Related papers: Stochastic Penna model for biological aging
We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned…
Inspired by the paper Greenhalgh et al. [5] we investigate a class of two dimensional stochastic differential equations related to susceptible-infected-susceptible epidemic models with demographic stochasticity. While preserving the key…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose a novel…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We first review an approach that had been developed in the past years to introduce concepts of "bivariate ageing" for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
This paper describes a general approach for stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income…
Dangerous damage to mitochondrial DNA (mtDNA) can be ameliorated during mammalian development through a highly debated mechanism called the mtDNA bottleneck. Uncertainty surrounding this process limits our ability to address inherited mtDNA…
A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years.…
This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and…
Aging, as defined in terms of the slope of the probability of death versus time (hazard curve), is a generic phenomenon observed in nearly all complex systems. Theoretical models of aging predict hazard curves that monotonically increase in…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
Since its proposition in 1995, the Heumann-Hotzel model has remained as an obscure model of biological aging. The main arguments used against it were its apparent inability to describe populations with many age intervals and its failure to…
Motivated by improving mortality tables from human demography databases, we investigate statistical inference of a stochastic age-evolving density of a population alimented by time inhomogeneous mortality and fertility. Asymptotics are…
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of…