The Impact of Covid-19 on Future Higher-Age Mortality

Covid-19 has predominantly affected mortality at high ages. It kills by inflaming and clogging the air sacs in the lungs, depriving the body of oxygen ‒ inducing hypoxia ‒ which closes down essential organs, in particular the heart, kidneys and liver, and causes blood clots (which can lead to stroke or pulmonary embolism) and neurological malfunction. Evidence from different countries points to the fact that people who die from Covid-19 are often, but not always, much less healthy than the average for their age group. This is true for England & Wales – the two countries we focus on in this study. The implication is that the years of life lost through early death are less than the average for each age group, with how much less being a source of considerable debate. We argue that many of those who die from coronavirus would have died anyway in the relatively near future due to their existing frailties or co-morbidities. We demonstrate how to capture this link to poorer-than-average health using a model in which individual deaths are ‘accelerated’ ahead of schedule due to Covid-19. The model structure and its parameterization build on the observation that Covid-19 mortality by age is approximately proportional to all-cause mortality. This, in combination with current predictions of total deaths, results in the important conclusion that, everything else being equal, the impact of Covid-19 on the mortality rates of the surviving population will be very modest. Specifically, the degree of anti-selection is likely to be very small, since the life expectancy of survivors does not increase by a significant amount over pre-pandemic levels. We also analyze the degree to which Covid-19 mortality varies with socio-economic status. Headline statistics suggest that the most deprived groups have been disproportionately affected by Covid-19. However, once we control for regional differences in mortality rates, Covid-19 deaths in both the most and least deprived groups are also proportional to the all-cause mortality of these groups. However, the groups in between have approximately 10-15% lower Covid-19 deaths compared with their all-cause mortality. We argue that useful lessons about the potential pattern of accelerated deaths from Covid-19 can be drawn from examining deaths from respiratory diseases, especially at different age ranges. We also argue that it is possible to draw useful lessons about volatility spikes in Covid-19 deaths from examining past seasonal flu epidemics. However, there is an important difference. Whereas the spikes in seasonal flu increase with age, our finding that Covid-19 death rates are approximately proportional to all-cause mortality suggests that any spike in Covid-19 mortality in percentage terms would be similar across all age ranges. Finally, we discuss some of the indirect consequences for future mortality of the pandemic and the ‘lockdown’ measures governments have imposed to contain it. For example, there is evidence that some surviving patients at all ages who needed intensive care could end up with a new impairment, such as organ damage, which will reduce their life expectancy. There is also evidence that many people in lockdown did not seek a timely medical assessment for a potential new illness, such as cancer, or deferred seeking treatment for an existing serious illness, with the consequence that non-Covid-19-related mortality rates could increase in future. Self-isolation during lockdown has contributed to an increase in alcohol and drug consumption by some people which might, in turn, reduce their life expectancy. If another consequence of the pandemic is a recession and/or an acceleration in job automation, resulting in long-term unemployment, then this could lead to so-called ‘deaths of despair’ in future. Other people, by contrast, might permanently change their social behaviour or seek treatments that delay the impact or onset of age-related diseases, one of the primary factors that make people more susceptible to the virus – both of which could have the effect of increasing their life expectancy. It is, however, too early to quantify these possibilities, although it is conceivable that these indirect consequences could have a bigger impact on future average life expectancy than the direct consequences measured by the accelerated deaths model

Orbital debris measurements

What is currently known about the orbital debris flux is from a combination of ground based and in-space measurements. These measurements have revealed an increasing population with decreasing size. A summary of measurements is presented for the following sources: the North American Aerospace Defense Command Catalog, the Perimeter Acquisition and Attack Characterization System Radar, ground based optical telescopes, the Explorer 46 Meteoroid Bumper Experiment, spacecraft windows, and Solar Max surfaces

From the area under the Bessel excursion to anomalous diffusion of cold atoms

Levy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Levy spatial diffusion has been observed for a collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice. Using the semiclassical theory of Sisyphus cooling, we treat the problem as a coupled Levy walk, with correlations between the length and duration of the excursions. The problem is related to the area under Bessel excursions, overdamped Langevin motions that start and end at the origin, constrained to remain positive, in the presence of an external logarithmic potential. In the limit of a weak potential, the Airy distribution describing the areal distribution of the Brownian excursion is found. Three distinct phases of the dynamics are studied: normal diffusion, Levy diffusion and, below a certain critical depth of the optical potential, x~ t^{3/2} scaling. The focus of the paper is the analytical calculation of the joint probability density function from a newly developed theory of the area under the Bessel excursion. The latter describes the spatiotemporal correlations in the problem and is the microscopic input needed to characterize the spatial diffusion of the atomic cloud. A modified Montroll-Weiss (MW) equation for the density is obtained, which depends on the statistics of velocity excursions and meanders. The meander, a random walk in velocity space which starts at the origin and does not cross it, describes the last jump event in the sequence. In the anomalous phases, the statistics of meanders and excursions are essential for the calculation of the mean square displacement, showing that our correction to the MW equation is crucial, and points to the sensitivity of the transport on a single jump event. Our work provides relations between the statistics of velocity excursions and meanders and that of the diffusivity.Comment: Supersedes arXiv: 1305.008

Nonlinear lattice model of viscoelastic Mode III fracture

We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state Mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure