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 genetic load has an exact but unfamiliar generalization.
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…
An agent-based computer simulation of death by inheritable mutations in a changing environment shows a maximal population, or avoids extinction, at so intermediate mutation rate of the individuals. Thus death seems needed to al for evolution of the fittest, as required by a changing environment.
Relevant events in a three state illness-death model (IDM) of a chronic disease are the diagnosis of the disease and death with or without the disease. In this article a simulation framework for populations moving in the IDM is presented. The simulation is closely related to the concept of Lexis diagrams in event history analysis. Details of the implementation and an example of a hypothetical disease are described.
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…
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 …
We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we present a full kinetic framework for age-structured interacting populations undergoing birth, death and fission processes, in spatially dependent environments. We define the complete probability density for the population-size-age-chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalizati…
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 …
After birth setting up an effective immune system is a major challenge for all living organisms. In this paper we show that this process can be explored by using the age-specific infant death rate as a kind of sensor. This is made possible because, as shown by the authors in Berrut et al. (2016), between birth and a critical age t_c, for all mammals the death rate decreases with age as an hyperbolic function. For humans t_c is equal to 10 years. At some ages the hyperbolic fall displays spikes which, it is assumed, correspond to specific events in the organism's response to exogenous factors. …
Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because molecular sequence data are not informative on absolute time, external data, most commonly fossil age estimates, are required to calibrate estimates of species divergence dates. For Bayesian divergence-time methods, the common practice for calibration using fossil information involves placing arbitrarily chosen parametric distributions on internal nodes, often disre…
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 …
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.
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…
The death of a biological population is an extreme event which we investigate here for a host-parasitoid system. Our simulations using the Penna ageing model show how biological evolution can ``teach'' the parasitoids to avoid extinction by waiting for the right age of the host. We also show the dependence of extinction time on the population size.
The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission. Here we introduce an epidemiological model where infectives leave the epidemic, either by recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an exp…
The illness-death model of a chronic disease consists of the states 'Normal', 'Disease' and 'Death'. In general, the transition rates between the states depend on three time scales: calendar time, age and duration of the chronic disease. Previous works have shown that the age-specific prevalence of the chronic disease can be described by differential equations if the duration is negligible. This article derives a partial differential equation (PDE) in the presence of duration dependency. As an important application, the PDE allows the calculation of the age-specific incidence from cross-sectio…
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…
Understanding how widely COVID-19 has spread is critical for examining the pandemic's progression. Despite efforts to carefully monitor the pandemic, the number of confirmed cases may underestimate the total number of infections. We introduce a demographic scaling model to estimate COVID-19 infections using an broadly applicable approach that is based on minimal data requirements: COVID-19 related deaths, infection fatality rates (IFRs), and life tables. As many countries lack reliable estimates of age-specific IFRs, we scale IFRs between countries using remaining life expectancy as a marker t…
A second wave of SARS-CoV-2 is unfolding in dozens of countries. However, this second wave manifests itself strongly in new reported cases, but less in death counts compared to the first wave. Over the past three months in Germany, the reported cases increased by a factor five or more, whereas the death counts hardly grew. This discrepancy fueled speculations that the rise of reported cases would not reflect a second wave but only wider testing. We find that this apparent discrepancy can be explained to a large extent by the age structure of the infected, and predict a pronounced increase of d…
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…
SARS-CoV-2 has disrupted the life of billions of people around the world since the first outbreak was officially declared in China at the beginning of 2020. Yet, important questions such as how deadly it is or its degree of spread within different countries remain unanswered. In this work, we exploit the `universal' growth of the mortality rate with age observed in different countries since the beginning of their respective outbreaks, combined with the results of the antibody prevalence tests in the population of Spain, to unveil both unknowns. We validate these results with an analogous antib…
Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such estimation is usually accomplished by analyzing patient data collected at unevenly spaced time points, referred to as panel data in the biostatistics literature. Fitting linear BDI processes to panel data…
