birth-death process, respectively. We give expressions for the expectation of all these quantities and showthat these expectations are insensitive to the distribution of Q. We also derive an asymptotic expression for the expected time to extinction of the SIS epidemic, but now starting at the endemic state, which is not independent of the distribution of Q. The results are also applied to the household SIS epidemic, showing that, in contrast to the household SIR (susceptible → infective → recovered) epidemic, its threshold parameter R* is insensitive to the distribution of Q. [ABSTRACT FROM AUTHOR]

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially directed meaning that certain edges are directed and others are undirected. In the paper we define a configuration model for such networks where vertices have in-, out-, and undirected degrees that may be dependent. We prove conditions under which the resulting degree distributions converge to the intended degree distributions. The new model is shown to better approximate several empirical networks compared to undirected and completely directed networks. [ABSTRACT FROM AUTHOR]

Social networks are often only partly observed, and it is sometimes desirable to infer global properties of the network from 'egocentric' data. In the current paper, we study different types of egocentric data, and show which global network properties are consistent with data. Two global network properties are considered: the size of the largest connected component (the giant) and the size of an epidemic outbreak taking place on the network. The main conclusion is that, in most cases, egocentric data allow for a large range of possible sizes of the giant and the outbreak, implying that egocentric data carry very little information about these global properties. The asymptotic size of the giant and the outbreak is also characterized, assuming the network is selected uniformly among networks with prescribed egocentric data. [ABSTRACT FROM AUTHOR]

Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that three different scenarios may occur: (i) an epidemic never takes off, (ii) an epidemic gets going and grows but at a slower rate than the community thus still being negligible in terms of population fractions, or (iii) an epidemic takes off and grows quicker than the community eventually leading to an endemic equilibrium. Depending on the parameter values, either scenario (i) is the only possibility, both scenarios (i) and (ii) are possible, or scenarios (i) and (iii) are possible. [ABSTRACT FROM AUTHOR]

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible $$\rightarrow $$ Infective $$\rightarrow $$ Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number $$R_*$$, the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation $$\rho $$ when $$R_*$$ is just above its threshold value of one and decreases with $$\rho $$ when $$R_*$$ is well above one. [ABSTRACT FROM AUTHOR]

Consider a random graph where the mean degree is given and fixed. In this paper we derive the maximal size of the largest connected component in the graph. We also study the related question of the largest possible outbreak size of an epidemic occurring 'on' the random graph (the graph describing the social structure in the community). More precisely, we look at two different classes of random graphs. First, the Poissonian random graph in which each node i is given an independent and identically distributed (i.i.d.) random weight Xi with E(Xi) = μ, and where there is an edge between i and j with probability 1 - e-Xi Xj/(μn), independently of other edges. The second model is the thinned configuration model in which the n vertices of the ground graph have i.i.d, ground degrees, distributed as D, with E(D) = μ. The graph of interest is obtained by deleting edges independently with probability 1 - p. In both models the fraction of vertices in the largest connected component converges in probability to a constant 1 - q, where q depends on X or D and p. We investigate for which distributions X and D with given # and p, 1 - q is maximized. We show that in the class of Poissonian random graphs, X should have all its mass at 0 and one other real, which can be explicitly determined. For the thinned configuration model, D should have all its mass at 0 and two subsequent positive integers. [ABSTRACT FROM AUTHOR]

Summary. Researchers in many scientific fields make inferences from individuals to larger groups. For many groups, however, there is no list of members from which to draw a random sample. Respondent-driven sampling (RDS) is a relatively new sampling methodology that circumvents this difficulty by using the social networks of the groups under study. The RDS method has been shown to provide unbiased estimates of population proportions given certain conditions. The method is now widely used in human immunodeficiency virus related studies among high risk populations globally. We test the RDS methodology by simulating RDS studies on the social networks of a large Lesbian, gay, bisexual and transgender Web community. The robustness of the RDS method is tested by violating, one by one, the conditions under which the method provides unbiased estimates. Simulations indicate that the bias is large if networks are directed or respondents choose to invite people on the basis of characteristics that are correlated with the study outcomes. The bias and variance increase if participants invite close as opposed to more distant friends whereas sampling in denser networks sharply reduces variance. However, the RDS method shows strong resistance to sampling without replacement, low response rates and certain errors in the participants' reporting of their network sizes, as well as the selection criteria of seeds. The effects of network structure and the number of seeds and coupons are also discussed. [ABSTRACT FROM AUTHOR]

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting how closely 'connected' the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that R can be substantially over- or underestimated if the correlation between degree and weight is not taken into account. [ABSTRACT FROM AUTHOR]

We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation ρ (of neighbouring nodes) which shows that ρ is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters. [ABSTRACT FROM AUTHOR]

The birth–death process is widely used in phylogenetics to model speciation and extinction. Recent studies have shown that the inferred rates are sensitive to assumptions about the sampling probability of lineages. Here, we examine the effect of the method used to sample lineages. Whereas previous studies have assumed random sampling (RS), we consider two extreme cases of biased sampling: “diversified sampling” (DS), where tips are selected to maximize diversity and “cluster sampling (CS),” where sample diversity is minimized. DS appears to be standard practice, for example, in analyses of higher taxa, whereas CS may occur under special circumstances, for example, in studies of geographically defined floras or faunas. Using both simulations and analyses of empirical data, we show that inferred rates may be heavily biased if the sampling strategy is not modeled correctly. In particular, when a diversified sample is treated as if it were a random or complete sample, the extinction rate is severely underestimated, often close to 0. Such dramatic errors may lead to serious consequences, for example, if estimated rates are used in assessing the vulnerability of threatened species to extinction. Using Bayesian model testing across 18 empirical data sets, we show that DS is commonly a better fit to the data than complete, random, or cluster sampling (CS). Inappropriate modeling of the sampling method may at least partly explain anomalous results that have previously been attributed to variation over time in birth and death rates. [ABSTRACT FROM PUBLISHER]

. A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings according to potentially different rates. For this model, we consider how different kinds of data can be used to estimate the infection rate parameters with a view to understanding what can and cannot be inferred. Among other things we find that temporal data can be of considerable inferential benefit compared with final size data, that the degree of heterogeneity in the data can have a considerable effect on inference for non-household transmission, and that inferences can be materially different from those obtained from a model with only two levels of mixing. We illustrate our findings by analysing a highly detailed dataset concerning a measles outbreak in Hagelloch, Germany. [ABSTRACT FROM AUTHOR]

This paper is concerned with SIR (susceptible → infected → removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data. [ABSTRACT FROM AUTHOR]

We have evaluated the performance of two classes of probabilistic models for substitution rate variation over phylogenetic trees. In the first class, branch rates are considered to be independent and identically distributed (i.i.d.) stochastic variables. Three versions with respect to the underlying distribution (Gamma, Inverse Gaussian, and LogNormal) are considered. The i.i.d. models are compared with the autocorrelated (AC) model, where rates of adjacent nodes in the tree are AC, so that a node rate is LogNormal distributed around the rate of the parent node. The performance of different models is evaluated using three empirical data sets. For all data sets, it was clear that all tested models extracted substantial knowledge from data when posterior divergence time distributions were compared with the prior distributions and, furthermore, that they clearly outperformed a molecular clock. Moreover, the descriptive power of the i.i.d. models, as evaluated by Bayes factors, was either equal to or clearly better than that of the AC model. The latter effect increased with extended taxon sampling. Likewise, under none of the models could we find compelling evidence, in any of the data sets, for rate correlation between adjacent branches/nodes. These findings challenge previous suggestions of universality of autocorrelation in sequence evolution. We also performed an additional comparison with a divergence time prior including calibration information from fossil evidence. Adding fossil information to the prior had negligible effect on Bayes factors and mainly affected the width of the posterior distribution of the divergence times, whereas the relative position of the mean divergence times were largely unaffected. [ABSTRACT FROM PUBLISHER]

We analyse a Markovian SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission. [ABSTRACT FROM AUTHOR]

We consider a random network evolving in continuous time in which new nodes are born and old may die, and where undirected edges between nodes are created randomly and may also disappear. The node population is Markovian and so is the creation and deletion of edges, given the node population. Each node is equipped with a random social index and the intensity at which a node creates new edges is proportional to the social index, and the neighbour is either chosen uniformly or proportional to its social index in a modification of the model. We derive properties of the network as time and the node population tends to infinity. In particular, the degree-distribution is shown to be a mixed Poisson distribution which may exhibit a heavy tail (e.g. power-law) if the social index distribution has a heavy tail. The limiting results are verified by means of simulations, and the model is fitted to a network of sexual contacts. [ABSTRACT FROM AUTHOR]

Background. We aimed to measure the extraction fraction of human immunoglobulin G (HIG) by the 1st echelon lymph node (sentinel node) following intradermal injection in patients with breast cancer undergoing axillary lymph node dissection (ALND) and examine its association with node size and presence and extent of nodal metastatic disease. Materials and methods. HIG labelled with either In-111 ( n = 21) or Tc-99m ( n = 9) was injected intradermally at the areolar. ALND was performed 2–4 h later. All lymph nodes were isolated and individually counted in a well-counter. The counts in the ‘hottest’ (1st echelon) node were expressed as a fraction of total counts in all the resected nodes. Since counts in the least hot nodes barely exceeded background, this fraction represents extraction fraction for the 1st echelon node. Presence of disease was noted in each 1st echelon node and the extent quantified as percentage replacement with disease. Results. Median extraction fraction in 1st echelon nodes with no or low (<1%) disease burden ( n = 21) was 68 (range 23–93)%, significantly higher ( p<0.05) than in diseased 1st echelon nodes ( n = 9), in which it was 44 (21–66)%. There was, however, no association between extraction fraction in diseased nodes and disease extent. In nodes with no/low disease, extraction fraction was similar for the two radiolabels. There was no association between extraction fraction and node size. Conclusion. Nodal extraction fraction of HIG is a novel physiological measurement. It is reduced as a result of metastatic invasion. In the absence of disease, it shows no correlation with node size. [ABSTRACT FROM AUTHOR]

OBJECTIVE--Adipose tissue may contain few large adipocytes (hypertrophy) or many small adipocytes (hyperplasia). We investigated factors of putative importance for adipose tissue morphology. RESEARCH DESIGN AND METHODS--Subcutaneous adipocyte size and total fat mass were compared in 764 subjects with BMI 18-60 kg/m². A morphology value was defined as the difference between the measured adipocyte volume and the expected volume given by a curved-line fit for a given body fat mass and was related to insulin values. In 35 subjects, in vivo adipocyte turnover was measured by exploiting incorporation of atmospheric [sup 14]C into DNA. RESULTS--Occurrence of hyperplasia (negative morphology value) or hypertrophy (positive morphology value) was independent of sex and body weight but correlated with fasting plasma insulin levels and insulin sensitivity, independent of adipocyte volume (β-coefficient = 0.3, P < 0.0001). Total adipocyte number and morphology were negatively related (r = -0.66); i.e., the total adipocyte number was greatest in pronounced hyperplasia and smallest in pronounced hypertrophy. The absolute number of new adipocytes generated each year was 70% lower (P < 0.001) in hypertrophy than in hyperplasia, and individual values for adipocyte generation and morphology were strongly related (r = 0.7, P < 0.001). The relative death rate (∼10% per year) or mean age of adipocytes (∼10 years) was not correlated with morphology. CONCLUSIONS--Adipose tissue morphology correlates with insulin measures and is linked to the total adipocyte number independently of sex and body fat level. Low generation rates of adipocytes associate with adipose tissue hypertrophy, whereas high generation rates associate with adipose hyperplasia. Diabetes 59:105-109, 2010 [ABSTRACT FROM AUTHOR]

The general stochastic SIR epidemic in a closed population under the influence of a term-time forced environment is considered. An 'environment' in this context is any external factor that influences the contact rate between individuals in the population, but is itself unaffected by the population. Here 'term-time forcing' refers to discontinuous but cyclic changes in the contact rate. The inclusion of such an environment into the model is done by replacing a single contact rate λ with a cyclically alternating renewal process with k different states denoted {A(t)}t≥0. Threshold conditions in terms of R⋆ are obtained, such that R⋆ > 1 implies that π, the probability of a large outbreak, is strictly positive. Examples are given where π is evaluated numerically from which the impact of the distribution of the time periods that Λ(t) spends in its different states is clearly seen. [ABSTRACT FROM AUTHOR]

The article examines the effect of cancer cachexia on the inflammatory reaction and adipocyte lipogenesis in subcutaneous white adipose tissue (WAT). Blood and subcutaneous WAT samples were obtained from weight-stable patients, cachexia patients with cancer and noncancer patients. Systemic inflammation and lipolysis were confirmed in the cachectic patients. Moreover, subcutaneous WAT does not contribute to the inflammatory reaction and does not induce adipocyte insulin in cancer cachexia.

Obesity is increasing in an epidemic manner in most countries and constitutes a public health problem by enhancing the risk for cardiovascular disease and metabolic disorders such as type 2 diabetes. Owing to the increase in obesity, life expectancy may start to decrease in developed countries for the first time in recent history. The factors determining fat mass in adult humans are not fully understood, but increased lipid storage in already developed fat cells (adipocytes) is thought to be most important. Here we show that adipocyte number is a major determinant for the fat mass in adults. However, the number of fat cells stays constant in adulthood in lean and obese individuals, even after marked weight loss, indicating that the number of adipocytes is set during childhood and adolescence. To establish the dynamics within the stable population of adipocytes in adults, we have measured adipocyte turnover by analysing the integration of 14C derived from nuclear bomb tests in genomic DNA. Approximately 10% of fat cells are renewed annually at all adult ages and levels of body mass index. Neither adipocyte death nor generation rate is altered in early onset obesity, suggesting a tight regulation of fat cell number in this condition during adulthood. The high turnover of adipocytes establishes a new therapeutic target for pharmacological intervention in obesity. [ABSTRACT FROM AUTHOR]

In phylogenetic inference, the support of an estimated phylogenetic tree topology and its interior branches is usually measured either with non -parametric bootstrap support (BS) values or with Bayesian posterior probabilities (BPPs). Extensive empirical evidence indicates that BPP values are systematically larger than BS when measured on the same data set, but there are no theoretical results supporting such a systematic difference. In the present note, we give a heuristic mathematical argument supporting the empirically observed phenomenon. The argument uses properties of the marginal and profile likelihoods of the normal distribution. The heuristic arguments are supported in a simulation study evaluating different steps in the argument. [ABSTRACT FROM AUTHOR]