Age-dependent Population Research Articles

Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion

Stochastic age-dependent population equations, one of the important classes of hybrid systems are studied. In general most equations of stochastic age-dependent population do not have explicit solutions. Thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the analytic solution. In the last section a numerical example is given.

Exponential Stability of Stochastic Age-Dependent Population with Diffusion

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is introduced. Exponential stability of paths of a strong solution for stochastic age-dependent population dynamic system in Hilbert space is established. The analyses use exponential martingale formula, Lyapunov functional and some special inequalities for our stability purposes. Various sufficient conditions are obtained to ensure the stability of the strong solutions. In particular, by means of our results we loosen the condition of stability.

Direct and inverse problems in age--structured population diffusion

An identification problem for a class of ultraparabolic equations with a non local boundary condition, arising from age-dependent population diffusion, is analized. For such problems existence and uniqueness results as well as continuous dependence upon the data are proved. Regularity results with respect to space variables are also proved, using the theory of parabolic equations in $L^1$-spaces.

NUMERICAL DISCRETIZATION OF A POPULATION DIFFUSION EQUATION

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

Asymptotically exponential solutions in nonlinear integral and differential equations

In this paper we investigate the growth/decay rate of solutions of an abstract integral equation which frequently arises in quasilinear differential equations applying a variation-of-constants formula. These results are applicable to some abstract equations which appear in the theory of age-dependent population models and also to some quasilinear delay differential equations with bounded and unbounded delays. Examples are given to illustrate the sharpness of the results.

Season- and fruit age-dependent population dynamics of Aceria guerreronis and its associated predatory mite Neoseiulus paspalivorus on coconut in Benin

The coconut mite Aceria guerreronis Keifer resides beneath the perianth of coconut fruits where it feeds on the tender meristematic tissue. A. guerreronis is one of the most important coconut pests but knowledge of its population dynamics is scant. We quantified seasonal and fruit age-related population fluctuations of A. guerreronis and its predator Neoseiulus paspalivorus DeLeon in Benin. N. paspalivorus was the most common and abundant beneath the bracts compared with other predators, which were very scarce and were largely found outside the bracts. Both percent fruit occupation and abundance of A. guerreronis and N. paspalivorus varied across sampling months as well as among coconut plantations and fruit age classes. Both parameters peaked in the middle of the rainy season and at the end of the dry season. Fruit age at which A. guerreronis and N. paspalivorus started to colonize the fruits was 0.9 and 1.2 months, respectively. The two species reached their peak abundance (1512 A. guerreronis and 2.3 N. paspalivorus per fruit) on 3 months-old fruits. Peak percent fruit occupation by A. guerreronis (∼70%) occurred after 4.3 months, which was ∼0.7 months earlier than that by N. paspalivorus (∼22%). Difficulties encountered by the predators in accessing the area beneath the perianth on the very young fruits allowed A. guerreronis a head-start in population build-up leading to strongly diverging population curves as a function of fruit age (higher population increase compared to N. paspalivorus). Protecting the very young fruits from A. guerreronis colonization should be a key issue for developing successful control strategies of this pest.

Solutions to boundary Cauchy problems with infinite delay

In this paper, we investigate the existence, uniqueness of solutions to boundary Cauchy equations with infinite delay, which are more general than the previous studies. The conclusions are applied to an age dependent population with delay in the birth process.

Numerical analysis for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching

In this paper, we shall examine the convergence of semi-implicit Euler approximation for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching. Here, the main ideas from the papers Ronghua et al. (2009) [2] and Wang and Wang (2010) [3] are successfully developed to the more general cases. Finally, a numerical example is provided to illustrate the theoretical result of convergence.

Global solutions for an age-dependent model of nucleation, growth and ageing with hysteresis

In this article we establish the global well-posedness of a recent model proposed by Noguera, Fritz, Clement and Baronnet for simultaneously describing the process of nucleation, growth and ageing of particles in thermodynamically closed and initially supersaturated systems. This model, which applies to precipitation in solution, vapor condensation and crystallization from a simple melt, can be seen as a highly nonlinear age-dependent population problem involving a delayed birth process and a hysteresis damage operator.

A Limit Harvesting Problem of Population Dynamics with Logistic Term

In this paper, a nonlinear age-dependent population model with logistic term is considered. In the first part is reminded a large time behavior result, and next an optimal harvesting problem associated to a limit problem is investigated. Existence of an optimal control and necessary optimality conditions are established. Mathematics Subject Classication 2000: 35B40, 49J15, 92D25.

Age-dependent single-species population dynamics with delayed argument

The model of age-dependent population dynamics was for the first time described by McKendrick (1926). This model was based on the first-order partial differential equation with the standard initial condition and the non-local boundary condition in integral form. Gurtin and MacCamy in their paper (1974) analyzed a more general model, where the progress of the population depends on its number. They proved the existence of the unique solution to their model for all time. In our paper the results of Gurtin and MacCamy will be generalized on the case, when the dependence on a number of a population is delayed. Copyright © 2009 John Wiley & Sons, Ltd.

Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps

We consider semi-implicit methods for stochastic age-dependent population equations with Poisson jumps. The main purpose of this paper is to show the convergence of the numerical approximation solution to the true solution with strong order p = 1 2 .

Optimal harvesting for periodic age-dependent population dynamics with logistic term

We prove an asymptotic behavior result for an age-dependent population dynamics with logistic term and periodic vital rates. We investigate next an optimal harvesting problem related to a periodic age-structured model with logistic term. Existence of an optimal control and necessary optimality conditions are established. A conceptual algorithm to approximate the optimal pair is derived and some numerical experiments are presented.

Convergence of numerical solutions to stochastic age-dependent population equations with Markovian switching

In this paper, a class of stochastic age-dependent population equations with Markovian switching is considered. The main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age-dependent population equations with Markovian switching. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. An example is given for illustration.

Optimal birth control of free horizon problems for predator-prey system with age-structure

We study optimal birth policies for three age-dependent populations in a predator-prey system, which is controlled by fertility. New results on problems with free final time and integral phase constraints are presented, the approximate controllability of system is discussed.

On the age-dependent population dynamics with delayed dependence of the structure

The paper deals with the description of the new model of the population with delayed dependence of the structure. We present the proof of the existence and the uniqueness of the solution of this problem.

An ultraparabolic problem arising from age-dependent population diffusion

A class of ultraparabolic equations arising from age-dependent population diffusion is analyzed. For suchproblems existence and uniqueness results as well as continuous dependence upon the data are proved. The regularity of solutions with respect to space variables is also proved, using the theory of interpolation spaces generated by analytic semigroups.

Positive Equilibrium Solutions for Age- and Spatially-Structured Population Models

The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility, it is shown that a branch of (positive) equilibria bifurcates from the trivial equilibrium. In some cases the direction of bifurcation is analyzed.

Global behavior for an age-dependent population model with logistic term and periodic vital rates

We investigate the large-time behavior of a nonlinear age-dependent population model with logistic term and T-periodic vital rates. We prove that there exists at most two T-periodic and nonnegative solutions of the given model, one of them being the trivial one. We show that for any initial distribution of population the solution tends to zero or to the nontrivial nonnegative T-periodic solution, if such solution exists. A numerical algorithm to approximate the solution corresponding to a given initial datum as well as the nontrivial nonnegative T-periodic solution of the given model is constructed. Results of the numerical tests are given.

P-26 Body mass index (BMI) and waist circumference in growth hormone (GH)-untreated adult-onset hypopituitarism in relation to age-dependent general population normative data

P-26 Body mass index (BMI) and waist circumference in growth hormone (GH)-untreated adult-onset hypopituitarism in relation to age-dependent general population normative data