Spreading speed of a food-limited population model with delay

This paper is concerned with the spreading speed of a food-limited population model with delay.First,the existence of the solution of Cauchy problem is proved.Then,the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality.Finally,we present some numerical simulations and investigate the dynamical behavior of the solution.

Closed-loop control of epileptiform activities in a neural population model using a proportional-derivative controller

Epilepsy is believed to be caused by a lack of balance between excitation and inhibitation in the brain. A promising strategy for the control of the disease is closed-loop brain stimulation. How to determine the stimulation control parameters for effective and safe treatment protocols remains, however, an unsolved question. To constrain the complex dynamics of the biological brain, we use a neural population model（NPM）. We propose that a proportional-derivative（PD） type closed-loop control can successfully suppress epileptiform activities. First, we determine the stability of root loci, which reveals that the dynamical mechanism underlying epilepsy in the NPM is the loss of homeostatic control caused by the lack of balance between excitation and inhibition. Then, we design a PD type closed-loop controller to stabilize the unstable NPM such that the homeostatic equilibriums are maintained; we show that epileptiform activities are successfully suppressed. A graphical approach is employed to determine the stabilizing region of the PD controller in the parameter space, providing a theoretical guideline for the selection of the PD control parameters. Furthermore, we establish the relationship between the control parameters and the model parameters in the form of stabilizing regions to help understand the mechanism of suppressing epileptiform activities in the NPM. Simulations show that the PD-type closed-loop control strategy can effectively suppress epileptiform activities in the NPM.

THE PERIODIC SOLUTIONS FOR TIME DEPENDENT AGE-STRUCTURED POPULATION MODELS

In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.

QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation modelwhere 0<a < 1 < a + 6,p, c ∈ (0, ∞) and k is a nonnegative integer, is investigated. Some necessary and sufficient as well as sufficient conditions for all solutions of the model to oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions are derived. Furthermore, the permanence of every positive solution of the model is also showed. Many known results are improved and extended and some new results are obtained for G. Ladas' open problems.

QUALITATIVE ANALYSIS OF A DICRETE POPULATION MODEL

In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.

Nonlinear dynamical wave structures of Zoomeron equation for population models

The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevéapproach method(PPAM).When the variables appearing in the exact solutions take specific values,the solitary wave solutions will be easily obtained.The realized results prove the efficiency of this technique.

A Guide to Population Modelling for Simulation

This paper outlines the fundamentals of a consistent theory of numerical modelling of a population system under study. The focus is on the systematic work to construct an executable simulation model. There are six fundamental choices of model category and model constituents to make. These choices have a profound impact on how the model is structured, what can be studied, possible introduction of bias, lucidity and comprehensibility, size, expandability, performance of the model, required information about the system studied and its range of validity. The first choice concerns a discrete versus a continuous description of the population system under study—a choice that leads to different model categories. The second choice is the model representation (based on agents, entities, compartments or situations) used to describe the properties and behaviours of the objects in the studied population. Third, incomplete information about structure, transitions, signals, initial conditions or parameter values in the system under study must be addressed by alternative structures and statistical means. Fourth, the purpose of the study must be explicitly formulated in terms of the quantities used in the model. Fifth, irrespective of the choice of representation, there are three possible types of time handling: Event Scheduling, Time Slicing or Micro Time Slicing. Sixth, start and termination criteria for the simulation must be stated. The termination can be at a fixed end time or determined by a logical condition. Population models can thereby be classified within a unified framework, and population models of one type can be translated into another type in a consistent way. Understanding the pros and cons for different choices of model category, representation, time handling etc. will help the modeller to select the most appropriate type of model for a given purpose and population system under study. By understanding the rules for consistent population modelling, an appropriate model can be created in a systematic way and a number of pitfalls can be avoided.

An efficient technique for two-dimensional fractional order biological population model

In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition scheme with natural transform,and three examples are considered to validate and illustrate its efficiency.The nature of FNDM solution has been captured for distinct arbitrary order.In order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been presented.The obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

On the Asymptotic Stability of Discrete Crocodilians Model

The sex ratio of crocodiles is strongly biased towards females, often as high as 10 females to 1 male. In crocodilians, the temperature of egg incubation is the environmental factor determining sex. If the temperature is low, around 30˚C, the hatchlings are all females. Higher temperature, around 34˚C, hatch all males. This study was made to consider the asymptotic stability of a positive equilibrium point in a nonlinear discrete model of the basic nesting population model, which is described in three-region depending on the temperature of egg incubation. This model is based on key life-historical data and Murray’s research. To study above, we have applied the classical linearization method and P. Cull’s method and moreover, we employ non-standard discretization methods for later our Equations (6)-(8) and (15).

Risk factors for acute kidney injury following coronary artery bypass graft surgery in a Chinese population and development of a prediction model

BACKGROUND Acute kidney injury(AKI)after coronary artery bypass graft(CABG)surgery is associated with significant morbidity and mortality.This retrospective study aimed to establish a risk score for postoperative AKI in a Chinese population.METHODS A total of 1138 patients undergoing CABG were collected from September 2018 to May 2020 and divided into a derivation and validation cohort.AKI was defined according to the Kidney Disease Improving Global Outcomes(KDIGO)criteria.Multivariable logistic regression analysis was used to determine the independent predictors of AKI,and the predictive ability of the model was determined using a receiver operating characteristic(ROC)curve.RESULTS The incidence of cardiac surgery–associated acute kidney injury(CSA-AKI)was 24.17%,and 0.53%of AKI patients required dialysis(AKI-D).Among the derivation cohort,multivariable logistic regression showed that age≥70 years,body mass index(BMI)≥25 kg/m2,estimated glomerular filtration rate(eGFR)≤60 mL/min per 1.73 m2,ejection fraction(EF)≤45%,use of statins,red blood cell transfusion,use of adrenaline,intra-aortic balloon pump(IABP)implantation,postoperative low cardiac output syndrome(LCOS)and reoperation for bleeding were independent predictors.The predictive model was scored from 0 to32 points with three risk categories.The AKI frequencies were as follows:0-8 points(15.9%),9-17 points(36.5%)and≥18 points(90.4%).The area under of the ROC curve was 0.730(95%CI:0.691-0.768)in the derivation cohort.The predictive index had good discrimination in the validation cohort,with an area under the curve of 0.735(95%CI:0.655-0.815).The model was well calibrated according to the Hosmer-Lemeshow test(P=0.372).CONCLUSION The performance of the prediction model was valid and accurate in predicting KDIGO-AKI after CABG surgery in Chinese patients,and could improve the early prognosis and clinical interventions.

Nonadiabatic Population Transfer in a Tangent-Pulse Driven Quantum Model

Fine control of the dynamics of a quantum system is the key element to perform quantum information processing and coherent manipulations for atomic and molecular systems. We propose a control protocol using a tangentpulse driven model and demonstrate that it indicates a desirable design, i.e., of being both fast and accurate for population transfer. As opposed to other existing strategies, a remarkable character of the present scheme is that high velocity of the nonadiabatic evolution itself not only will not lead to unwanted transitions but also can suppress the error caused by the truncation of the driving pulse.

Modeling the dynamics of a spruce forest and dwarf mistletoe population:a coupled system

The parasitic plant dwarf mistletoe(Arceuthobium) is currently one of the most threatening infestations of coniferous forests worldwide,especially in Eurasia and North America,but its population dynamics in relation to one of its hosts(spruce) remain unclear.Here,toward understanding the population dynamics,differential equations were used to construct a life history model for the two populations,and two relatively independent subsystems,host and parasite,were generated from their symbiotic relationships.A suspected-infection model was used to couple them.The resulting models were used to analyze structural changes in the forest.When each infected spruce was assumed to support 1000 parasite shoots,the spruce population first increased rapidly,then slows.When 2000 parasite shoots were assumed,the forest declined dramatically,slipping to zero in the 10 th year,and the spruce seedlings were unable to regenerate.Parasite shoot population curves transformed from exponential J-shapes to logistic S-shapes,reaching population limitations as germination rates changed.These results provide important clues to understanding developmental trends of the present parasite population and will assist in reconstructing invasion histories.

On the optimal harvesting of size-structured population dynamics

This work is concerned with a kind of optimal control problem for a size-structured biological population model.Well-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point theorem.Existence and uniqueness of optimal control are shown by functional analytical approach.Optimality conditions describing the optimal strategy are established via tangent and normal cones technique.The results are of the first ones for this novel structure.

EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.

Properties of Solutions of Kolmogorov-Fisher Type Biological Population Task with Variable Density

In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.

Dynamical behavior of a mosquito population suppression model composed of two sub-models

In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain sexually active for time T.For the case T<T,three thresholds T^(*),m^(*)and c^(*)are determined for the release period T and release amount c.According to the values of T and c in different ranges determined by these thresholds,we study the dynamical behavior of the system for different release strategies,mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions.Finally,some numerical simulations are performed to illustrate our results.

Exploring nationally and regionally defined models for large area population mapping

Interactions between humans,diseases,and the environment take place across a range of temporal and spatial scales,making accurate,contemporary data on human population distributions critical for a variety of disciplines.Methods for disaggregating census data to finer-scale,gridded population density estimates continue to be refined as computational power increases and more detailed census,input,and validation datasets become available.However,the availability of spatially detailed census data still varies widely by country.In this study,we develop quantitative guidelines for choosing regionally-parameterized census count disaggregation models over country-specific models.We examine underlying methodological considerations for improving gridded population datasets for countries with coarser scale census data by investigating regional versus country-specific models used to estimate density surfaces for redistributing census counts.Consideration is given to the spatial resolution of input census data using examples from East Africa and Southeast Asia.Results suggest that for many countries more accurate population maps can be produced by using regionally-parameterized models where more spatially refined data exists than that which is available for the focal country.This study highlights the advancement of statistical toolsets and considerations for underlying data used in generating widely used gridded population data.

ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

In this paper we investigate the existence and stability of almost periodic solutions of some single population models with almost periodic environment. We obtain some results about the existence and stability of the positive almost periodic solutions.

A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz Equations

Many curves have been proposed and debated to model individual growth of marine invertebrates. Broadly, they fall into two classes, first order (e.g. von Bertalanffy) and sigmoidal (e.g. Gompertz). We provide an innovative approach which demonstrates that the growth curves are not mutually exclusive but that either may arise from a simple three-stage growth model with two steps (k1 and k2) depending on the ratio of the growth parameters . The new approach predicts sigmoidal growth when is close to 1, but if either growth from stage A to stage B or B to C is fast relative to the other, the slower of the two steps becomes the growth limiting step and the model reduces to first order growth. The resulting curves indicate that there is a substantial difference in the estimated size at time t during the period of active growth. This novel two-step rate model generates a growth surface that allows for changes in the rate parameters over time as reflected in the new parameter n(t) = k1(t) - k2(t). The added degree of freedom brings about individual growth trajectories across the growth surface that is not easily mapped using conventional growth modeling techniques. This two (or more) stage growth model yields a growth surface that allows for a wide range of growth trajectories, accommodating staged growth, growth lags, as well as indeterminate growth and can help resolve debates as to which growth curves should be used to model animal growth. This flexibility can improve estimates of growth parameters used in population models influencing model outcomes and ultimately management decisions.=

CFD-PBE simulation of gas-phase hydrodynamics in a gas-liquid-solid combined loop reactor

The computational fluid dynamics （CFD）-population balance equations （PBE） coupled model is employed to investigate the hydrodynamics in a gas-slurry internal loop reactor with external slurry circulation. The predicted radial profiles of local gas holdup and bubble diameter are in good agreement with the corresponding experimental data. The spatio-temporal velocity profile of the gas phase reveals that the upward movement of gas is slowed down and the residence time of gas is prolonged by the downward momentum of the slurry, introduction of the external slurry can greatly improve the uniformity of gas holdup distribution in the reactor, especially in the downcomer-tube action region. Moreover, the interaction between the downward slurry and upward gas can lead to small bubble size and high interfacial area as well as good mass and heat transfer. The above results suggest the function of external slurry circulation for the internal loop reactor and would be helpful for optimizing the design and scale up of reactors.