Related papers: A nonlinear population model

This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of initial distributions for the population such that for small…

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…

In this study, we forecast the population of the Philippines using a discrete age-structured compartmental model. We estimated the future population structure of the Philippines if the government imposes an n-child policy on top of the…

This paper analyses a nonlinear age-maturity structured system which arises as a model of the blood cellular production in the bone marrow. The resulting model is a nonlinear first-order partial differential equation in which there is a…

We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources.…

We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…

In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males…

A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory…

With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework…

Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…

A large amount of population models use the concept of a carrying capacity. Simulated populations are bounded by invoking finite resources through a survival probability, commonly referred to as the Verhulst factor. The fact, however, that…

We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…

A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium…

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…

We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We propose a new regularization technique based on a…

This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose…

We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…

Macro-level modeling is still the dominant approach in many demographic applications because of its simplicity. Individual-level models, on the other hand, provide a more comprehensive understanding of observed patterns; however, their…

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…

In this work first we consider a physiologically structured population model with a distributed recruitment process. That is, our model allows newly recruited individuals to enter the population at all possible individual states, in…