Related papers: Modelling the age distribution of longevity leader…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
The Gompertz model since 1825 has significantly contributed to interpretation of ageing in biological and social sciences. However, in modern research findings, it is clear that the Gompertz model is not successful to describe the whole…
In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
People are living longer than ever before, and with this arises new complications and challenges for humanity. Among the most pressing of these challenges is of understanding the role of aging in the development of dementia. This paper is…
The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these branching models is the Bellman-Harris process, where the…
There is sustained and widespread interest in understanding the limit, if any, to the human lifespan. Apart from its intrinsic and biological interest, changes in survival in old age have implications for the sustainability of social…
We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…
Human aging is marked by a steady rise in the risk of dying with age-a process demographers call senescence. Over the past century, life expectancy has risen dramatically, but is this because we are aging slower, or simply starting it…
Trends in human longevity are puzzling, especially when considering the limits of human longevity. Partially, the conflicting assertions are based upon demographic evidence and the interpretation of survival and mortality curves using the…
Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age.…
We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the…
The Gompertz law of mortality quantitatively describes the mortality rate of humans and almost all multicellular animals. However, its underlying kinetic mechanism is unclear. The Gompertz law cannot explain the effect of temperature on…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
\noindent The modal age at death is an increasingly used measure for understanding longevity and mortality patterns. However, existing estimation methods focus on point estimates, overlooking the inherent variability and uncertainty in…
A birth-death-move process with mutations is a Markov model for a system of marked particles in interaction, that move over time, with births and deaths. In addition the mark of each particle may also change, which constitutes a mutation.…
We consider a scenario where a monitor is interested in being up to date with respect to the status of some system which is not directly accessible to this monitor. However, we assume a source node has access to the status and can send…