Related papers: A Path Integral Approach to Age Dependent Branchin…
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…
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates.…
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state…
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…
Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectories' degeneracy,…
Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then…
We study a linear model of McKendrick-von Foerster-Keyfitz type for the temporal development of the age structure of a two-sex human population. For the underlying system of partial integro-differential equations, we exploit the semigroup…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording…
In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling of…
We apply the operator approach to a stochastic system belonging to a class of death-birth processes, which we introduce utilizing the master equation approach. By employing Doi- Peliti formalism we recast the master equation in the form of…
Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
Duality relations between continuous-state and discrete-state stochastic processes with continuous-time have already been studied and used in various research fields. We propose extended duality relations, which enable us to derive…
Cell populations invade through a combination of proliferation and motility. Proliferation depends on the internal timing of cell division: how long cells take to complete the cell cycle. This timing varies substantially within (and across)…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…