Parameter estimation in nonlinear age-dependent population dynamics

This paper studies a parameter estimation problem for the Gurtin-MacCamyequation, which is a nonlinear model of age-dependent populationdynamics. In estimating parameters such as the death rate andthe fertility which depend on the age and the total populationfrom a set of fully discrete observations of the population,we use a backward finite-difference scheme. The function-spaceparameter estimation convergence (FSPEC) of this scheme is provedand numerical simulations are performed.     

An innovative multistage, physiologically structured, population model to understand the European grapevine moth dynamics

We present a multistage, physiologically structured, population model for studying the dynamics of one of the most important grapevine insect pests. Growth of the population at each stage is modeled considering the climatic variations and the grape variety. A result of existence and uniqueness of solutions is presented for this original hyperbolic system as well as simulations of experimental field data.     

On a size-structured population dynamics model

We consider a linear size-structured population dynamics model. For this model with a nonlinear global boundary condition that has a biological meaning, we obtain a solution in constructive form.     

A size-structured population dynamics model of Daphnia

The stability of a size-structured population dynamics model of Daphnia coupled with the dynamics of an unstructured algal food source is investigated for the case where there is also an inflow of newborns from an external source. We determine the steady states and study the stability of the nontrivial steady states. We also identify a demographic-algae parameter that determines a condition for the stability.     

An improved model of age-structured population dynamics

The classical model of age-dependent population dynamics is improved. Instead of the traditional renewal equation, a new approach is developed to describe the reproduction process of the population. The composition of a population is redefined to contain the pre-birth individuals, and the disadvantages of the classical model avoided. Moreover, the improved model turns out to be an initial value problem, which is mathematically more convenient to deal with. Existence and uniqueness results for the nonlinear nonautonomous system of model equations are obtained. It is shown that the classical model and its time delay generalization are two degenerate cases of the improved model.     

A population dynamics model with nonautonomous past

Abstract

In this paper we study a two-phase population model, which distinguishes the population by two different stages

By the standard technique of characteristics, this population equation is transformed as the ordinary differential equation with nonautonomous past

where 1 ≤ p < ∞ and I = [?r, 0] (finite delay) or I = (?∞, 0] (infinite delay), E a Banach space, Φ : W^1,p(I, E) → E a linear delay operator and B a nonlinear operator on E. The main result of this paper is the well-posedness of this delay equation by using the (right) multiplicative perturbation result of Desch and Schappacher in [8].     

Global weak solution for a multistage physiologically structured population model with resource interaction

We construct a multistage kinetic model of a physiologically structured insect population whose life history consists of fourth stages of development termed eggs, larval, pupal and adult moth (male and female). The model is a system of weakly coupled hyperbolic partial differential equations with nonlocal boundary conditions. The vital rates depend on the resource which satisfy an ordinary differential equation. We discretize the physiological space and formulate an implicit scheme and we prove the existence and uniqueness of the solution. The numerical simulation provides an analytical tool to improve the understanding of the moth’s biology.     

Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate

In this paper, a multistage susceptible‐infectious‐recovered model with distributed delays and nonlinear incidence rate is investigated, which extends the model considered by Guo et al. [H. Guo, M. Y. Li and Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72 (2012), 261–279]. Under some appropriate and realistic conditions, the global dynamics is completely determined by the basic reproduction number R₀. If R₀≤1, then the infection‐free equilibrium is globally asymptotically stable and the disease dies out in all stages. If R₀>1, then a unique endemic equilibrium exists, and it is globally asymptotically stable, and hence the disease persists in all stages. The results are proved by utilizing the theory of non‐negative matrices, Lyapunov functionals, and the graph‐theoretical approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A population dynamics model with strong maternal care

A two-sex age-structured nondispersing population dynamics deterministic model is presented taking into account strong maternal and weak paternal care of offspring. The model includes a weighted harmonic-mean type pair formation function and neglects the spatial dispersal and separation of pairs. It is assumed that each sex has pre-reproductive and reproductive age intervals. All adult individuals are divided into single males, single females, permanent pairs, and female-widows taking care of their offsprings after the death of their partners. All pairs are of two types: pairs without offspring under parental care at the given time and pairs taking child care. All individuals of pre-reproductive age are divided into young and juvenile groups. The young offspring are assumed to be under parental or maternal (after the death of their father) care. Juveniles can live without parental or maternal care but they cannot reproduce offsprings. It is assumed that births can only occur from couples. The model consists of nine integro-PDEs subject to the conditions of integral type. A class of separable solutions is studied, and a system for macro-moments evolving in time is derived in the case of age-independent vital ones. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 215–255, April–June, 2006.     

An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification

The bioconversion of glycerol to 1,3-propanediol is a complex bioprocess. In this study, we aim to explore a novel model for describing the multistage cell growth in batch culture. This is achieved by a modification at the specific rate of cell growth in consideration of its time-dependent changes. The existence, uniqueness and boundedness of solutions to the system and the continuity of solutions with respect to the parameters are discussed. In addition, a parameter identification problem of the system is developed and a feasible optimization algorithm is constructed to solve it. Numerical result shows that the improved model could describe the batch culture well.     

Eventual stability properties in a non-autonomous model of population dynamics

We prove that (λ^∗,C/λ^∗) is an eventually uniform-asymptotically stable point in the large of the system

     

Global dynamics of a population model from river ecology

In this paper, we investigate the population dynamics of a two-species Lotka-Volterra competition system arising in river ecology. An interesting feature of this modeling system lies in the boundary conditions at the downstream end, where the populations may be exposed to differing magnitudes of loss of individuals. By applying the theory of principal eigenvalue and monotone dynamical systems, we obtain a complete understanding on the global dynamics, which suggests that slower dispersal is selected for. Our results can be seen as a further development of a recent work by Tang and Chen (J. Differential Equations, 2020, 2020(269), 1465--1483).     

Approximation of a population dynamics model by parabolic regularization

The basic linear model for describing an age structured population spreading in a limited habitat is considered with the purpose of investigating an approximation procedure based on parabolic regularization. In fact, a viscosity model is introduced by considering an appropriate approximating regularized parabolic problem and it is proved that the sequence of the approximating solutions tends to the solution to the original problem. The advantage of this approach is that it leads to the numerical solution of a parabolic problem that has more stable solutions than the hyperbolic‐parabolic original problem and avoids the restrictions (compatibility conditions) needed to treat the latter. Moreover, for the solution of the approximating problem, it is possible to take advantage of established software packages dedicated to parabolic problems. Some examples of the approach are provided using COMSOL Multiphysics. Copyright © 2012 John Wiley & Sons, Ltd.     

Non-autonomous dynamics of a semi-Kolmogorov population model with periodic forcing

In this paper we study a semi-Kolmogorov type of population model, arising from a predator–prey system with indirect effects. In particular we are interested in investigating the population dynamics when the indirect effects are time dependent and periodic. We first prove the existence of a global pullback attractor. We then estimate the fractal dimension of the attractor, which is done for a subclass by using Leonov’s theorem and constructing a proper Lyapunov function. To have more insights about the dynamical behavior of the system we also study the coexistence of the three species. Numerical examples are provided to illustrate all the theoretical results.     

Age-time continuous Galerkin methods for a model of population dynamics

Continuous Galerkin finite element methods in the age-time domain are proposed to approximate the solution to the model of population dynamics with unbounded mortality (coefficient) function. Stability of the method is established and a priori L²$L^2$-error estimates are obtained. Treatment of the nonlocal boundary condition is straightforward in this framework. The approximate solution is computed strip by strip marching in time. Some numerical examples are presented.     

Parameter identification of dynamical systems

This paper deals with the problem of identification of the unknown parameters of a dynamical system. Our work in this paper largely simulation related, follows the approach suggested by Kim and Lee [IEEE Int. Conf. Neural Networks (1993) 438–443] and it depends on the introduction of auxiliary polynomial. The merit of our work lies on the facts that no assumptions are placed on the stability of auxiliary polynomial and also that it does not require the a priori knowledge of the stability of the dynamical system, in question. Our method applies to both linear and quasi-linear dynamical systems. The results obtained involve the construction of appropriate neural networks. A variety of configurations of the dynamical systems are considered for simulation.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.