Qualitative Analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

In this paper,we establish a delayed predator-prey model with nonlocal fear effect.Firstly,the existence,uniqueness,and persistence of solutions of the model are studied.Then,the local stability,Turing bifurcation,and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic equation.The global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function method.Finally,the correctness of the theoretical analysis results is verified through numerical simulations.

Dynamical Behaviors of a Modified Leslie-Gower Predator-Prey System with Fear Effect and Prey Refuge

In this paper, the dynamical behaviors of a modified Leslie-Gower predator-prey model incorporating fear effect and prey refuge are investigated. We delve into the construction of the model and its biological significance, with preliminary results encompassing positivity, boundedness, and persistence. The stability of the system’s boundary and positive equilibrium points is proven by calculating the real part of the eigenvalues of the Jacobian matrix. At the positive equilibrium point, we demonstrate that the system’s unique positive equilibrium is globally asymptotically stable by using the Dulac criterion. Furthermore, at this equilibrium point, we employ the Implicit Function Theorem to discuss how fear effects and prey refuges influence the population densities of both prey and predators. Finally, numerical simulations are conducted to validate the above-mentioned conclusions and explored the impact of Predator-taxis sensitivity αon dynamics of the system.

Study of Fractional Order Tri-Tropic Prey-Predator Model with Fear Effect on Prey Population

In this manuscript, we have studied a fractional-order tri-trophic model with the help of Caputo operator. The total population is divided into three parts, namely prey, intermediate predator and top predator. In addition, the predator fear impact on prey population is suggested in this paper. Existence and uniqueness along with non-negativity and boundedness of the model system have been investigated. We have studied the local stability at all equilibrium points. Also, we have discussed global stability and Hopf bifurcation of our suggested model at interior equilibrium point. The Adam-Bashforth-Moulton approach is utilized to approximate the solution to the proposed model. With the help of MATLAB, we were able to conduct graphical demonstrations and numerical simulations.

SIRS epidemic modeling using fractional-ordered differential equations:Role of fear effect

In this paper,an SIRS epidemic model using Grunwald-Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases.The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number.The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter.Additionally,using the Grunwald-Letnikov approximation,the simulation is carried out to confirm the validity of analytic results graphically.Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021,we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one.Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.

Dynamical behaviors of a constant prey refuge ratio-dependent prey-predator model with Allee and fear effects

In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population.Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population.The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail.Hopf bifurcation including its direction and stability for the model is also studied.We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system.It is also observed that for a fixed strength of fear,an increase in the Allee parameter makes the system unstable,whereas an increase in prey refuge drives the system toward stability.However,higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction.Further,we explore the variation of densities of the populations in different bi-parameter spaces,where the coexistence equilibrium point remains stable.Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software.

Hopf bifurcation in a delayed prey-predator model with prey refuge involving fear effect

This work investigates a prey-predator model featuring a Holling-type II functional response,in which the fear effect of predation on the prey species,as well as prey refuge,are considered.Specifically,the model assumes that the growth rate of the prey population decreases as a result of the fear of predators.Moreover,the detection of the predator by the prey species is subject to a delay known as the fear response delay,which is incorporated into the model.The paper establishes the preliminary conditions for the solution of the delayed model,including positivity,boundedness and permanence.The paper discusses the existence and stability of equilibrium points in the model.In particular,the paper considers the discrete delay as a bifurcation parameter,demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter.The direction and stability of periodic solutions are determined using central manifold and normal form theory.Additionally,the global stability of the model is established at axial and positive equilibrium points.An extensive numerical simulation is presented to validate the analytical findings,including the continuation of the equilibrium branch for positive equilibrium points.

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

In this study,we consider a diffusive predator-prey model with multiple Allee effects induced by fear factors.We investigate the existence,boundedness and permanence of the solution of the system.We also discuss the existence and non-existence of non-constant solutions.We derive sufficient conditions for spatially homogeneous(non-homogenous)Hopf bifurcation and steady state bifurcation.Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

THE STABILITY OF A PREDATOR-PREY MODEL WITH FEAR EFFECT IN PREY AND SQUARE ROOT FUNCTIONAL RESPONSE

In this paper, we consider a predator-prey model with fear effect and square root functional response. We give the singularity of the origin and discuss the stability and Hopf bifurcation of the trivial equilibrium and the positive equilibrium. We show that the fear effect has no effect on prey density, but will lead to the decrease of predator populations.

Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting

In this paper,we propose a delayed prey-predator-scavenger system with fear effect and linear harvesting.First,we discuss the existence and stability of all possible equilibria.Next,we investigate the existence of Hopf bifurcation of the delayed system by regarding the gestation period of the scavenger as a bifurcation parameter.Furthermore,we obtain the direction of Hopf bifurcation and the stability of bifurcating periodic solutions by using the normal form theory and the central manifold theorem.In addition,we give the optimal harvesting strategy of the delayed system based on Pontryagin's maximum principle with delay.Finally,some numerical simulations are carried out to verify our theoretical results.

The impact of fear effect on the dynamics of a delayed predator-prey model with stage structure

In this paper,a stage structure predator-prey model consisting of three nonlinear ordinary differential equations is proposed and analyzed.The prey populations are divided into two parts:juvenile prey and adult prey.From extensive experimental data,it has been found that prey fear of predators can alter the physiological behavior of individual prey,and the fear effect reduces their reproductive rate and increases their mortality.In addition,we also consider the presence of constant ratio refuge in adult prey populations.Moreover,we consider the existence of intraspecific competition between adult prey species and predator species separately in our model and also introduce the gestation delay of predators to obtain a more realistic and natural eco-dynamic behaviors.We study the positivity and boundedness of the solution of the non-delayed system and analyze the existence of various equilibria and the stability of the system at these equilibria.Next by choosing the intra-specific competition coeficient of adult prey as bifurcation parameter,we demonstrate that Hopf bifurcation may occur near the positive equilibrium point.Then by taking the gestation delay as bifurcation parameter,the suficient conditions for the existence of Hopf bifurcation of the delayed system at the positive equilibrium point are given.And the direction of Hopf bifurcation and the stability of the periodic solution are analyzed by using the center manifold theorem and normal form theory.What's more,numerical experiments are performed to test the theoretical results obtained in this paper.

久坐与社区老年人下肢肌力:跌倒恐惧与年龄的中介和调节作用

背景:人体老龄化进程中,下肢肌肉力量会随着年龄的增长呈现显著的生理性下降,久坐、跌倒恐惧、年龄与下肢肌力之间可能存在一定关联,但它们之间的影响路径与效应关系尚不明确。目的:探究社区老年人久坐和下肢肌肉力量之间的关系,并探讨跌倒恐惧和年龄在上述两者关系中的作用。方法:共招募331名60岁及以上的上海市社区老年人。采用问卷调查法收集基本信息、人口学资料等;采用国际身体活动问卷-短卷评估久坐时间,采用30 s坐站测试测量下肢肌力,采用中文版国际跌倒效能量表测评跌倒恐惧。对数据进行描述统计、相关分析、基于回归的路径分析和中介效应检验。结果与结论:最终以318名老年人[78.9%为女性,平均年龄(67.8±5.5)岁]的有效数据纳入分析,其中久坐时间≥3 h的185名,<3 h的133名。①久坐和跌倒恐惧呈正相关关系(P<0.01),下肢肌力和久坐(P<0.01)、跌倒恐惧(P<0.001)均呈负相关关系。②久坐显著负向预测下肢肌力(β=-0.125,P<0.05),久坐显著正向预测跌倒恐惧(β=0.182,P<0.01);跌倒恐惧显著负向预测下肢肌力(β=-0.293,P<0.001)。③跌倒恐惧在久坐和下肢肌力之间起中介作用(β=-0.053,95%CI:-0.100至-0.018)。④久坐对跌倒恐惧的预测效应具有统计学意义(β=0.164,P<0.01),这说明年龄调节了久坐对跌倒恐惧的影响。

生酸枣仁拮抗条件性恐惧致焦虑大鼠作用及作用机制研究

目的探讨生酸枣仁拮抗条件性恐惧致焦虑大鼠的作用和作用机制。方法SD大鼠随机分为4组:空白组、模型组、地西泮组(3.6 mg/kg)和生酸枣仁组(5.0 g/kg)。利用条件性恐惧方法复制焦虑模型,模型复制后,经灌胃途径给药10d。于末次给药1h后,用旷场实验(OFT)和高架十字迷宫实验(EPM)评价条件性恐惧致焦虑大鼠的焦虑样行为;酶联免疫吸附法(ELisa)检测血清中皮质酮(CORT)含量,皮质、海马和杏仁核中CORT、脑源性神经营养因子(BDNF)、5-羟色胺(5-HT)、去甲肾上腺素(NE)、多巴胺(DA)、谷氨酸(GLU)和γ-氨基丁酸(GABA)含量并计算Glu/GABA的比值。结果在行为学实验中,与空白组相比,模型组大鼠在OFT实验中的跨格次数、中央格运动时间和进入中央格次数均减少(P<0.05或P<0.01);在EPM实验中开/总时间百分比和开/总次数百分比均减少(P<0.01)。与模型组相比,地西泮组大鼠在OFT中跨格次数及中央格运动时间均增加(P<0.01),生酸枣仁组在OFT中各指标均无显著性差异(P>0.05);地西泮组和生酸枣仁组大鼠在EPM中的总入臂次数、开/总时间百分比和开/总次数百分比均增加(P<0.05或P<0.01)。在Elisa法实验中,与空白组相比,模型组皮质、海马与杏仁核中的CORT、Glu的含量和Glu/GABA均增加、GABA的含量均减少(P<0.05或P<0.01),在皮质和海马中BDNF的含量均减少、5-HT、NE和DA的含量均增加(P<0.05或P<0.01),但杏仁核中仅DA的含量增加(P<0.01),BDNF、5-HT及NE的含量减少或增加(P>0.05)。与模型组相比,地西泮组和生酸枣仁组大鼠皮质、海马与杏仁核中的CORT、NE、Glu和GABA的含量均减少、Glu/GABA的比值均增加(P<0.05或P<0.01),皮质和海马中BDNF的含量均增加(P<0.01),皮质中5-HT和DA含量均减少(P<0.01)、但杏仁核中BDNF的含量增加、5-HT的含量减少和海马中DA的含量减少(P>0.05);地西泮组大鼠杏仁核中DA的含量减少(P<0.05),但海马5-HT的含量减少(P>0.05);生酸枣仁组海马中5-HT含量减少(P<0.05),但杏仁核中DA含量减少(P>0.05)。各组实验动物之间血清中CORT的含量变化均无显著性差异(P>0.05)。结论生酸枣仁能有效改善条件性致焦虑大鼠焦虑样行为,其抗焦虑作用机制可能与皮质、海马和杏仁核内CORT、BDNF及神经递质含量变化有关。

具有恐惧效应和Holling Ⅱ类功能性反应捕食-食饵斑块模型的研究

本文提出食饵具有恐惧效应和Holling Ⅱ类功能性反应的捕食-食饵斑块模型,讨论平衡点的存在性和稳定性.并进一步得到边界平衡点的全局稳定性.我们发现,随着恐惧效应因子的增加,系统唯一正平衡点的稳定性会发生变化.因此,在适当条件下,系统会在唯一的正平衡点附近产生Hopf分支现象.数值模拟验证了所得理论结果的正确性.

抑郁症患者参加网络正念认知治疗的疗效及其抑郁症状与恐惧自我的关系

目的:探讨抑郁症患者参加网络正念认知治疗(MBCT)的疗效,重点考察抑郁症患者恐惧自我的特征及其抑郁症状与恐惧自我的关系。方法:采用自身前后对照设计,招募心理咨询门诊抑郁症患者,对其进行为期10周的网络MBCT,采用24项汉密顿抑郁量表(HAMD24)、抑郁自评量表(SDS)、恐惧自我问卷(FSQ)和正念注意觉知量表(MAAS)对患者进行3次评估:网络MBCT开始前一周(T1)、第五周(T2)、第十周(T3)。结果:①64名患者完成研究,抑郁症状显著改善(HAMD24,T2<T1,T3<T1;SDS,T3<T1,均P<0.05)。②在T2,抑郁症状更严重患者的FSQ评分显著高于症状相对不严重的患者(F=4.23,P<0.05)。除了两个相关系数不显著,其余时间点的FSQ与HAMD24显著正相关(r=0.30~0.90,P<0.05)。③T1、T2和T3的SDS可以显著预测对应时间点的HAMD24(调整后R 2=0.07,0.24,0.15;均P<0.05)。结论:网络MBCT显著改善了心理咨询门诊抑郁症患者的抑郁症状,恐惧自我水平对抑郁症状严重程度具有一定的预测性。

急性心肌梗死病人疾病进展恐惧与康复水平的关系:基于应对方式的中介效应分析

目的:调查急性心肌梗死病人疾病进展恐惧与康复水平的关系,探讨应对方式在急性心肌梗死病人疾病进展恐惧与康复水平间的中介效应。方法:选取2020年1月—2022年10月在医院就诊的181例急性心肌梗死病人作为研究对象,采用一般资料调查问卷、疾病进展恐惧问卷简化版(FoP-Q-SF)、心肌梗死多维度评估量表(MIDAS)、医学应对方式问卷(MCMQ)对其进行调查,采用Pearson相关性分析疾病进展恐惧、康复水平、应对方式三者之间的关系,并通过结构方程模型中的路径分析检验应对方式在疾病进展恐惧与康复水平之间的中介效应。结果:181例急性心肌梗死病人疾病进展恐惧总分为(31.25±6.09)分,康复水平总分为(67.34±11.24)分,应对方式中面对、回避、屈服各维度的评分分别为(17.33±3.65)分、(14.54±2.14)分、(9.67±2.01)分;Pearson相关性分析结果显示,急性心肌梗死病人疾病进展恐惧与康复水平、面对均呈负相关(r值分别为-0.611,-0.644,P<0.05),与回避、屈服呈正相关(r值分别为0.512,0.706,P<0.05);康复水平与面对呈正相关(r=0.421,P<0.05),与回避、屈服呈负相关(r值分别为-0.502,-0.478,P<0.05);Bootstrap检验结果显示,疾病进展恐惧对康复水平的直接效应为-0.36,间接效应为-0.17,中介效应占总效应的32.08%。结论:急性心肌梗死病人疾病进展恐惧、康复水平、应对方式具有两两相关性,且应对方式在急性心肌梗死病人疾病进展恐惧与康复水平间存在部分中介效应。

垂体神经内分泌肿瘤术后患者积极应对方式在疾病感知与恐惧疾病进展的中介效应

目的 调查垂体神经内分泌肿瘤术后患者恐惧疾病进展现状,探讨积极应对方式、疾病感知与在恐惧疾病进展的中介效应。方法 采用便利抽样法,选取2022年1月至2023年1月在山西省某三级甲等综合医院神经外科行手术治疗后的垂体神经内分泌肿瘤患者345例作为研究对象,采用一般资料调查表、疾病感知问卷、医学应对方式问卷和恐惧疾病进展简化量表进行调查,采用Pearson相关分析患者疾病感知、积极应对方式及恐惧疾病进展之间的相关性,采用结构方程模型分析积极应对方式在疾病感知与恐惧疾病进展间的中介效应。结果 共337例患者完成研究。垂体神经内分泌肿瘤术后患者恐惧疾病进展得分为(35.02±4.92)分;恐惧疾病进展与疾病感知呈正相关(r=0.672,P<0.01),与积极应对方式呈负相关(r=-0.679,P<0.01),积极应对方式与疾病感知呈负相关(r=-0.610,P<0.01);疾病感知不仅对恐惧疾病进展存在直接影响,还可通过积极应对方式对恐惧疾病进展产生间接影响(中介效应值为0.202,P<0.001)占总效应的25.50%。结论 垂体神经内分泌肿瘤术后患者的积极应对方式是疾病感知与恐惧疾病进展的中介变量。医护人员应动态评估、早期识别患者的应对方式,采取个性化的指导方案,引导患者积极应对,从而降低其负性疾病感知对恐惧疾病进展的影响。

心理韧性和家庭支持在肺癌患者围手术期恐惧与焦虑症状间的中介效应

目的分析心理韧性和家庭支持在肺癌患者围手术期恐惧与焦虑症状间的中介效应。方法纳入2021年1月至2023年4月中山大学孙逸仙纪念医院收治的225例肺癌围手术期患者作为研究对象,采用一般资料调查量表、心理韧性评定量表、领悟社会支持量表、外科手术恐惧问卷、状态-特质焦虑量表进行问卷调查,采用Pearson相关性分析心理韧性、家庭支持及手术恐惧与焦虑症状的相关性,采用Process的Model 6分析心理韧性及家庭支持在肺癌患者围手术期恐惧与焦虑症状的中介效应。结果研究纳入220例肺癌患者,焦虑症状得分为(49.22±10.17)分。不同年龄、受教育年限、肿瘤分期、心理韧性及家庭支持得分的患者的焦虑症状得分差异有统计学意义(P<0.05)。焦虑症状得分与恐惧得分呈正相关(r=0.85,P<0.05),与心理韧性(r=-0.90,P<0.05)及家庭支持得分(r=-0.81,P<0.05)呈负相关。链式中介效应分析显示,围手术期恐惧→心理韧性→焦虑症状的效应值为0.36,占总效应的63.54%,占总间接效应的75.30%,间接效应1成立(P=0.0214);围手术期恐惧→家庭支持→焦虑症状的效应值为0.06,占总效应的11.21%,占总间接效应的13.29%,间接效应2成立(P=0.0013);围手术期恐惧→心理韧性→家庭支持→焦虑症状的效应值为0.05,占总效应的9.63%,占总间接效应的11.41%,间接效应3成立(P=0.0025)。结论肺癌患者围手术期表现出较为显著的焦虑症状,心理韧性和家庭支持在肺癌患者围手术期恐惧与焦虑症状间存在链式中介效应,临床医护人员可以根据围手术期恐惧影响焦虑症状的路径,促进患者的心理韧性和家庭支持,改善肺癌患者焦虑症状。

具有恐惧效应和Holling Ⅲ功能性反应的随机捕食-食饵系统

该文研究了一类具有恐惧效应和Holling Ⅲ功能反应的随机捕食-食饵系统.首先,证明了在任意给定正初始值下,系统全局正解的存在唯一性与均值有界性及随机最终有界性;其次,研究了食饵种群和捕食者种群灭绝和平均持续生存的充分条件,并构造Lyapunov函数证明了系统存在平稳分布及遍历性;最后,通过数值模拟验证了文章的结果.

具有相互干扰和恐惧效应的捕食模型的稳定性

研究一类具有相互干扰和恐惧效应的Lotka-Volterra食饵-捕食模型,分析解的有界性和系统平衡点的存在性,并给出系统持续性的充分条件,通过Dulac判别法得出正平衡点是全局渐近稳定的,具有相互干扰和恐惧效应的食饵-捕食模型能长期共存并保持生态平衡。

一类具有恐惧效应和避难所的捕食者-食饵模型的动力学分析

为探究恐惧效应和避难所对生物种群的影响,建立一类食饵具有恐惧效应和避难所的服从Gompertz增长规律的捕食者-食饵模型。首先,证明了模型解的非负性;其次,给出了正平衡点的存在条件以及平衡点局部稳定的条件,利用Dulac准则证明模型在解的有界区域Ω上不存在极限环,进一步表明其全局渐近稳定性;最后,分析了恐惧强度及避难所的规模对种群密度的影响。研究发现食饵种群密度不受恐惧效应的影响,但是食饵避难所有利于食饵种群密度的增加;随着恐惧强度的增加,捕食者的种群密度会减少;较大的食饵避难所规模不利于捕食者种群的增长。