Related papers: Deciphering infant mortality. Part 1: empirical ev…
Excess mortality is defined as an increase in the number of deaths above what is expected based on historical trends, hereafter called baseline. In a previous paper, we introduced a statistical method that allows an unbiased and robust…
Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erd\H{o}s-R\'{e}nyi and Barab\'asi-Albert networks. It is known that the contact network influences the spread of an epidemic within a…
We consider a birth-death process with the birth rates $i\lambda$ and death rates $i\mu +i(i-1)\theta$, where $i$ is the current state of the process. A positive competition rate $\theta$ is assumed to be small. In the supercritical case…
In ecological systems, be it a petri dish or a galaxy, populations evolve from some initial value (say zero) up to a steady state equilibrium, when the mean number of births and deaths per unit time are equal. This equilibrium point is a…
Small-scale locomotion plays an important role in biology. Different modelling approaches have been proposed in the past. The simplest model is an infinite inextensible two-dimensional waving sheet, {originally introduced by Taylor}, which…
We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces…
In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition…
The analysis of the demographic transition of the past century and a half, using both empirical data and mathematical models, has rendered a wealth of well-established facts, including the dramatic increases in life expectancy. Despite…
The recent Covid-19 epidemic has lead to comparisons of the countries suffering from it. These are based on the number of excess deaths attributed either directly or indirectly to the epidemic. Unfortunately the data on which such…
We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results…
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…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
We study a general class of birth-and-death processes with state space $\mathbb{N}$ that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
This paper develops a granular regime-switching framework to model mortality deviations from seasonal baseline trends driven by temperature and epidemic shocks. The framework features three states: (1) a baseline state that captures…