Extending backcalculation to analyse BSE data.

We review the origins of backcalculation (or back projection) methods developed for the analysis of AIDS (acquired immunodeficiency syndrome) incidence data. These techniques have been used extensively for >15 years to deconvolute clinical case incidence, given knowledge of the incubation period distribution, to obtain estimates of past HIV (human immunodeficiency virus) infection incidence and short-term predictions of future AIDS incidence. Adaptations required for the analysis of bovine spongiform encephalopathy (BSE) incidence included: stratification of BSE incidence by age as well as birth cohort; allowance for incomplete survival between infection and the onset of clinical signs of disease; and decomposition of the age- and time-related infection incidence into a time-dependent feed risk component and an age-dependent exposure/susceptibility function. The most recent methodological developments focus on the incorporation of data from clinically unaffected cattle screened using recently developed tests for preclinical BSE infection. Backcalculation-based predictions of future BSE incidence obtained since 1996 are examined. Finally, future directions of epidemiological analysis of BSE epidemics are discussed taking into account ongoing developments in the science of BSE and possible changes in BSE-related policies

Tilings, tiling spaces and topology

To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the spectrum of the translation operator) are closely related to bulk properties of the individual tilings (such as the diffraction pattern). The topology of the space of tilings, particularly the Cech cohomology, gives information on how the original tiling can be deformed. Tiling spaces can be constructed as inverse limits of branched manifolds.Comment: 8 pages, including 2 figures, talk given at ICQ

Pulmonary Mycobacterium avium-intracellulare is the main driver of the rise in non-tuberculous mycobacteria incidence in England, Wales and Northern Ireland, 2007-2012

BACKGROUND: The incidence of non-tuberculous mycobacteria (NTM) isolation from humans is increasing worldwide. In England, Wales and Northern Ireland (EW&NI) the reported rate of NTM more than doubled between 1996 and 2006. Although NTM infection has traditionally been associated with immunosuppressed individuals or those with severe underlying lung damage, pulmonary NTM infection and disease may occur in people with no overt immune deficiency. Here we report the incidence of NTM isolation in EW&NI between 2007 and 2012 from both pulmonary and extra-pulmonary samples obtained at a population level. METHODS: All individuals with culture positive NTM isolates between 2007 and 2012 reported to Public Health England by the five mycobacterial reference laboratories serving EW&NI were included. RESULTS: Between 2007 and 2012, 21,118 individuals had NTM culture positive isolates. Over the study period the incidence rose from 5.6/100,000 in 2007 to 7.6/100,000 in 2012 (p < 0.001). Of those with a known specimen type, 90 % were pulmonary, in whom incidence increased from 4.0/100,000 to 6.1/100,000 (p < 0.001). In extra-pulmonary specimens this fell from 0.6/100,000 to 0.4/100,000 (p < 0.001). The most frequently cultured organisms from individuals with pulmonary isolates were within the M. avium-intracellulare complex family (MAC). The incidence of pulmonary MAC increased from 1.3/100,000 to 2.2/100,000 (p < 0.001). The majority of these individuals were over 60 years old. CONCLUSION: Using a population-based approach, we find that the incidence of NTM has continued to rise since the last national analysis. Overall, this represents an almost ten-fold increase since 1995. Pulmonary MAC in older individuals is responsible for the majority of this change. We are limited to reporting NTM isolates and not clinical disease caused by these organisms. To determine whether the burden of NTM disease is genuinely increasing, a standardised approach to the collection of linked national microbiological and clinical data is required

Evaluation of the Northern Territory Library's Libraries and Knowledge Centres Model

Evaluation of the Northern Territory Library's model for Libraries and Knowledge Centres in Indigenous communities

Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Error growth in the Mesosphere and Lower Thermosphere Based on Hindcast Experiments in a Whole Atmosphere Model

The capability to forecast conditions in the mesosphere and lower thermosphere is investigated based on 30‐day hindcast experiments that were initialized bimonthly during 2009 and 2010. The hindcasts were performed using the Whole Atmosphere Community Climate Model with thermosphere‐ionosphere eXtension (WACCMX) with data assimilation provided by the Data Assimilation Research Testbed (DART) ensemble Kalman filter. Analysis of the WACCMX+DART hindcasts reveals several important features that are relevant to forecasting the middle atmosphere. The results show a clear dependence on spatial scale, with the slowest error growth occurring in the zonal mean and the fastest error growth occurring for small‐scale waves. The error growth rate is also found to be significantly greater in the upper mesosphere and lower thermosphere compared to in the upper stratosphere to lower mesosphere, suggesting that the forecast skill decreases with increasing altitude. The results demonstrate that the errors in the lower thermosphere reach saturation, on average, in less than 5 days, at least with the current version of WACCMX+DART. A seasonal dependency to the error growth is found at high latitudes in the Northern and Southern Hemispheres but not in the tropics or global average. We additionally investigate the error growth rates for migrating and nonmigrating atmospheric tides and find that the errors saturate after ∼5 days for tides in the lower thermosphere. The results provide an initial assessment of the error growth rates in the mesosphere and lower thermosphere and are relevant for understanding how whole atmosphere models can potentially improve space weather forecasting

The time to extinction for an SIS-household-epidemic model

We analyse a stochastic 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

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider

Antigenic Diversity, Transmission Mechanisms, and the Evolution of Pathogens

Pathogens have evolved diverse strategies to maximize their transmission fitness. Here we investigate these strategies for directly transmitted pathogens using mathematical models of disease pathogenesis and transmission, modeling fitness as a function of within- and between-host pathogen dynamics. The within-host model includes realistic constraints on pathogen replication via resource depletion and cross-immunity between pathogen strains. We find three distinct types of infection emerge as maxima in the fitness landscape, each characterized by particular within-host dynamics, host population contact network structure, and transmission mode. These three infection types are associated with distinct non-overlapping ranges of levels of antigenic diversity, and well-defined patterns of within-host dynamics and between-host transmissibility. Fitness, quantified by the basic reproduction number, also falls within distinct ranges for each infection type. Every type is optimal for certain contact structures over a range of contact rates. Sexually transmitted infections and childhood diseases are identified as exemplar types for low and high contact rates, respectively. This work generates a plausible mechanistic hypothesis for the observed tradeoff between pathogen transmissibility and antigenic diversity, and shows how different classes of pathogens arise evolutionarily as fitness optima for different contact network structures and host contact rates

The Impact of the Unstructured Contacts Component in Influenza Pandemic Modeling

Individual based models have become a valuable tool for modeling the spatiotemporal dynamics of epidemics, e.g. influenza pandemic, and for evaluating the effectiveness of intervention strategies. While specific contacts among individuals into diverse environments (family, school/workplace) can be modeled in a standard way by employing available socio-demographic data, all the other (unstructured) contacts can be dealt with by adopting very different approaches. This can be achieved for instance by employing distance-based models or by choosing unstructured contacts in the local communities or by employing commuting data.Here we show how diverse choices can lead to different model outputs and thus to a different evaluation of the effectiveness of the containment/mitigation strategies. Sensitivity analysis has been conducted for different values of the first generation index G(0), which is the average number of secondary infections generated by the first infectious individual in a completely susceptible population and by varying the seeding municipality. Among the different considered models, attack rate ranges from 19.1% to 25.7% for G(0) = 1.1, from 47.8% to 50.7% for G(0) = 1.4 and from 62.4% to 67.8% for G(0) = 1.7. Differences of about 15 to 20 days in the peak day have been observed. As regards spatial diffusion, a difference of about 100 days to cover 200 km for different values of G(0) has been observed.To reduce uncertainty in the models it is thus important to employ data, which start being available, on contacts on neglected but important activities (leisure time, sport mall, restaurants, etc.) and time-use data for improving the characterization of the unstructured contacts. Moreover, all the possible effects of different assumptions should be considered for taking public health decisions: not only sensitivity analysis to various model parameters should be performed, but intervention options should be based on the analysis and comparison of different modeling choices