Periodic variations in the Covid-19 infection and fatality rates

Power spectra of infection and mortality rate curves for nineteen countries of different continents were computed. Nine of them show the presence of oscillations with a period of about seven says either in the infection or in the mortality data sets. The computed power spectra for seven countries do no indicate any significant signal of periodicity while the three remaining countries indicate periodic oscillations only in the infection or only in the mortality curve. Data indicate that minima occur generally on weekends. The seven-day periodicity present in infection data of nine countries is robust and seems to be the consequence of different factors as, for instance, higher testing frequency during weekdays or/and an enhanced contamination during social activities during weekends. For the moment, there is no convincing explanation for the seven-day oscillations observed in the mortality curves of some countries.

The UK Covid-19 lockdown weakened in April and May 2020: implications for the size of the epidemic and for outcomes had lockdown been earlier

The number of active cases in the UK Covid-19 epidemic, the case fatality rate, the susceptible proportion of the population, and how well the lockdown was maintained during April-May 2020 are unknown. These four have a relationship with the shape of the daily mortality curve once one considers the intervals from infection to death or recovery. Without an understanding of this relationship we cannot say that an earlier lockdown would have saved lives. Using a small stochastic model, the lockdown had to be weakened, in April and May, for simulated deaths to match ongoing actual daily deaths. Google mobility data was found to be consistent with the weakening required in the model with similar changes from baseline in time and magnitude. If in an earlier lockdown, mobility and interactions would have followed a similar course, then with a large epidemic curve an earlier lockdown might be associated with many more deaths than some currently believe. This was confirmed in the stochastic model and in two modified SIR models of epidemics of various sizes. The first SIR model had a fixed period to recovery and the second used random periods, both models had random periods to death. Weakening of the mitigations was required to tune the output in large but not in small epidemics. This gives weight to the epidemic having affected many more individuals than some reports currently suggest. In both one and two-week earlier lockdowns, total deaths were found to depend on the size of the epidemic and to vary from 2,000-49,000 deaths. There was a linear relationship between the peak proportion of the population infected and the reciprocal of the case fatality rate. This work questions the low prevalence of < 0.1%, reported by the Office for National Statistics in May and June 2020, since to accommodate a weakening lockdown, the shape of the daily mortality curve, and an acceptable case fatality rate a much larger epidemic curve is required.

On Estimate of Malaysian Mortality Rates Using Interpolation Methods

Life table is a table that shows mortality experience of a nation. However, in Malaysia, the information in this table is provided in the five-year age groups (abridged) instead of every one-year age. Hence, this study aims to estimate the one-year age mortality rates from the abridged mortality rates using several interpolation methods. We applied Kostaki method and the Akima spline method to five sets of Malaysian group mortality rates ranging from period of 2012 to 2016. The results were then compared with the one-year mortality rates. We found that the method by Akima is the best method for the Malaysian mortality experience as it gives the least minimum of sum of square errors. The method does not only provide a good fit but also, shows a smooth mortality curve.

Estimating local mortality tables for small areas: An application using Belgian sub-arrondissements

Standardised mortality ratios (SMR) may give a good estimate of the relative level of mortality in a local area, and its relation to local social conditions, but if we wish to understand changes in the age distribution of mortality as mortality declines, we need an estimate of the local mortality curve. Such fine detail can be elusive when examining small populations for which the number of people in each age group is small, the number of deaths minuscule, and estimation errors are large. A possible solution to this problem is to estimate age-specific mortality rates simultaneously for all the subunits of a particular country, using the reported number of deaths, by age and sex, for each unit as the input data. The national mortality rates then serve as a model from which local deviations, by age and sex, are estimated, on the basis of overall mortality (SMR) and local social conditions. We demonstrate this approach using data from 87 sub-national units in Belgium to construct local-level life tables, using a multilevel model with the local sex- and age-specific cells as units, nested within sex-age groups and regional units at the second level. The results indicate that life expectancy is closely related to SMR, but the specific shape of the mortality curve, in particular the range over which mid-life mortality is low and the age at which mortality begins to rise into senescence, varies by level of mortality and social conditions.

AGE-SPECIFIC ADJUSTMENT OF GRADUATED MORTALITY

Recently, there has been an increasing interest from life insurers to assess their portfolios' mortality risks. The new European prudential regulation, namely Solvency II, emphasized the need to use mortality and life tables that best capture and reflect the experienced mortality, and thus policyholders' actual risk profiles, in order to adequately quantify the underlying risk. Therefore, building a mortality table based on the experience of the portfolio is highly recommended and, for this purpose, various approaches have been introduced into actuarial literature. Although such approaches succeed in capturing the main features, it remains difficult to assess the mortality when the underlying portfolio lacks sufficient exposure. In this paper, we propose graduating the mortality curve using an adaptive procedure based on the local likelihood. The latter has the ability to model the mortality patterns even in presence of complex structures and avoids relying on expert opinions. However, such a technique fails to offer a consistent yet regular structure for portfolios with limited deaths. Although the technique borrows the information from the adjacent ages, it is sometimes not sufficient to produce a robust life table. In the presence of such a bias, we propose adjusting the corresponding curve, at the age level, based on a credibility approach. This consists in reviewing the assumption of the mortality curve as new observations arrive. We derive the updating procedure and investigate its benefits of using the latter instead of a sole graduation based on real datasets. Moreover, we look at the divergences in the mortality forecasts generated by the classic credibility approaches including Hardy–Panjer, the Poisson–Gamma model and the Makeham framework on portfolios originating from various French insurance companies.

A longevity basis risk analysis in a joint FDM framework

Purpose The improvements of longevity are intensifying the need for capital markets to be used to manage and transfer the risk through longevity-linked securities. Nevertheless, the difference between the reference population of the hedging instrument and the population of members of a pension plan, or the beneficiaries of an annuity portfolio, determines a significant heterogeneity causing the so-called basis risk. In particular, it is shown that if insurers use financial instruments based on national indices to hedge longevity risk, this hedge can become imperfect. For this reason, it is fundamental to arrange a model allowing to quantify the basis risk for minimising it through a correct calibration of the hedging instrument. Design/methodology/approach The paper provides a framework for measuring the basis risk impact on the. To this aim, we propose a model that measures the population basis risk involved in a longevity hedge, in the functional data model setting. hedging strategies. Findings The innovative contribution of the paper occurs in two key points: the modelling of mortality and the hedging strategy. Regarding the first point, the paper proposes a functional demographic model framework (FDMF) for capturing the basis risk. The FDMF model generally designed for single population combines functional data analysis, nonparametric smoothing and robust statistics. It allows to capture the variability of the mortality trend, by separating out the effects of several orthogonal components. The novelty is to set the FDMF for modelling the mortality of the two populations, the hedging and the exposed one. Regarding the second point, the basic idea is to calibrate the hedging strategy determining a suitable mixture of q-forwards linked to mortality rates to maximise the degree of longevity risk reduction. This calibration is based on the key q-duration intended as a measure allowing to estimate the price sensitivity of the annuity portfolio to the changes in the underlying mortality curve. Originality/value The novelty lies in linking the shift in the mortality curve to the standard deviation of the historical mortality rates of the exposed population. This choice has been determined by the observation that the shock in a mortality rate is age dependent. The main advantage of the presented framework is its strong versatility, being the functional demographic setting a generalisation of the Lee-Carter model commonly used in mortality forecasting, it allows to adapt to different demographic scenarios. In the next developments, we set out to compare other common factor models to assess the most effective longevity hedge. Moreover, the parsimony for considering together two trajectories of the populations under consideration and the convergence of long-term forecast are important aspects of our approach.

What we can read and what we cannot read in the mortality curve of the neonatal surgery - the progress of the neonatal surgery in Japan

not availableJ. Paediatr. Surg. Bangladesh 5(1): 1, 2014 (January)