Related papers: Equilibrium Equations for Human Populations with I…
One of the critical measures to control infectious diseases is a lockdown. Once past the lockdown stage in many parts of the world, the crucial question now concerns the effects of relaxing the lockdown and finding the best ways to…
We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for…
Most capture-recapture models assume that individuals either do not emigrate or emigrate permanently from the sampling area during the sampling period. This assumption is violated when individuals temporarily leave the sampling area and…
This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species: prey, predator, and food for the…
For multivariant Wright-Fisher models in population genetics, we introduce equilibrium states, expressed by fluctuations of probability ratio, in contrast to the traditionally used fluctuations, expressed by the difference between the…
The Constitutionally mandated task of assigning Congressional seats to the various U.S. States proportional to their represented populations ("according to their numbers") has engendered much contention, but rather less consensus. Using the…
In this paper, we study continuous-state interacting multi-type branching processes with immigration (CIMBI processes), where inter-specific interactions -- whether competitive, cooperative, or of a mixed type -- are proportional to the…
This article proposes a new model to describe human intra-city mobility. The goal is to combine the convection-diffusion equation to describe commuting people's movement and the density of individuals at home. We propose a new model…
Migration's impact spans various social dimensions, including demography, sustainability, politics, economy and gender disparities. Yet, the decision-making process behind migrants choosing their destination remains elusive. Existing models…
We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary…
This paper characterizes optimal classification when individuals adjust their behavior in response to the classification rule. We model the interaction between a designer and a population as a Stackelberg game: the designer selects a…
A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give characterization for a general inhomogeneous skew convolution semigroup in terms of probability…
We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random…
We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…
Discrete choice models with social interactions or spillovers may exhibit multiple equilibria. This paper provides a systematic approach to enumerating them for a quantitative spatial model with discrete locations, social interactions, and…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the…
This paper addresses mechanisms for boundedly rational decision makers in discrete choice problem. First, we introduce two mathematical models of population dynamics with conformity biases. We next analyze the models in terms of…
Population size estimation based on capture-recapture experiment under triple record system is an interesting problem in various fields including epidemiology, population studies, etc. In many real life scenarios, there exists inherent…
We establish upper bounds for the expected excess risk of models trained by proper iterative algorithms which approximate the local minima. Unlike the results built upon the strong globally strongly convexity or global growth conditions…
We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the…