The church and religion in the Anglo Scottish border counties, 1534 to 1572

The 16th century Borders have been viewed traditionally as violent, feudal and catholic, but their feudalism is now questioned. The verdict on their religion seems often to be based either on general impressions or on lack of evidence. Recently the value of studying the social and political life of the English and Scottish Borders together has been recognised, and this approach is also viable for their religious life. The scattered evidence shows that in terms of material wealth and personnel the Border church was badly served, and that the changes of the Reformation often made the situation worse. Moreover it suffered from too close an association with the violent aspects of Border society. Popular religion in the area seems to have been more concerned with the magical aspect of the church's ceremonies than with orthodox Catholicism or Protestantism. At the same time there was a realisation of the problems, and there were educative and civilising influences at work. By the end of this period they were beginning to have some little effect, while at the same time the weakened traditional Catholicism was declining through lack of organised support. The 1569 revolt, which at first sight might suggest that the situation had changed little since 1536, in fact by its failure demonstrates the changes which had occurred. However the problems of the Border ' church went too deep to be solved easily, and the Borderers' independence in matters social, political, and religious would have to be overcome to achieve any great measure of success. Throughout this period both English and Scottish governments were by turn unable or unwilling to effect the necessary changes, and the inadequate church organisations were left to struggle on alone

Enhanced vaccine control of epidemics in adaptive networks

We study vaccine control for disease spread on an adaptive network modeling disease avoidance behavior. Control is implemented by adding Poisson distributed vaccination of susceptibles. We show that vaccine control is much more effective in adaptive networks than in static networks due to an interaction between the adaptive network rewiring and the vaccine application. Disease extinction rates using vaccination are computed, and orders of magnitude less vaccine application is needed to drive the disease to extinction in an adaptive network than in a static one

History of El Nino impacts on the global carbon cycle 1957-2017 : a quantification from atmospheric CO2 data

Interannual variations in the large-scale net ecosystem exchange (NEE) of CO2 between the terrestrial biosphere and the atmosphere were estimated for 1957-2017 from sustained measurements of atmospheric CO2 mixing ratios. As the observations are sparse in the early decades, available records were combined into a 'quasi-homogeneous' dataset based on similarity in their signals, to minimize spurious variations from beginning or ending data records. During El Nino events, CO2 is anomalously released from the tropical band, and a few months later also in the northern extratropical band. This behaviour can approximately be represented by a linear relationship of the NEE anomalies and local air temperature anomalies, with sensitivity coefficients depending on geographical location and season. The apparent climate sensitivity of global total NEE against variations in pan-tropically averaged annual air temperature slowly changed over time during the 1957-2017 period, first increasing (though less strongly than in previous studies) but then decreasing again. However, only part of this change can be attributed to actual changes in local physiological or ecosystem processes, the rest probably arising from shifts in the geographical area of dominating temperature variations. This article is part of a discussion meeting issue 'The impact of the 2015/2016 El Nino on the terrestrial tropical carbon cycle: patterns, mechanisms and implications'.Peer reviewe

The impact of contact tracing in clustered populations

The tracing of potentially infectious contacts has become an important part of the control strategy for many infectious diseases, from early cases of novel infections to endemic sexually transmitted infections. Here, we make use of mathematical models to consider the case of partner notification for sexually transmitted infection, however these models are sufficiently simple to allow more general conclusions to be drawn. We show that, when contact network structure is considered in addition to contact tracing, standard “mass action” models are generally inadequate. To consider the impact of mutual contacts (specifically clustering) we develop an improvement to existing pairwise network models, which we use to demonstrate that ceteris paribus, clustering improves the efficacy of contact tracing for a large region of parameter space. This result is sometimes reversed, however, for the case of highly effective contact tracing. We also develop stochastic simulations for comparison, using simple re-wiring methods that allow the generation of appropriate comparator networks. In this way we contribute to the general theory of network-based interventions against infectious disease

How does the terrestrial carbon exchange respond to inter-annual climatic variations? : A quantification based on atmospheric CO2 data

The response of the terrestrial net ecosystem exchange (NEE) of CO2 to climate variations and trends may crucially determine the future climate trajectory. Here we directly quantify this response on inter-annual timescales by building a linear regression of inter-annual NEE anomalies against observed air temperature anomalies into an atmospheric inverse calculation based on long-term atmospheric CO2 observations. This allows us to estimate the sensitivity of NEE to inter-annual variations in temperature (seen as a climate proxy) resolved in space and with season. As this sensitivity comprises both direct temperature effects and the effects of other climate variables co-varying with temperature, we interpret it as "inter-annual climate sensitivity". We find distinct seasonal patterns of this sensitivity in the northern extratropics that are consistent with the expected seasonal responses of photosynthesis, respiration, and fire. Within uncertainties, these sensitivity patterns are consistent with independent inferences from eddy covariance data. On large spatial scales, northern extratropical and tropical interannual NEE variations inferred from the NEE-T regression are very similar to the estimates of an atmospheric inversion with explicit inter-annual degrees of freedom. The results of this study offer a way to benchmark ecosystem process models in more detail than existing effective global climate sensitivities. The results can also be used to gap-fill or extrapolate observational records or to separate inter-annual variations from longer-term trends.Peer reviewe

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

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