Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility

We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.Comment: 5 pages, 3 figures. Submitted to Physical Review Letter

On the tear resistance of skin.

Tear resistance is of vital importance in the various functions of skin, especially protection from predatorial attack. Here, we mechanistically quantify the extreme tear resistance of skin and identify the underlying structural features, which lead to its sophisticated failure mechanisms. We explain why it is virtually impossible to propagate a tear in rabbit skin, chosen as a model material for the dermis of vertebrates. We express the deformation in terms of four mechanisms of collagen fibril activity in skin under tensile loading that virtually eliminate the possibility of tearing in pre-notched samples: fibril straightening, fibril reorientation towards the tensile direction, elastic stretching and interfibrillar sliding, all of which contribute to the redistribution of the stresses at the notch tip

Children's construction task performance and spatial ability: controlling task complexity and predicting mathematics performance.

This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7-8, 10-11, and 13-14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability

Moral Distress in Critical Care Nursing: The State of the Science

Background: Moral distress is a complex phenomenon frequently experienced by critical care nurses. Ethical conflicts in this practice area are related to technological advancement, high intensity work environments, and end-of-life decisions. Objectives: An exploration of contemporary moral distress literature was undertaken to determine measurement, contributing factors, impact, and interventions. Review Methods: This state of the science review focused on moral distress research in critical care nursing from 2009 to 2015, and included 12 qualitative, 24 quantitative, and 6 mixed methods studies. Results: Synthesis of the scientific literature revealed inconsistencies in measurement, conflicting findings of moral distress and nurse demographics, problems with the professional practice environment, difficulties with communication during end-of-life decisions, compromised nursing care as a consequence of moral distress, and few effective interventions. Conclusion: Providing compassionate care is a professional nursing value and an inability to meet this goal due to moral distress may have devastating effects on care quality. Further study of patient and family outcomes related to nurse moral distress is recommended

Singularities of Nonlinear Elliptic Systems

Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class of quadratic functionals inducing harmonic maps.Comment: 18 pages Communications in Partial Differential Equation