Simple approximations for epidemics with exponential and fixed infectious periods

Analytical approximations have generated many insights into the dynamics of epidemics, but there is only one well-known approximation which describes the dynamics of the whole epidemic. In addition, most of the well-known approximations for different aspects of the dynamics are for the classic susceptible–infected–recovered model, in which the infectious period is exponentially distributed. Whilst this assumption is useful, it is somewhat unrealistic. Equally reasonable assumptions are that the infectious period is finite and fixed or that there is a distribution of infectious periods centred round a nonzero mean. We investigate the effect of these different assumptions on the dynamics of the epidemic by deriving approximations to the whole epidemic curve. We show how the well-known sech-squared approximation for the infective population in ‘weak’ epidemics (where the basic reproduction rate R0≈1) can be extended to the case of an arbitrary distribution of infectious periods having finite second moment, including as examples fixed and gamma-distributed infectious periods. Further, we show how to approximate the time course of a ‘strong’ epidemic, where R0≫1, demonstrating the importance of estimating the infectious period distribution early in an epidemic

The dynamics of Ascaris lumbricoides infections

The Anderson–May model of human parasite infections and specifically that for the intestinal worm Ascaris lumbricoides is reconsidered, with a view to deriving the observed characteristic negative binomial distribution which is frequently found in human communities. The means to obtaining this result lies in reformulating the continuous Anderson–May model as a stochastic process involving two essential populations, the density of mature worms in the gut, and the density of mature eggs in the environment. The resulting partial differential equation for the generating function of the joint probability distribution of eggs and worms can be partially solved in the appropriate limit where the worm lifetime is much greater than that of the mature eggs in the environment. Allowing for a mean field nonlinearity, and for egg immigration from neighbouring communities, a negative binomial worm distribution can be predicted, whose parameters are determined by those in the continuous Anderson–May model; this result assumes no variability in predisposition to the infection

Temporal diversification of Central American cichlids

<p>Abstract</p> <p>Background</p> <p>Cichlid fishes are classic examples of adaptive radiation because of their putative tendency to explosively diversify after invading novel environments. To examine whether ecological opportunity increased diversification (speciation minus extinction) early in a species-rich cichlid radiation, we determined if Heroine cichlids experienced a burst of diversification following their invasion of Central America.</p> <p>Results</p> <p>We first reconstructed the Heroine phylogeny and determined the basal node to use as the root of Central American Heroine diversification. We then examined the influence of incomplete taxon sampling on this group's diversification patterns. First, we added missing species randomly to the phylogeny and assessed deviations from a constant rate of lineage accumulation. Using a range of species numbers, we failed to recover significant deviations from a pure-birth process and found little support for an early burst of diversification. Then, we examined patterns of lineage accumulation as nodes were increasingly truncated. We assumed that as we removed more recently diverged lineages that sampling would become more complete thereby increasing the power to detect deviations from a pure-birth model. However, truncation of nodes provided even less support for an early burst of diversification.</p> <p>Conclusions</p> <p>Contrary to expectations, our analyses suggest Heroine cichlids did not undergo a burst of diversification when they invaded from South America. Throughout their history in Central America, Heroine cichlids appear to have diversified at a constant rate.</p

Quantifying engineered nanomaterial toxicity: comparison of common cytotoxicity and gene expression measurements

BACKGROUND: When evaluating the toxicity of engineered nanomaterials (ENMS) it is important to use multiple bioassays based on different mechanisms of action. In this regard we evaluated the use of gene expression and common cytotoxicity measurements using as test materials, two selected nanoparticles with known differences in toxicity, 5 nm mercaptoundecanoic acid (MUA)-capped InP and CdSe quantum dots (QDs). We tested the effects of these QDs at concentrations ranging from 0.5 to 160 µg/mL on cultured normal human bronchial epithelial (NHBE) cells using four common cytotoxicity assays: the dichlorofluorescein assay for reactive oxygen species (ROS), the lactate dehydrogenase assay for membrane viability (LDH), the mitochondrial dehydrogenase assay for mitochondrial function, and the Comet assay for DNA strand breaks. RESULTS: The cytotoxicity assays showed similar trends when exposed to nanoparticles for 24 h at 80 µg/mL with a threefold increase in ROS with exposure to CdSe QDs compared to an insignificant change in ROS levels after exposure to InP QDs, a twofold increase in the LDH necrosis assay in NHBE cells with exposure to CdSe QDs compared to a 50% decrease for InP QDs, a 60% decrease in the mitochondrial function assay upon exposure to CdSe QDs compared to a minimal increase in the case of InP and significant DNA strand breaks after exposure to CdSe QDs compared to no significant DNA strand breaks with InP. High-throughput quantitative real-time polymerase chain reaction (qRT-PCR) data for cells exposed for 6 h at a concentration of 80 µg/mL were consistent with the cytotoxicity assays showing major differences in DNA damage, DNA repair and mitochondrial function gene regulatory responses to the CdSe and InP QDs. The BRCA2, CYP1A1, CYP1B1, CDK1, SFN and VEGFA genes were observed to be upregulated specifically from increased CdSe exposure and suggests their possible utility as biomarkers for toxicity. CONCLUSIONS: This study can serve as a model for comparing traditional cytotoxicity assays and gene expression measurements and to determine candidate biomarkers for assessing the biocompatibility of ENMs.1R01GM84702-01 - National Institute of General Medical Science

Rotational Evolution During Type I X-Ray Bursts

The rotation rates of six weakly-magnetic neutron stars accreting in low-mass X-ray binaries have most likely been measured by Type I X-ray burst observations with RXTE. The nearly coherent oscillations detected during the few seconds of thermonuclear burning are most simply understood as rotational modulation of brightness asymmetries on the neutron star surface. We show that, as suggested by Strohmayer and colleagues, the frequency changes of 1-2 Hz observed during bursts are consistent with angular momentum conservation as the burning shell hydrostatically expands and contracts. We calculate how vertical heat propagation through the radiative outer layers of the atmosphere and convection affect the coherence of the oscillation. We show that the evolution of the rotational profile depends strongly on whether the burning layers are composed of pure helium or mixed hydrogen/helium. Our results help explain the absence (presence) of oscillations from hydrogen-burning (helium-rich) bursts that was found by Muno and collaborators. We investigate angular momentum transport within the burning layers and the recoupling of the burning layers with the star. We show that the Kelvin-Helmholtz instability is quenched by the strong stratification, and that mixing between the burning fuel and underlying ashes by the baroclinic instability does not occur. However, the baroclinic instability may have time to operate within the differentially rotating burning layer, potentially bringing it into rigid rotation.Comment: To appear in The Astrophysical Journal; minor corrections made to tables and figure

Data for Elimination of visceral leishmaniasis in the Indian subcontinent: a comparison of predictions from three transmission models: Warwick model description and parameter uncertainty analysis

We present three transmission models of visceral leishmaniasis (VL) in the Indian subcontinent (ISC) with structural differences regarding the disease stage that provides the main contribution to transmission, including models with a prominent role of asymptomatic infection, and fit them to recent case data from 8 endemic districts in Bihar, India. Following a geographical cross-validation of the models, we compare their predictions for achieving the WHO VL elimination targets with ongoing treatment and vector control strategies. All the transmission models suggest that the WHO elimination target (<1 new VL case per 10,000 capita per year at sub-district level) is likely to be met in Bihar, India, before or close to 2020 in sub-districts with a pre-control incidence of 10 VL cases per 10,000 people per year or less, when current intervention levels (60% coverage of indoor residual spraying (IRS) of insecticide and a delay of 40 days from onset of symptoms to treatment (OT)) are maintained, given the accuracy and generalizability of the existing data regarding incidence and IRS coverage. In settings with a pre-control endemicity level of 5/10,000, increasing the effective IRS coverage from 60 to 80% is predicted to lead to elimination of VL 1–3 years earlier (depending on the particular model), and decreasing OT from 40 to 20 days to bring elimination forward by approximately 1 year. However, in all instances the models suggest that L. donovani transmission will continue after 2020 and thus that surveillance and control measures need to remain in place until the longer-term aim of breaking transmission is achieved

Explosive diversification following a benthic to pelagic shift in freshwater fishes

BACKGROUND: Interspecific divergence along a benthic to pelagic habitat axis is ubiquitous in freshwater fishes inhabiting lentic environments. In this study, we examined the influence of this habitat axis on the macroevolution of a diverse, lotic radiation using mtDNA and nDNA phylogenies for eastern North America\u27s most species-rich freshwater fish clade, the open posterior myodome (OPM) cyprinids. We used ancestral state reconstruction to identify the earliest benthic to pelagic transition in this group and generated fossil-calibrated estimates of when this shift occurred. This transition could have represented evolution into a novel adaptive zone, and therefore, we tested for a period of accelerated lineage accumulation after this historical habitat shift. RESULTS: Ancestral state reconstructions inferred a similar and concordant region of our mtDNA and nDNA based gene trees as representing the shift from benthic to pelagic habitats in the OPM clade. Two independent tests conducted on each gene tree suggested an increased diversification rate after this inferred habitat transition. Furthermore, lineage through time analyses indicated rapid early cladogenesis in the clade arising after the benthic to pelagic shift. CONCLUSIONS: A burst of diversification followed the earliest benthic to pelagic transition during the radiation of OPM cyprinids in eastern North America. As such, the benthic/pelagic habitat axis has likely influenced the generation of biodiversity across disparate freshwater ecosystems. doi: 10.1186/1471-2148-13-27

Resolving Fine-Scale Heterogeneity of Co-seismic Slip and the Relation to Fault Structure

Fault slip distributions provide important insight into the earthquake process. We analyze high-resolution along-strike co-seismic slip profiles of the 1992 M_w = 7.3 Landers and 1999 M_w = 7.1 Hector Mine earthquakes, finding a spatial correlation between fluctuations of the slip distribution and geometrical fault structure. Using a spectral analysis, we demonstrate that the observed variation of co-seismic slip is neither random nor artificial, but self-affine fractal and rougher for Landers. We show that the wavelength and amplitude of slip variability correlates to the spatial distribution of fault geometrical complexity, explaining why Hector Mine has a smoother slip distribution as it occurred on a geometrically simpler fault system. We propose as a physical explanation that fault complexity induces a heterogeneous stress state that in turn controls co-seismic slip. Our observations detail the fundamental relationship between fault structure and earthquake rupture behavior, allowing for modeling of realistic slip profiles for use in seismic hazard assessment and paleoseismology studies

Estimating the public health impact of the effect of herpes simplex virus suppressive therapy on plasma HIV-1 viral load.

OBJECTIVE: Trials of herpes simplex virus (HSV) suppressive therapy among HSV-2/HIV-1-infected individuals have reported an impact on plasma HIV-1 viral loads (PVLs). Our aim was to estimate the population-level impact of suppressive therapy on female-to-male HIV-1 sexual transmission. DESIGN AND METHODS: By comparing prerandomization and postrandomization individual-level PVL data from the first two HSV suppressive therapy randomized controlled trials in sub-Saharan Africa, we estimated the effect of treatment on duration of asymptomatic infection and number of HIV-1 transmission events for each trial. RESULTS: Assuming that a reduction in PVL is accompanied by an increased duration of HIV-1 asymptomatic infection, 4-6 years of HSV suppressive therapy produce a 1-year increase in the duration of this stage. To avert one HIV-1 transmission requires 8.8 [95% confidence interval (CI), 5.9-14.9] and 11.4 (95% CI, 7.8-27.5) women to be treated from halfway through their HIV-1 asymptomatic period, using results from Burkina Faso and South African trials, respectively. Regardless of the timing of treatment initiation, 51.6 (95% CI, 30.4-137.0) and 66.5 (95% CI, 36.7-222.6) treatment-years are required to avert one HIV-1 infection. Distributions of set-point PVL values from sub-Saharan African populations suggest that unintended adverse consequences of therapy at the population level (i.e. increased HIV-1 transmission due to increased duration of infection) are unlikely to occur in these settings. CONCLUSION: HSV suppressive therapy may avert relatively few HIV-1 transmission events per person-year of treatment. Its use as a prevention intervention may be limited; however, further research into its effect on rate of CD4 cell count decline and the impact of higher dosing schedules is warranted

How new technology is addressed by researchers in educational studies: approaches from high-performing universities in China and the UK

There is a crisis of expectation in relation to educational technology. This is sometimes interpreted as a failure of academic researchers to disseminate their work to educational practitioners. However, another interpretation dwells on the lack of vision characterising such research. Because teachers often encounter research most intensely during their own pre-service and in-service education, we review academic research here through a snapshot of output from 10 leading university Education departments sampled in the UK and China. Empirical papers with a central interest in new technology were scarce, representing around 10% of the sample. Research was strongly situated in 'classroom' contexts although, as critics have suggested, with limited attention to the wider ecology of those places and with teachers being the focal interest as much as students. An 'outcomes' research orientation was less common than an interest in process. Although this was approached with different methodologies in China and the UK. Discussion addresses the challenge of effective and authoritative dissemination and constraints arising from the political economy of research itself