Growth, reproduction numbers and factors affecting the spread of SARS-CoV-2 novel variants of concern in the UK from October 2020 to July 2021: a modelling analysis

ObjectivesImportations of novel variants of concern (VOC), particularly B.1.617.2, have become the impetus behind recent outbreaks of SARS-CoV-2. Concerns around the impact on vaccine effectiveness, transmissibility and severity are now driving the public health response to these variants. This paper analyses the patterns of growth in hospitalisations and confirmed cases for novel VOCs by age groups, geography and ethnicity in the context of changing behaviour, non-pharmaceutical interventions (NPIs) and the UK vaccination programme. We seek to highlight where strategies have been effective and periods that have facilitated the establishment of new variants.DesignWe have algorithmically linked the most complete testing and hospitalisation data in England to create a data set of confirmed infections and hospitalisations by SARS-CoV-2 genomic variant. We have used these linked data sets to analyse temporal, geographic and demographic distinctions.Setting and participantsThe setting is England from October 2020 to July 2021. Participants included all COVID-19 tests that included RT-PCR CT gene target data or underwent sequencing and hospitalisations that could be linked to these tests.MethodsTo calculate the instantaneous growth rate for VOCs we have developed a generalised additive model fit to multiple splines and varying day of the week effects. We have further modelled the instantaneous reproduction number Rt for the B.1.1.7 and B.1.617.2 variants and included a doubly interval censored model to temporally adjust the confirmed variant cases.ResultsWe observed a clear replacement of the predominant B.1.1.7 by the B.1.617.2 variant without observing sustained exponential growth in other novel variants. Modelled exponential growth of RT PCR gene target triple-positive cases was initially detected in the youngest age groups, although we now observe across all ages a very small doubling time of 10.7 (95% CI 9.1 to 13.2) days and 8 (95% CI 6.9 to 9.1) days for cases and hospitalisations, respectively. We observe that growth in RT PCR gene target triple-positive cases was first detected in the Indian ethnicity group in late February, with a peak of 0.06 (95% CI 0.07 to 0.05) in the instantaneous growth rate, but is now maintained by the white ethnicity groups, observing a doubling time of 6.8 (95% CI 4.9 to 11) days. Rt analysis indicates a reproduction number advantage of 0.45 for B.1.617.2 relative to B.1.1.7, with the Rt value peaking at 1.85 for B.1.617.2.ConclusionsOur results illustrate a clear transmission advantage for the B.1.617.2 variant and the growth in hospitalisations illustrates that this variant is able to maintain exponential growth within age groups that are largely doubly vaccinated. There are concerning signs of intermittent growth in the B.1.351 variant, reaching a 28-day doubling time peak in March 2021, although this variant is presently not showing any evidence of a transmission advantage over B.1.617.2. Step 1b of the UK national lockdown easing was sufficient to precipitate exponential growth in B.1.617.2 cases for most regions and younger adult age groups. The final stages of NPI easing appeared to have a negligible impact on the growth of B.1.617.2 with every region experiencing sustained exponential growth from step 2. Nonetheless, early targeted local NPIs appeared to markedly reduced growth of B.1.617.2. Later localised interventions, at a time of higher prevalence and greater geographic dispersion of this variant, appeared to have a negligible impact on growth.

Distribution, Feeding Habits, and Growth of Chub Mackerel, Scomber japonicus, Larvae During a High-Stock Period in the Northern Satsunan Area, Southern Japan

To evaluate the importance of the northern Satsunan area in southern Japan as a spawning and nursery ground for chub mackerel (Scomber japonicus), we investigated the early life history characteristics (e.g., larval distribution, feeding habits, and growth) of S. japonicus over five successive years. This area is considered the main habitat and spawning ground of the congeneric species, S. australasicus. Using polymerase chain reaction-restriction fragment length polymorphism analysis, we first confirmed that S. japonicus larvae were abundant in the northern Satsunan area, potentially representing a major spawning and nursery ground in the Japanese Pacific coastal area. The number of recorded larvae started to increase in 2016, corresponding to the population dynamics of the Pacific stock of the species, which has shown increasing trends in recent years. Morphological and DNA metabarcoding analyses of gut contents and stable isotope analysis showed that, in addition to copepods, the larvae fed substantially on appendicularians. The trophic pathway involving appendicularians might support the feeding habits of S. japonicus, promoting its coexistence with other dominant species. Both the instantaneous growth rate and daily specific growth rate were comparable to those in the southern East China Sea, which is the main spawning and nursery ground of the species. Our data strongly suggest that the northern Satsunan area has favorable conditions for sustaining high larval population densities, even during phases with high population numbers. Our results provide insights for the fisheries management for S. japonicus in the Japanese Pacific coastal area, especially during high-stock periods.

Influence of environmental change, harvest exposure, and human disturbance on population trends of greater sage-grouse

Hunter harvest of greater sage-grouse (Centrocercus urophasianus; hereafter “sage-grouse”) has been regulated by wildlife agencies during most of the past century. Hunting season regulations were maintained with the intention of providing sustainable hunting opportunities. Sage-grouse populations oscillate over time, and population growth can be influenced by seasonal weather and habitat disturbance. From 1995–2013, we compared sage-grouse lek trends from 22 relatively distinct sage-grouse population segments in 9 western U.S. states and 2 Canadian provinces. We stratified these populations into 3 broad categories (non-hunted [n = 8], continuously hunted [n = 10], and hunting season discontinued between 1996–2003 [n = 4]) with 8 different regulation histories to evaluate the potential impact of harvest on sage-grouse populations. Concomitantly, we assessed the effects of proportion burned, forested and cropland habitat; winter, spring, and summer precipitation; and human population, road, and oil and gas well densities on initial and time-varying lek counts. Density-dependent models fit lek trend data best for all regulation histories. In general, higher proportions of burnt, forested, and cropland habitat; and greater human population and oil and gas well densities were associated with lower equilibrium abundance (K). We found mixed results regarding the effect of hunting regulations on instantaneous growth rate (r). The cessation of harvest from 1996–2001 in approximately half of the largest sage-grouse population in our analysis was associated with higher r. Continuously harvested sage-grouse populations with permit hunting seasons had higher r during years with higher proportion of area exposed to permitted hunting rather than general upland game seasons. However, more liberal hunting regulations were positively associated with higher r in populations continuously harvested under general upland game hunts. Our results suggest that discontinuing harvest in the largest population resulted in greater population growth rates; however, this was not consistently the case for smaller populations. To no surprise, not all sage-grouse populations were influenced by the same environmental change or human disturbance factors. Our results will assist managers to understand factors associated with K, which provides the best targets for conservation efforts.

Selection of nonlinear mixed models for growth curves of dairy buffaloes (Bubalus bubalis)

The determination of livestock growth patterns is important for meat or milk production systems, and nonlinear models are used to summarize and interpret the information. The aim of this study was to more accurately estimate growth curve parameters in buffalo cows by evaluating and selecting nonlinear mixed models that employ different types of residuals and include or not contemporary groups (CG) as a covariate. Weight records from 720 animals obtained over a period of 60 months were used. The growth curves were fit using nonlinear mixed-effects models. The Bertalanffy, Gompertz and Logistic models were evaluated. Modelling residuals using four structures (constant, combined, exponential and proportional) and the inclusion or not of CG in the models were also evaluated. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used to select the model. In addition to estimating the parameters of the nonlinear growth models and their correlations, the instantaneous growth rate and inflection point were obtained. The Bertalanffy model with a combined residual structure and CG exhibited the lowest AIC and BIC values. Asymptotic weight (A) estimates ranged from 621.8 to 742.1 kg, and the maturity rate (k) ranged from 0.068 to 0.115 kg/month. The correlation between A and k ranged from −0.32 to −0.82 among the models evaluated. The selection criteria indicated that the Bertalanffy model was the most suitable for growth curve analysis in buffaloes.

Robust, linear correlations between growth rates and β-lactam–mediated lysis rates

It is widely acknowledged that faster-growing bacteria are killed faster by β-lactam antibiotics. This notion serves as the foundation for the concept of bacterial persistence: dormant bacterial cells that do not grow are phenotypically tolerant against β-lactam treatment. Such correlation has often been invoked in the mathematical modeling of bacterial responses to antibiotics. Due to the lack of thorough quantification, however, it is unclear whether and to what extent the bacterial growth rate can predict the lysis rate upon β-lactam treatment under diverse conditions. Enabled by experimental automation, here we measured >1,000 growth/killing curves for eight combinations of antibiotics and bacterial species and strains, including clinical isolates of bacterial pathogens. We found that the lysis rate of a bacterial population linearly depends on the instantaneous growth rate of the population, regardless of how the latter is modulated. We further demonstrate that this predictive power at the population level can be explained by accounting for bacterial responses to the antibiotic treatment by single cells. This linear dependence of the lysis rate on the growth rate represents a dynamic signature associated with each bacterium–antibiotic pair and serves as the quantitative foundation for designing combination antibiotic therapy and predicting the population-structure change in a population with mixed phenotypes.

Noise propagation in an integrated model of bacterial gene expression and growth

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing > 1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations

We derive and assess the sharpness of analytic upper bounds for the instantaneous growth rate and finite-time amplification of palinstrophy in solutions of the two-dimensional incompressible Navier–Stokes equations. A family of optimal solenoidal fields parametrized by initial values for the Reynolds number $Re$ and palinstrophy ${\mathcal{P}}$ which maximize $\text{d}{\mathcal{P}}/\text{d}t$ is constructed by numerically solving suitable optimization problems for a wide range of $Re$ and ${\mathcal{P}}$, providing numerical evidence for the sharpness of the analytic estimate $\text{d}{\mathcal{P}}/\text{d}t\leqslant (a+b\sqrt{\ln Re+c}){\mathcal{P}}^{3/2}$ with respect to both $Re$ and ${\mathcal{P}}$. This family of instantaneously optimal fields is then used as initial data in fully resolved direct numerical simulations, and the time evolution of different relevant norms is carefully monitored as the palinstrophy is transiently amplified before decaying. The peak values of the palinstrophy produced by these initial data, i.e. $\sup _{t>0}{\mathcal{P}}(t)$, are observed to scale with the magnitude of the initial palinstrophy ${\mathcal{P}}(0)$ in accord with the corresponding a priori estimate. Implications of these findings for the question of finite-time singularity formation in the three-dimensional incompressible Navier–Stokes equation are discussed.

Mass marking of juvenile Schizothorax wangchiachii (Fang) with alizarin red S and evaluation of stock enhancement in the Jinping area of the Yalong River

Schizothorax wangchiachii is a key fish species in the stock enhancement program of the Yalong River hydropower project, China. Alizarin red S (ARS) was used to mark large numbers of juvenile S. wangchiachii in the Jinping Hatchery and later used to evaluate stock enhancement in the Jinping area of the Yalong River. In a small-scale pilot study, 7,000 juveniles of the 2014 cohort were successfully marked by immersion in ARS solution, and no mortality was recorded during the marking process. The ARS mark in the fish otoliths remained visible 20 months later. In the large-scale marking study, approximately 600,000 juveniles of the 2015 cohort were successfully marked. Mortalities of both marked and unmarked juveniles were very low and did not differ significantly. Total length, wet mass and condition factor did not differ significantly between unmarked and marked individuals after three months. On 24 July 2015, about 840,000 Jinping Hatchery-produced young S. wangchiachii, including 400,000 marked individuals, were released at two sites in the Jinping area. Recapture surveys showed that (1) marked and unmarked S. wangchiachii did not differ significantly in total length, wet mass and condition factor; (2) stocked individuals became an important part of recruitment of the 2015 cohort; (3) instantaneous growth rate of marked individuals tended to slightly increase; and (4) most stocked individuals were distributed along a 10–15 km stretch near the release sites. These results suggest that the ARS method is a cost-efficient way to mass mark juvenile S. wangchiachii and that releasing juveniles is an effective means of stock recruitment.

The effect of different feeding and starvation frequencies on growth utilization and nutrients, for Piaractus brachypomus (Cuvier, 1818)

A possible practical use of compensatory growth, subjecting Piaractus brachypomus at different weekly feeding and fasting frequencies was sought. For this purpose, 450 individuals with an initial average weight of 20 g, arranged in five treatments with three replicates, were used. T1 = feed to satiation 5 days and fasting for two days; T2 = feed to satiation 6 days and fasting one day; T3 = feed to satiation 7 days; T4 = fasting 14 days and subsequent feedback to satiety and T5 = power following the manufacturer's recommended food tables. Individuals of T1 treatment had the final weight and instantaneous growth rate lowest results compared to T2 and T3. This meant that fast two days a week influenced growth negatively, but the one-day fast (T2), did not affect it. The daily highest feeding rate was present with treatment T4 but only relative to T3 and T5, due to a voluntary increase in food intake after the fasting period. By contrast, there were no differences between the T1, T2 and T3, which indicate that individuals of T1 and T2 treatments, voluntarily increased intake after fasting days equaling intake T3 treatment. The body composition of the fish was not affected by the treatments, so that after refeeding, all reserves used during fasting were restored. The values of protein and energy retention were better with treatment T5, because it used less food and its growth was similar to the other treatments. These results indicated that feeding could be deleted in one day but increasing ration during the rest of the week. However, the T5 results are relevant to the cultivation of the species, since the production cost of each kilogram is low and net profit is higher.