We consider an SIR (susceptible $\to$ infective $\to$ recovered) epidemic in a closed population of size n, in which infection spreads via mixing events, comprising individuals chosen uniformly at random from the population, which occur at the points of a Poisson process. This contrasts sharply with most epidemic models, in which infection is spread purely by pairwise interaction. A sequence of epidemic processes, indexed by n, and an approximating branching process are constructed on a common probability space via embedded random walks. We show that under suitable conditions the process of infectives in the epidemic process converges almost surely to the branching process. This leads to a threshold theorem for the epidemic process, where a major outbreak is defined as one that infects at least $\log n$ individuals. We show further that there exists $\delta \gt 0$, depending on the model parameters, such that the probability that a major outbreak has size at least $\delta n$ tends to one as $n \to \infty$.

During an epidemic outbreak, typically only partial information about the outbreak is known. A common scenario is that the infection times of individuals are unknown, but individuals, on displaying symptoms, are identified as infectious and removed from the population. We study the distribution of the number of infectives given only the times of removals in a Markovian susceptible–infectious–removed (SIR) epidemic. Primary interest is in the initial stages of the epidemic process, where a branching (birth–death) process approximation is applicable. We show that the number of individuals alive in a time-inhomogeneous birth–death process at time $t \geq 0$, given only death times up to and including time t, is a mixture of negative binomial distributions, with the number of mixing components depending on the total number of deaths, and the mixing weights depending upon the inter-arrival times of the deaths. We further consider the extension to the case where some deaths are unobserved. We also discuss the application of the results to control measures and statistical inference.

Observational studies suggest that 25-hydroxy vitamin D (25(OH)D) concentration is inversely associated with pain. However, findings from intervention trials are inconsistent. We assessed the effect of vitamin D supplementation on pain using data from a large, double-blind, population-based, placebo-controlled trial (the D-Health Trial). 21 315 participants (aged 60–84 years) were randomly assigned to a monthly dose of 60 000 IU vitamin D3 or matching placebo. Pain was measured using the six-item Pain Impact Questionnaire (PIQ-6), administered 1, 2 and 5 years after enrolment. We used regression models (linear for continuous PIQ-6 score and log-binomial for binary categorisations of the score, namely ‘some or more pain impact’ and ‘presence of any bodily pain’) to estimate the effect of vitamin D on pain. We included 20 423 participants who completed ≥1 PIQ-6. In blood samples collected from 3943 randomly selected participants (∼800 per year), the mean (sd) 25(OH)D concentrations were 77 (sd 25) and 115 (sd 30) nmol/l in the placebo and vitamin D groups, respectively. Most (76 %) participants were predicted to have 25(OH)D concentration >50 nmol/l at baseline. The mean PIQ-6 was similar in all surveys (∼50·4). The adjusted mean difference in PIQ-6 score (vitamin D cf placebo) was 0·02 (95 % CI (−0·20, 0·25)). The proportion of participants with some or more pain impact and with the presence of bodily pain was also similar between groups (both prevalence ratios 1·01, 95 % CI (0·99, 1·03)). In conclusion, supplementation with 60 000 IU of vitamin D3/month had negligible effect on bodily pain.

Scrub typhus is a common bacterial infection in Asia caused by Orientia tsutsugamushi. This serological cohort study estimated the incidence of infection in a rural population in South India. Participants were enrolled through systematic sampling in 46 villages at baseline, and revisited the following year. Blood samples were tested for IgG antibodies using ELISA, followed by indirect immunofluorescence assays (IFA) in those positive for ELISA at both rounds. A case was defined as sero-conversion (ELISA), or at least a 4-fold titre increase (IFA), between the two time points. In addition to crude incidence rate estimates, we used piecewise linear rates across calendar months, with rates proportional to the monthly incidence of local hospital cases to address seasonality and unequal follow-up times. Of 402 participants, 61.7% were female. The mean age was 46.7 years, (range 13–88). 21 participants showed evidence for serological infection. The estimated incidence was 4.4 per 100 person-years (95% CI 2.8–6.7). The piecewise linear rates approach resulted in a similar estimate of 4.6 per 100 person years (95% CI 2.9–6.9). Considering previous estimates of symptomatic scrub typhus incidence in the same study population, only about 2–5% of infections may result in clinically relevant disease.

The first demonstration of laser action in ruby was made in 1960 by T. H. Maiman of Hughes Research Laboratories, USA. Many laboratories worldwide began the search for lasers using different materials, operating at different wavelengths. In the UK, academia, industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of applications. This historical review looks at the contribution the UK has made to the advancement of the technology, the development of systems and components and their exploitation over the last 60 years.

The reported associations between birth weight and childhood cardiovascular disease (CVD) risk factors have been inconsistent. In this study, we investigated the relationship between birth weight and CVD risk factors at 11 years of age. This study used longitudinally linked data from three cross-sectional datasets (N = 22,136) in West Virginia; analysis was restricted to children born full-term (N = 19,583). The outcome variables included resting blood pressure [systolic blood pressure (SBP), diastolic blood pressure (DBP)] and lipid profile [total cholesterol (TC), low-density lipoprotein (LDL) cholesterol, high-density lipoprotein (HDL) cholesterol, non-HDL, and triglycerides (TG)]. Multiple regression analyses were performed, adjusting for child’s body mass index (BMI), sociodemographics, and lifestyle characteristics. Unadjusted analyses showed a statistically significant association between birth weight and SBP, DBP, HDL, and TG. When adjusted for the child’s BMI, the association between birth weight and HDL [b = 0.14 (95% CI: 0.11, 0.18) mg/dl per 1000 g increase] and between birth weight and TG [b = –0.007 (–0.008, –0.005) mg/dl per 1000 g increase] remained statistically significant. In the fully adjusted model, low birth weight was associated with higher LDL, non-HDL, and TGs, and lower HDL levels. The child’s current BMI at 11 years of age partially (for HDL, non-HDL, and TG) and fully mediated (for SBP and DBP) the relationship between birth weight and select CVD risk factors. While effects were modest, these risk factors may persist and amplify with age, leading to potentially unfavorable consequences in later adulthood.

Where polythermal glaciers have frozen margins that buttress otherwise temperate-based sliding ice, longitudinal compression can strongly influence ice-flow trajectory, and consequently sediment transport paths. Past efforts to model flow in the vicinity of a basal thermal transition (BTT) have generally relied on simplified boundary conditions or rheological idealizations, making these model results difficult to apply to real glacier termini. Herein, we present results of numerical simulations using a power-law rheology and with boundary conditions that better represent the frozen margin. Model results indicate that a transition to a non-sliding frozen margin causes a decline in surface velocity made possible by upward ice flow, implying either enhanced ablation for steady-state simulations or the formation of a surface bulge. Permitting ice loss by ablation combined with numerical smoothing of the basal slip transition subdues basal stress concentrations and thereby inhibits development of structural discontinuities such as thrust faults. Upward ice flow is accommodated by vertical extension up-glacier of the BTT. This strain regime can potentially account for key structural features in polythermal glacier termini without appealing to thrusting.

The cold-based termini of polythermal glaciers are usually assumed to adhere strongly to an immobile substrate and thereby supply significant resistance to the flow of warm-based ice up-glacier. This compressive environment is commonly thought to uplift basal sediment to the surface of the glacier by folding and thrust faulting. We present model and field evidence from the terminus of Storglaciären, Sweden, showing that the cold margin provides limited resistance to flow from up-glacier. Ice temperatures indicate that basal freezing occurs in this zone at 10−1 −10−2 m a−1, but model results indicate that basal motion at rates greater than 1 m a−1 must, nevertheless, persist there for surface and basal velocities to be consistent with measurements. Estimated longitudinal compressive stresses of 20–25 kPa within the terminus further indicate that basal resistance offered by the cold-based terminus is small. These results indicate that where polythermal glaciers are underlain by unlithified sediments, ice-flow trajectories and sediment transport pathways may be affected by subglacial topography and hydrology more than by the basal thermal regime.

The shear strength of deforming till beneath Storglaciären, Sweden, was continuously measured with a new instrument, a “dragometer”. A cylinder with conical ends, roughened with till from the glacier bed, was dragged through the till, and the force on the cylinder was recorded. Consistent with studies of cone penetration in soils, it was assumed that the till behaves as a Coulomb plastic material. This allows the residual strength of the till to be calculated from the measured force. Results from laboratory experiments confirm the validity of the analytical procedure.

The average residual strength of the till was ∼55 kPa. A source of error is the potential generation of pore pressure in excess of hydrostatic ahead of the cylinder, which could significantly weaken the till. Calculations indicate that excess pore pressure did not develop during the experiment, but could develop during similar experiments beneath rapidly sliding glaciers with less permeable basal till layers.

In order to study, in situ, the rheology of a deforming subglacial till, various instruments were emplaced in till beneath Storglaciären, Sweden. Boreholes were used to gain access to the till beneath about 100 m of ice. Tiltmeters provided an estimate of the shear strain rate in the till. Two other instruments yielded measures of till strength. In addition, water pressures were recorded in boreholes and in the till, a computer-controlled distance meter provided an effectively continuous record of the surface velocity and data from frequent surveys of a stake network were used to estimate the mean basal drag, based on a force-balance calculation.

Tilt rates varied directly with effective pressure, so decreases in water pressure apparently increased the coupling between the glacier and the bed. Surface speed was either out of phase with tilt or varied independently of tilt. Thus, increases in speed were apparently a consequence either of longitudinal coupling or of reduced coupling between the glacier and the bed; they were not a result of till deformation! Till strength varied directly with effective pressure, which is consistent with it being a Mohr – Coulomb, or frictional material. The devices measuring till strength are presumed to have been pulled through the till at a speed that varied in phase with the surface speed but till strength did not vary systematically with surface speed. This implies that the residual strength of the till is insensitive to strain rate. Thus, the appropriate constitutive equation for till rheology may be of the form:

where k is a constant. This is consistent with experimental data reported in the geotechnical literature.

Force variations on a "ploughmeter" and fluctuations in subglacial water pressure have been measured in the same borehole at Storglaciaren, Sweden, to investigate hydraulic properties of the basal till layer. A strong inverse correlation of the pressure and force records, in conjunction with a significant lime lag between the two signals, suggests that pore-water pressures directly affect the strength of the till. Variations in sub-glacial water pressure result in potential gradients across the water till interlace at the bottom of the borehole that drive pressure waves downwards through the till layer when the borehole water level is high and back upwards when the water level is low. Analysis of the propagation velocity of this pressure wave indicates that the hydraulic diffusivity of Storglaciaren till is in the range 1.9−3.6 x 10−6m2s−1,in good agreement with estimates obtained in the laboratory. Hydraulic conductivity values associated with these difrusivities are between 10−9 and 10−8ms−1 and thus are well within the range of values for other glacial tills.

To predict the distribution of motion beneath glaciers on soft beds, the strength of the coupling between the ice and the bed and its variation with effective pressure must be known. A record of shear strain, acquired with a tiltmeter emplaced in till beneath Storglaciären, Sweden, indicates that fluctuations in water pressure cause variations in the local shear stress on the bed and that the bed deforms elastically in response to these variations. To estimate the shear stress from the elastic component of the total shear strain, the shear modulus of the till was measured in relaxation tests conducted in the laboratory with a ring-shear device. After accounting for the elastic compliance of the device, these tests yielded shear moduli of about 1000 and 1800 kPa at confining pressures of 85 and 280 kPa, respectively. These values are comparable to those of other granular materials undergoing recoverable shear strains of the same magnitude. The local shear stress on the till, calculated by applying the measured shear moduli to the tilt record, scales with Pe1.7, where Pe is the effective pressure. This relation implies that as Pe decreases at the ice/till interface, shear stresses on the till are reduced and concentrated elsewhere on the bed, perhaps where the till is absent or the glacier is frozen to the bed. When compared with the strength of the till determined from ring-shear tests, this relation also accounts for the lack of permanent deformation at depth in the bed during periods of low Pe and indicates that most basal motion was by sliding or ploughing.

During the course of a day an individual typically mixes with different groups of individuals. Epidemic models incorporating population structure with individuals being able to infect different groups of individuals have received extensive attention in the literature. However, almost exclusively the models assume that individuals are able to simultaneously infect members of all groups, whereas in reality individuals will typically only be able to infect members of any group they currently reside in. In this paper we develop a model where individuals move between a community and their household during the course of the day, only infecting within their current group. By defining a novel branching process approximation with an explicit expression for the probability generating function of the offspring distribution, we are able to derive the probability of a major epidemic outbreak.

C band backscatter parameters contain information about the upper snowpack/firn in the dry snow zone. The wide incidence angle diversity of the Advanced Scatterometer (ASCAT) gives unprecedented characterisation of backscatter anisotropy, revealing the backscatter response to climatic forcing. The A (isotropic component) and M2 (bi-sinusoidal azimuth anisotropy) parameters are investigated here, in conjunction with data from atmospheric and snowpack models, to identify the backscatter response to surface forcing parameters (wind speed and persistence, precipitation, surface temperature, density and grain size). The long-term mean A parameter is successfully recreated with a regression using these drivers, indicating strong links between the A parameter and precipitation on long timescales. While the ASCAT time series is too short to determine which factors drive observed trends, factors influencing the seasonal and short timescale variability are revealed. On these timescales, A strongly responds to the propagation of surface temperature cycles/anomalies downward through the firn, via direct modulation of the dielectric constant. The influence of precipitation on A is small at shorter timescales. The M2 parameter is controlled by wind speed and persistence, through modification of monodirectionally-aligned surface roughness. This variability indicates that throughout much of coastal Antarctica, a microwave ‘snapshot’ is generally not representative of longer-term conditions.

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) = λ n 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 show that 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.

Conservation agriculture (CA) based on minimum soil disturbance, crop residue retention and crop rotations is considered as a soil and crop management system that could potentially increase soil quality and mitigate the negative effects of climate variability. When CA is combined with drought-tolerant (DT) maize varieties, farmers can reap the benefits of both—genetic improvement and sustainable land management. New initiatives were started in 2007 in Mozambique to test the two climate-smart agriculture technologies on farmers' fields. Long-term trends showed that direct seeded manual CA treatments outyielded conventional tillage treatments in up to 89% of cases on maize and in 90% of cases on legume in direct yield comparisons. Improved DT maize varieties outyielded the traditional control variety by 26–46% (695–1422 kg ha−1) on different tillage treatment, across sites and season. However a direct interaction between tillage treatment and variety performance could not be established. Maize and legume grain yields on CA plots in this long-term dataset did not increase with increased years of practice due to on-site variability between farmer replicates. It was evident from the farmers' choice that, beside taste and good milling quality, farmers in drought-prone environments considered the potential of a variety to mature faster more important than larger potential yields of long season varieties. Population growth, labor shortage to clear new land areas and limited land resources in future will force farmers to change toward more permanent and sustainable cropping systems and CA is a viable option to improve their food security and livelihoods.