The risk of dying increases exponentially with age, in humans as well as in many other species. This increase is often attributed to the "accumulation of damage" known to occur in many biological structures and systems. The aim of this paper is to describe a generic model of damage accumulation and death in which mortality increases exponentially with age. The damage-accumulation process is modeled by a stochastic process know as a queue, and risk of dying is a function of the accumulated damage, i.e. length of the queue. The model has four parameters and the main characteristics of the model are: (i) damage occurs at random times with a constant high rate; (ii) the damage is repaired at a limited rate, and consequently damage can accumulate; (iii) the efficiency of the repair mechanism decays linearly with age; (iv) the risk of dying is a function of the accumulated damage. Using standard results from the mathematical theory of queues it is shown that there is an exponential dependence between risk of dying and age in these models, and that this dependency holds irrespective of how the damage-accumulation process is modeled. Furthermore, the ways in which this exponential dependence is shaped by the model parameters are also independent of the details of the damage accumulation process. These generic features suggest that the model could be useful when interpreting changes in the relation between age and mortality in real data. To examplify, historical mortality data from Sweden are interpreted in the light of the model. The decrease in mortality seen between cohorts born in 1905, compared to those born in 1885, can be accounted for by higher threshold to damage. This fits well with the many advances made in public health during the 20th century.
Background: Information on influenza-associated mortality in Russia is limited. Methods: Using previously developed methodology (Goldstein et al., Epidemiology 2012), we regressed the monthly rates of mortality for respiratory causes, as well as circulatory causes linearly against the monthly proxies for the incidence of influenza A/H3N2, A/H1N1 and B (obtained using data from the Smorodintsev Research Institute of Influenza (RII)), adjusting for the baseline rates of mortality not associated with influenza circulation and temporal trends. Results: For the 2013/14 through the 2018/19 seasons, …
Background: Information on influenza-associated mortality in Russia is limited. Methods: Using previously developed methodology (Goldstein et al., Epidemiology 2012), we regressed the monthly rates of mortality for respiratory causes, as well as circulatory causes linearly against the monthly proxies for the incidence of influenza A/H3N2, A/H1N1 and B (obtained using data from the Smorodintsev Research Institute of Influenza (RII)), adjusting for the baseline rates of mortality not associated with influenza circulation and temporal trends. Results: For the 2013/14 through the 2018/19 seasons, …
Recently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). In case of a chronic disease, we show that the PDE can be used to estimate excess mortality from prevalence and incidence. Applicability of the new method is demonstrated in a simulation and claims data about diabetes in German men.
In this article, we use the illness-death model to present a mathematical framework for studying the compression of morbidity (COM) hypothesis. It turns out that questions about COM are completely determined by the transition rates in the illness-death model and a closely related partial differential equation. By this, the COM hypothesis is analytically tractable. To demonstrate the usefulness of the mathematical framework, an example is given, which has been motivated by empirical findings from Germany.
To better understand mortality change with age capturing the variability in individuals' rates of aging, we performed comprehensive analysis of statistical properties of a cumulative index of age-associated disorders (deficits), called a "frailty index" (FI). This index is calculated as the proportion of the health deficits in an individual. It is found, first, that frequency, time-to-death, mortality-rate, and relative-risk-of-death exhibit remarkably similar FI- and age- patterns. Second, the FI, on the one hand, and mortality rate and relative risk, on the other hand, also exhibit similar a…
Background: There is limited information on the volume of influenza-associated mortality in Russia. Methods: Using previously developed methodology (Goldstein et al., Epidemiology 2012), we regressed the monthly rates of mortality for respiratory causes, circulatory causes, and for certain infectious and parasitic diseases (available from the Russian Federal State Statistics Service (Rosstat)) linearly against the monthly proxies for the incidence of influenza A/H3N2, A/H1N1 and B (obtained using data from the Smorodintsev Research Institute of Influenza (RII) on levels of ILI/ARI consultation…
Background: Although recorded cancer mortality should include both deaths from cancer and deaths from cancer treatment, there is evidence suggesting that the measure may be incomplete. To investigate the completeness of recorded prostate cancer mortality, we compared other-cause (non-prostate cancer) mortality in men found and not found to have prostate cancer following a needle biopsy. Methods: We linked Medicare claims data to SEER data to analyze survival in the population of men aged 65+ enrolled in Medicare who resided in a SEER area and received a needle biopsy in 1993-2001. We compared …
A recent study in the 2017 Living to 100 Monograph published by the Society of Actuaries suggests, in contrast to previous research, that the risk of death after 110 increases with age. By fitting a Gompertz model to estimated central death rates for the oldest old, the authors challenge existing theory and empirical research indicating a deceleration of mortality at older ages and the emergence of a plateau. We argue that their results are inconclusive for three reasons: (1) the data selection was arbitrary; (2) the statistical analysis was inappropriate; and (3) the presentation of the resul…
Background: There is a lack of population-based studies on the effectiveness and durability of the SARS-CoV-2-induced immune protection during the Omicron wave. Methods: This retrospective study included 470 159 cases aged 60 years or older, who tested positive for SARS-CoV-2 between January 1 and June 30, 2022 in Bavaria, Germany. We examined time to death, measured from the earliest date of reporting/symptom onset until day 60. Cox models were used to estimate adjusted hazard ratios (HR) for sex, age, earliest calendar date of documented infection, and level of vaccine-induced or hybrid immu…
Objective: Determining the structure of mortality from causes and sociodemographic characteristics, in the municipality of San Francisco, Antioquia, 2001-2010. Methodology: Quantitative descriptive study with retrospective longitudinal data obtained from secondary source of death events through databases in electronic media supplied by the DANE. A description of the sociodemographic variables was performed by groups of cause of death, the life table by sex and years of potential life lost (APVP) for each year group and cause of death was calculated. Results: External causes and assaults, homic…
This paper introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of \emph{virulence matrices} to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce \emph{three-way incons…
The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individuals genomes are represented by bit-strings. It provides a simple metaphor for the evolutionary process in terms of the mutation accumulation theory. In its original version, an individual dies due to inherited diseases when its current number of accumulated mutations, n, reaches a threshold value, T. Since the number of accumulated diseases increases with age, the probability to die is zero for very young ages (n < T) and equals 1 for the old ones (n >= T). Here, instead of using …
W. D. Hamilton's celebrated formula for the age-specific force of natural selection furnishes predictions for senescent mortality due to mutation accumulation, at the price of reliance on a linear approximation. Applying to Hamilton's setting the full non-linear demographic model for mutation accumulation of Evans et al. (2007), we find surprising differences. Non-linear interactions cause the collapse of Hamilton-style predictions in the most commonly studied case, refine predictions in other cases, and allow Walls of Death at ages before the end of reproduction. Haldane's Principle for genet…
Currently, Brazil has one of the fastest increasing COVID-19 epidemics in the world, that has caused at least 94 thousand confirmed deaths until now. The city of Sao Paulo is particularly vulnerable because it is the most populous in the country. Analyzing the spatiotemporal dynamics of COVID-19 is important to help the urgent need to integrate better actions to face the pandemic. Thus, this study aimed to analyze the COVID-19 mortality, from March to July 2020, considering the spatio-time architectures, the socio-economic context of the population, and using a fine granular level, in the most…
This paper is not (or at least not only) about human infant mortality. In line with reliability theory, "infant" will refer here to the time interval following birth during which the mortality (or failure) rate decreases. This definition provides a systems science perspective in which birth constitutes a sudden transition which falls within the field of application of the "Transient Shock" (TS) conjecture put forward in Richmond et al. (2016c). This conjecture provides predictions about the timing and shape of the death rate peak. (i) It says that there will be a death rate spike whenever exte…
This paper introduces new methods to analyze the changing progression of COVID-19 cases to deaths in different waves of the pandemic. First, an algorithmic approach partitions each country or state's COVID-19 time series into a first wave and subsequent period. Next, offsets between case and death time series are learned for each country via a normalized inner product. Combining these with additional calculations, we can determine which countries have most substantially reduced the mortality rate of COVID-19. Finally, our paper identifies similarities in the trajectories of cases and deaths fo…
Imperial College London（伦敦帝国理工学院）；National University of Singapore（新加坡国立大学）；University of Copenhagen（哥本哈根大学）
The COVID-19 pandemic has caused over 6.4 million registered deaths to date and has had a profound impact on economic activity. Here, we study the interaction of transmission, mortality, and the economy during the SARS-CoV-2 pandemic from January 2020 to December 2022 across 25 European countries. We adopt a Bayesian Mixed Effects model with auto-regressive terms. We find that increases in disease transmission intensity decreases Gross domestic product (GDP) and increases daily excess deaths, with a longer lasting impact on excess deaths in comparison to GDP, which recovers more rapidly. Broad…
By fitting a compartment ODE model for Covid-19 propagation to cumulative case and death data for US states and European countries, we find that the case mortality rate seems to have decreased by at least 80% in most of the US and at least 90% in most of Europe. These are much larger and faster changes than reported in empirical studies, such as the 18% decrease in mortality found for the New York City hospital system from March to August 2020 (Horwitz et al, Trends in Covid-19 risk-adjusted mortality rates, J. Hosp. Med. 2020). Our reported decreases surprisingly do not have strong correlatio…
In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a $2$-dimensional lattice having three cyclically-competing species. The spatio-temporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of sp…
The demographic factors have a substantial impact on the overall casualties caused by the COVID-19. In this study, the spatial association between the key demographic variables and COVID-19 cases and deaths were analyzed using the spatial regression models. Total 13 (for COVID-19 case factor) and 8 (for COVID-19 death factor) key variables were considered for the modelling. Total five spatial regression models such as Geographically weighted regression (GWR), Spatial Error Model (SEM), Spatial Lag Model (SLM), Spatial Error_Lag model (SEM_SLM), and Ordinary Least Square (OLS) were performed fo…
The severe acute respiratory syndrome COVID-19 has been in the center of the ongoing global health crisis in 2020. The high prevalence of mild cases facilitates sub-notification outside hospital environments and the number of those who are or have been infected remains largely unknown, leading to poor estimates of the crude mortality rate of the disease. Here we use a simple model to describe the number of accumulated deaths caused by COVID-19. The close connection between the proposed model and an approximate solution of the SIR model provides a system of equations whose solutions are robust …
We develop an agent-based model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the second through social contacts in public places: schools, hospitals, airports, etc., where many people meet, who live in remote geographic locations. Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks. We use…
A large percentage of the deaths from COVID-19 occur among residents of long-term care facilities. There are two possible reasons for this phenomenon. First, the structural features of such settings may lead to death. Alternatively, it is possible that individuals in these facilities are in poorer health than those living elsewhere, and that these individuals would have died even if they had not been in these facilities. Our findings show that, controlling for the population density and the percentage of older adults in the population, there is a significant positive association between the nu…
Although accumulation of molecular damage is suggested to be an important molecular mechanism of aging, a quantitative link between the dynamics of damage accumulation and mortality of species has so far remained elusive. To address this question, we examine stability properties of a generic gene regulatory network (GRN) and demonstrate that many characteristics of aging and the associated population mortality rate emerge as inherent properties of the critical dynamics of gene regulation and metabolic levels. Based on the analysis of age-dependent changes in gene-expression and metabolic profi…
