Age-dependent Population Research Articles

Hierarchical Stackelberg Control for a Two-Stroke Linear System in Population Dynamics

We study a unique hierarchical control problem for a two-stoke linear system, adjoint to an age and space dependent population dynamics problem. Using Stackelberg's method, we introduce two levels of control: a boundary control to achieve optimal flow regulation and a distributed control for null controllability. Our approach employs Carleman inequalities to address non-homogeneous Dirichlet boundary conditions, leading to new insights in controlling invasive species populations. These results highlight the applicability of hierarchical controls in ecological systems, providing a robust framework for future studies in control theory and population dynamics.

Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching

Stationary Distribution of Stochastic Age-Dependent Population–Toxicant Model with Markov Switching

Uncertain Stochastic Hybrid Age-Dependent Population Equation Based on Subadditive Measure: Existence, Uniqueness and Exponential Stability

The existing literature lacks a study on age-dependent population equations based on subadditive measures. In this paper, we propose a hybrid age-dependent population dynamic system (referred to as APDS) that incorporates uncertain random perturbations driven by both the well-known Wiener process and the Liu process associated with belief degree, which have similar symmetry in terms of form. Firstly, we redefine the Liu integral in a mean square sense and then extend Liu’s lemma and the Itô-Liu formula. We then utilize the extensions of the Itô-Liu formula, Barkholder-Davis-Gundy (BDG) inequality, the Liu’s lemma, the Gronwall’s lemma and the symmetric nature of calculus itself to establish the uniqueness of a strong solution for the hybrid APDS. Additionally, we prove the existence of the hybrid APDS by combining the proof of uniqueness with some important lemmas. Finally, under appropriate assumptions, we demonstrate the exponential stability of the hybrid system.

Existence results and behavior analysis for nonlinear age-dependent population dynamics problems with conformable fractional operator

In this paper, we investigate the existence of solutions and analyze the large-time behavior for Gurtin–Maccamy population model involving conformable fractional derivatives. As a preliminary step, we construct a generic structure of the solution associated with our proposed model by utilizing some basic properties and tools of conformable fractional calculus. We establish the existence of a unique solution of the given model with the given initial conditions. At last, by using the upper and lower solutions for the characteristic equation, we define the upper and lower boundaries for the obtained solution and describe the large-time behavior of the total population.

A positivity-preserving numerical algorithm for stochastic age-dependent population system with Lévy noise in a polluted environment

This paper develops a model for describing a stochastic age-dependent population system (SADPS) with Lévy noise in a polluted environment. As the model includes a nonlinear drift term and Lévy noise, it is difficult, if not impossible, to derive an analytical solution of the model. This study thus aims at developing a numerical algorithm that is based on a modified truncated Euler-Maruyama (EM) method and positivity preserving. We first study global positivity for the solution of the SADPS model in a polluted environment. Subsequently, we present a semi-discrete Galerkin finite element method in an age variable, and construct a full-discrete numerical approximation using modified truncated EM scheme on time to preserve positivity. Under certain suitable regularity conditions, estimates of convergence error of the full-discrete and a semi-discrete scheme are presented. Finally, a numerical example is given to illustrate the theoretical results.

Uncertain age-dependent population equation with migration source

Uncertain age-dependent population equation with migration source

The numerical algorithm for stochastic age-dependent population system with Lévy noise in a polluted environment

Environmental pollution has significant effects on population systems worldwide. In this study, we established a numerical algorithm for modelling stochastic age-dependent population systems driven by Lévy noise in a polluted environment. A modified explicit Euler–Maruyama (EM) discretization scheme was employed for ensuring the positiveness of the numerical solution used for modelling the stochastic age-dependent population hybrid system with Lévy noise in a polluted environment. The convergence of the numerical solution was confirmed by It's formula and a projection operator under the condition that the drift coefficient satisfies the local Lipschitz and global one-sided Lipschitz conditions. The theoretical results were finally verified with a numerical example.

Longitudinal analysis of blood markers reveals progressive loss of resilience and predicts human lifespan limit

We investigated the dynamic properties of the organism state fluctuations along individual aging trajectories in a large longitudinal database of CBC measurements from a consumer diagnostics laboratory. To simplify the analysis, we used a log-linear mortality estimate from the CBC variables as a single quantitative measure of the aging process, henceforth referred to as dynamic organism state indicator (DOSI). We observed, that the age-dependent population DOSI distribution broadening could be explained by a progressive loss of physiological resilience measured by the DOSI auto-correlation time. Extrapolation of this trend suggested that DOSI recovery time and variance would simultaneously diverge at a critical point of 120 − 150 years of age corresponding to a complete loss of resilience. The observation was immediately confirmed by the independent analysis of correlation properties of intraday physical activity levels fluctuations collected by wearable devices. We conclude that the criticality resulting in the end of life is an intrinsic biological property of an organism that is independent of stress factors and signifies a fundamental or absolute limit of human lifespan.

Stability results for a nonlinear two-species competition model with size-structure

We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community, in which the mortality, fertility and growth are size-dependent. Existence and uniqueness of nonnegative solutions to the system are analyzed. The existence of the stationary size distributions is discussed, and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique. Some sufficient conditions for asymptotical stability / instability of steady states are obtained. The resulting conclusion extends some existing results involving age-independent and age-dependent population models.

Mckendrick–Tornquist Age-Dependent Population Model

The paper considers an age-dependent population model where the mortality function is given by the Tornquist distribution. As a result of the investigation, we obtain conditions of the existence of nonnegative stationary states in this model.

Investigate future population projection of Bangladesh with the help of Malthusian model, Sharpe-lotka model and Gurtin Mac-Camy model

A nonlinear deterministic model of age-dependent population growth is formulated in terms of joint integral equations in the total population size function and the total birth rate function. Existence of a unique solution of the model equation is established using Banach fixed point theorem. Then we investigate the total population size of Malthusian model, Sharpe-Lotka linear model and Gurtin Mac-Camy model for some specific age group and compare our investigated solutions with the total population of Bangladesh by using numerical method “Newton divided difference formula”. In our present study, we also investigate future population projection of Bangladesh with the help of Malthusian model, Sharpe-Lotka model and Gurtin Mac-Camy model.

Florida neighborhood analysis of social determinants and their relationship to life expectancy

BackgroundSocial determinants of health (SDOH) contribute to unequal life expectancy (LE). Only a handful of papers have analyzed these relationships at the neighborhood level as opposed to the county level. This study draws on both the SDOH and social vulnerability literature to identify relevant factors affecting LE.MethodsLE was calculated from mortality records for Florida from 2009 to 2013 for 3640 census tracts with reliable estimates. A spatial Durbin error model (SDEM) quantified the direction and magnitude of the factors to LE. The SDEM contains a spatial error term and jointly estimates both local and neighborhood associations. This methodology controls for non-independence between census tracts to provide unbiased statistical estimates.ResultsFactors significantly related to an increase in LE, include percentage (%) of the population who identify as Hispanic (beta coefficient [β]: 0.06, p-value [P] < 0.001) and % of age dependent populations (% population < 5 years old and % population > 65) (β: 0.13, P < 0.001). Conversely, the following factors exhibited significant negative LE associations, % of households with no automobile (β: -0.05, P < 0.001), % of mobile homes (β: -0.02, P < 0.001), and % of female headed households (β: -0.11, P < 0.001).ConclusionsResults from the SDEM demonstrate social vulnerability indicators account for additional geographic LE variability beyond commonly studied SDOH. Empirical findings from this analysis can help local health departments identify drivers of spatial health disparities at the local level.

Taylor approximation of the solution of age-dependent stochastic delay population equations with Ornstein-Uhlenbeck process and Poisson jumps.

Numerical approximation is a vital method to investigate the properties of stochastic age-dependent population systems, since most stochastic age-dependent population systems cannot be solved explicitly. In this paper, a Taylor approximation scheme for a class of age-dependent stochastic delay population equations with mean-reverting Ornstein-Uhlenbeck (OU) process and Poisson jumps is presented. In case that the coefficients of drift and diffusion are Taylor approximations, we prove that the numerical solutions converge to the exact solutions for these equations. Moreover, the convergence order of the numerical scheme is given. Finally, some numerical simulations are discussed to illustrate the theoretical results.

TASARRUFLAR İLE DIŞ BORÇLAR ARASINDAKİ İLİŞKİNİN AMPİRİK ANALİZİ: TÜRKİYE ÖRNEĞİ

Toplumların organize olmuş halini ifade eden devlet yapılanmalarına son birkaç yüzyıl içinde eskiye kıyasla çok daha fazla sorumluluk yüklenmektedir. Kamu hizmetlerinin devamlılığının gerekliliği, giderlerin gelirleri aştığı dönemlerde devletleri borçlanmaya mecbur bırakmaktadır. Devletlerin borçlanma sebepleri her ne olursa olsun, borçlanma amacıyla yönelecekleri kaynak ulusal veya uluslararası tasarruflar olacaktır. Tasarruflar ile borçlar arasında var olan bu organik bağ, bu çalışmanın temel hareket noktasını oluşturmaktadır. Çalışmanın amacı, ülkemizin dış borçlanmaya olan gereksinimi ile tasarruf ve tasarrufu etkileyen bir dizi değişken arasındaki kısa ve uzun dönemli ilişkinin varlığını tespit edebilmektir. 1980-2016 yıllarını kapsayan verilerle gerçekleştirilen analiz sonucunda, tasarruflar ile dış borçlar arasında negatif bir ilişkinin olduğu görülmüştür. Bir başka ifade ile, tasarruflarda yaşanan %1’lik bir artışın dış borçları uzun dönemde %1.4 azalttığı bulgusuna ulaşılmıştır. Analiz neticesinde ulaşılan diğer bir sonuca göre de, ekonomik büyümedeki %1’lik artış dış borçları uzun dönemde %1.6 azaltmaktadır. Elde edilen diğer ampirik bulgular arasında enflasyon, kamu gelirleri ve yaşa bağımlı nüfusta yaşanacak %1’lik artışların uzun dönemde dış borcu sırasıyla %0.12, %1.3 ve %1.9 oranında arttırdığı yer almaktadır. Kısa dönemli ilişkinin analizi sonucunda ise, bahse konu değişkenlerden kaynaklanan herhangi bir şokun etkisinin yaklaşık olarak iki buçuk dönemde ortadan kalktığı ve uzun dönemli denge seviyesine geri dönüldüğü görülmüştür.

Analysis of an epidemiological model structured by time-since-last-infection

Modeling time-since-last-infection (TSLI) provides a means of formulating epidemiological models with fewer state variables (or epidemiological classes) and more flexible descriptions of infectivity after infection and susceptibility after recovery than usual. The model considered here has two time variables: chronological time (t) and the TSLI (τ), and it has only two classes: never infected (N) and infected at least once (i). Unlike most age-structured epidemiological models, in which the i equation is formulated using (∂∂τ+∂∂t)i(τ,t), ours uses a more general differential operator. This allows weaker conditions for the infectivity and susceptibility functions, and thus, is more generally applicable. We reformulate the model as an age dependent population problem for analysis, so that published results for these types of problems can be applied, including the existence and regularity of model solutions. We also show how other coupled models having two types of time variables can be stated as age dependent population problems.

Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ-method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switching. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results.

Optimal harvesting for age-structured population dynamics with size-dependent control

We investigate two optimal harvesting problems related to age-dependent population dynamics; namely we consider two problems of maximizing the profit for age-structured population dynamics with respect to a size-dependent harvesting effort. We evaluate the directional derivatives for the cost functionals. The structure of the harvesting effort is uniquely determined by its intensity (magnitude) and by its area of action/distribution. We derive an iterative algorithm to increase at each iteration the profit by changing the intensity of the harvesting effort and its distribution area. Some numerical tests are given to illustrate the effectiveness of the theoretical results for the first optimal harvesting problem.

Mean-square stability of stochastic age-dependent delay population systems with jumps

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems (SADDPSs) with Poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally, the theoretical results are also confirmed by a numerical experiment.

An Age-Structured Population Approach for the Mathematical Modeling of Urban Burglaries

We propose a nonlinear model for the dynamics of urban burglaries which takes into account the deterring effect of the police. The model focuses on the timing of criminal activity rather than on the spatial spreading of burglaries and it is inspired in the age-dependent population dynamics. The structuring variables are the time elapsed between two consecutive offenses committed by a burglar or suffered by a house. The main ingredients of the model are the propensity of burglars to commit a crime and the rate at which houses are being burgled. These rates are taken as general as possible to allow different scenarios, including the widely used repeat victimization pattern. The dissuasive effect of the active police deployment is introduced by means of a memory term that depends on the number of the last committed burglaries. The asymptotic behavior of the model and the existence of a globally stable equilibrium are determined thanks to a suitable change of variables that involves a continuous rescaling of the time variable. This new approach provides some interesting analytic results on the equilibrium and the expected times between consecutive offenses. Numerical simulations are shown to illustrate these results.

Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps

This paper focuses on asymptotic mean-square boundedness of several numerical methods applied to a class of stochastic age-dependent population equations with Poisson jumps. The conditions under which the underlying systems are asymptotic mean-square boundedness are considered. It is shown that the asymptotic mean-square boundedness is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce asymptotic mean-square boundedness under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of asymptotic mean-square boundedness. Finally, an example is given for illustration.