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

SADD: STOCHASTIC ANALYSIS OF DESTRUCTIVELY MEASURED DATA - POSSIBILITIES TO INCLUDE BIOLOGICAL VARIATIONS IN STATISTICAL ANALYSIS

Three techniques are presented to include the structural variation always present in measured data in statistical analysis. The methods are investigated and compared using cross sectional data, generated based on an exponential model as if gathered by destructive measuring methods. All three methods are based on optimising objective functions based on the data and the biological shift model. These objective functions are calculated for each separate measuring point in time either according the specific density function belonging to the model applied, or after conversion into biological shift factors (also according to the model applied) according to a Gaussian distribution. The procedures used need to be improved, embedded in the existing statistical framework and all available statistical expertise and skills need to be combined into robust procedures capable of analysing everyday data

Scattering Calculations with Wavelets

We show that the use of wavelet bases for solving the momentum-space scattering integral equation leads to sparse matrices which can simplify the solution. Wavelet bases are applied to calculate the K-matrix for nucleon-nucleon scattering with the s-wave Malfliet-Tjon V potential. We introduce a new method, which uses special properties of the wavelets, for evaluating the singular part of the integral. Analysis of this test problem indicates that a significant reduction in computational size can be achieved for realistic few-body scattering problems.Comment: 26 pages, Latex, 6 eps figure

The Universal Gaussian in Soliton Tails

We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.Comment: 4 pages, 2 figures, revtex with eps

Equation-free Dynamic Renormalization of a KPZ-type Equation

In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems

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

Application of wavelets to singular integral scattering equations

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.Comment: 11 pages, 4 figure