Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure

Estimating loss of Brucella abortus antibodies from age-specific serological data in elk

Serological data are one of the primary sources of information for disease monitoring in wildlife. However, the duration of the seropositive status of exposed individuals is almost always unknown for many free-ranging host species. Directly estimating rates of antibody loss typically requires difficult longitudinal sampling of individuals following seroconversion. Instead, we propose a Bayesian statistical approach linking age and serological data to a mechanistic epidemiological model to infer brucellosis infection, the probability of antibody loss, and recovery rates of elk (Cervus canadensis) in the Greater Yellowstone Ecosystem. We found that seroprevalence declined above the age of ten, with no evidence of disease-induced mortality. The probability of antibody loss was estimated to be 0.70 per year after a five-year period of seropositivity and the basic reproduction number for brucellosis to 2.13. Our results suggest that individuals are unlikely to become re-infected because models with this mechanism were unable to reproduce a significant decline in seroprevalence in older individuals. This study highlights the possible implications of antibody loss, which could bias our estimation of critical epidemiological parameters for wildlife disease management based on serological data

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Performance of Proximity Loggers in Recording Intra- and Inter-Species Interactions: A Laboratory and Field-Based Validation Study

Knowledge of the way in which animals interact through social networks can help to address questions surrounding the ecological and evolutionary consequences of social organisation, and to understand and manage the spread of infectious diseases. Automated proximity loggers are increasingly being used to record interactions between animals, but the accuracy and reliability of the collected data remain largely un-assessed. Here we use laboratory and observational field data to assess the performance of these devices fitted to a herd of 32 beef cattle (Bos taurus) and nine groups of badgers (Meles meles, n  = 77) living in the surrounding woods. The distances at which loggers detected each other were found to decrease over time, potentially related to diminishing battery power that may be a function of temperature. Loggers were highly accurate in recording the identification of contacted conspecifics, but less reliable at determining contact duration. There was a tendency for extended interactions to be recorded as a series of shorter contacts. We show how data can be manipulated to correct this discrepancy and accurately reflect observed interaction patterns by combining records between any two loggers that occur within a 1 to 2 minute amalgamation window, and then removing any remaining 1 second records. We make universally applicable recommendations for the effective use of proximity loggers, to improve the validity of data arising from future studies

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Invasion and Persistence of Infectious Agents in Fragmented Host Populations

One of the important questions in understanding infectious diseases and their prevention and control is how infectious agents can invade and become endemic in a host population. A ubiquitous feature of natural populations is that they are spatially fragmented, resulting in relatively homogeneous local populations inhabiting patches connected by the migration of hosts. Such fragmented population structures are studied extensively with metapopulation models. Being able to define and calculate an indicator for the success of invasion and persistence of an infectious agent is essential for obtaining general qualitative insights into infection dynamics, for the comparison of prevention and control scenarios, and for quantitative insights into specific systems. For homogeneous populations, the basic reproduction ratio plays this role. For metapopulations, defining such an ‘invasion indicator’ is not straightforward. Some indicators have been defined for specific situations, e.g., the household reproduction number . However, these existing indicators often fail to account for host demography and especially host migration. Here we show how to calculate a more broadly applicable indicator for the invasion and persistence of infectious agents in a host metapopulation of equally connected patches, for a wide range of possible epidemiological models. A strong feature of our method is that it explicitly accounts for host demography and host migration. Using a simple compartmental system as an example, we illustrate how can be calculated and expressed in terms of the key determinants of epidemiological dynamics

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

A review and meta-analysis of prospective studies of red and processed meat intake and prostate cancer

Over the past decade, several large epidemiologic investigations of meat intake and prostate cancer have been published. Therefore, a meta-analysis of prospective studies was conducted to estimate potential associations between red or processed meat intake and prostate cancer. Fifteen studies of red meat and 11 studies of processed meat were included in the analyses. High vs. low intake and dose-response analyses were conducted using random effects models to generate summary relative risk estimates (SRRE). No association between high vs. low red meat consumption (SRRE = 1.00, 95% CI: 0.96-1.05) or each 100 g increment of red meat (SRRE = 1.00, 95% CI: 0.95-1.05) and total prostate cancer was observed. Similarly, no association with red meat was observed for advanced prostate cancer (SRRE = 1.01, 95% CI: 0.94-1.09). A weakly elevated summary association between processed meat and total prostate cancer was found (SRRE = 1.05, 95% CI: 0.99-1.12), although heterogeneity was present, the association was attenuated in a sub-group analysis of studies that adjusted for multiple potential confounding factors, and publication bias likely affected the summary effect. In conclusion, the results of this meta-analysis are not supportive of an independent positive association between red or processed meat intake and prostate cancer

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

A process model for developing learning design patterns with international scope

This paper investigates the process of identifying design patterns in international collaborative learning environments. In this context, design patterns are referred to as structured descriptions of best practice with pre-defined sections such as problem, solution and consequences. We pay special attention to how the scope of a design pattern is identified and articulated. Based on a review of the seminal design patterns literature and current practice in the area of learning design, the lack of a more specific process description for developing patterns with international scope is identified. The paper suggests a process model for developing patterns with international scope. This model is exemplified in a case study that links the analysis of observation in international learning environments to the articulation of design patterns by identifying culturally independent core values that constitute the foundations of a design pattern with international scope. These core values are linked to recurrent learning behaviors and specific artefacts that support learning in the articulation of a design pattern. The findings contribute to gaining a deeper understanding of the pattern scoping and abstraction process in international learning environments