Analysis of a delay prey-predator model with disease in the prey species only

Xueyong Zhou,Xiangyun Shi,Xinyu Song 대한수학회 2009 대한수학회지 Vol.46 No.4

In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings. In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings.

Global stability of the viral dynamics with Crowley-Martin functional response

Xueyong Zhou,Jingan Cui 대한수학회 2011 대한수학회보 Vol.48 No.3

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of CD4^+ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number R_0<1, the HIV infection is cleared from the T-cell population and the disease dies out; if R_0>1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if R_0>1. Numerical simulations are presented to illustrate the results.

DYNAMIC BEHAVIOR OF A PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND DISTRIBUTED DELAY

Xueyong Zhou 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence,extinction and stability are performed. By the comparison theorem,a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

DYNAMIC BEHAVIOR OF A PREDATOR-PREY MODEL WITH STAGE STRUCTURE AND DISTRIBUTED DELAY

Zhou, Xueyong The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.1

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

GLOBAL STABILITY OF THE VIRAL DYNAMICS WITH CROWLEY-MARTIN FUNCTIONAL RESPONSE

Zhou, Xueyong,Cui, Jingan Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3

It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of $CD4^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_0$ < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if $R_0$ > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0$ > 1. Numerical simulations are presented to illustrate the results.

ANALYSIS OF A DELAY PREY-PREDATOR MODEL WITH DISEASE IN THE PREY SPECIES ONLY

Zhou, Xueyong,Shi, Xiangyun,Song, Xinyu Korean Mathematical Society 2009 대한수학회지 Vol.46 No.4

In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay ${\tau}$ passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings.

Studying the Eradication of Ebola through the Propagation Modelling and Vaccine Delivery Evaluation

Shuoping Wang,Xueyong Yu,Honghao Gao 보안공학연구지원센터 2016 International Journal of u- and e- Service, Scienc Vol.9 No.12

Ebola is a disease of humans and other primates caused by Ebola viruses. This disease has a high risk of death, killing between 25 and 90 percent of those infected, with an average of about 50 percent. Ebola has become one of the most horrible threats to human beings. In this paper, we develop accurate propagation model of Ebola in order to understand its spread dynamics. In the modeling, human beings are of three exclusive states: ‘Susceptible’, ‘Infected’ and ‘Recovered’. We evaluate the proposed model according to Ebola’s data published by WHO. The experiment results suggest that our model can accurately present the Ebola propagation dynamics in Guinea, Liberia and Sierra Leone. We further study the optimal vaccine delivery strategies in order to restrain the outbreaks of Ebola. When human beings are in short of vaccines, the proposed model analyses the delivery destination, the tendency of Ebola’s propagation, locations of medical centers and labs, and the conditions of patients. According to Ebola’s data from WHO, the model identifies seven cities as the optimal venues to start the vaccine delivery. The work in this paper greatly benefits the eradication of Ebola when it outbreaks in our society.

Periodic solutions for discrete one-predator two-prey system with the modified Leslie-Gower functional response

Xiangyun Shi,Xueyong Zhou,Xinyu Song 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.. In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings..

Allometric Effects of Agriophyllum squarrosum in Response to Soil Nutrients, Water, and Population Density in the Horqin Sandy Land of China

Yingxin Huang,Xueyong Zhao,Hongxuan Zhang,Wisdom Japhet,Xiaoan Zuo,Yayong Luo,Gang Huang 한국식물학회 2009 Journal of Plant Biology Vol.52 No.3

We monitored the allometric effects for greenhouse- grown Agriophyllum squarrosum plants in response to variations in population density and the availability of soil nutrients and water. Biomass allocations were sizedependent. The plasticity of roots, stems, leaves, and reproductive effort was “true” in response to changes in nutrient content. At a low level of soil minerals, plants allocated more resources to the development of roots and reproductive organs than to leaves, but data for stem allocations were consistent for tradeoffs between the effects of nutrients and plant size. The plasticities of leaf allocation and reproductive effort were “true” whereas those of root and stem allocations were “apparent” in response to fluctuations in soil water, being a function of plant size. Decreasing soil water content was associated with higher leaf allocation and lower reproductive effort. Except for this “apparent” plasticity of leaf allocation, none was detected with population density on biomass allocation. Architectural traits were determinants of the latter. For roots, the determining trait was the ratio of plant height to total biomass; for stems and reproduction, plant height; and for leaves, the ratio of branch numbers to plant height.

Experimental study on shear, tensile, and compression behaviors of composite insulated concrete sandwich wall

Zhang, Xiaomeng,Zhang, Xueyong,Liu, Wenting,Li, Zheng,Zhang, Xiaowei,Zhou, Yilun Techno-Press 2021 Advances in concrete construction Vol.11 No.1

A new type of composite insulated concrete sandwich wall (ICS-wall), which is composed of a triangle truss steel wire network, an insulating layer, and internal and external concrete layers, is proposed. To study the mechanical properties of this new ICS-wall, tensile, compression, and shearing tests were performed on 22 specimens and tensile strength and corrosion resistance tests on 6 triangle truss joints. The variables in these tests mainly include the insulating plate material, the thickness of the insulating plate, the vertical distance of the triangle truss framework, the triangle truss layout, and the connecting mode between the triangle truss and wall and the material of the triangle truss. Moreover, the failure mode, mechanical properties, and bearing capacity of the wall under tensile, shearing, and compression conditions were analyzed. Research results demonstrate that the concrete and insulating layer of the ICS-wall are pulling out, which is the main failure mode under tensile conditions. The ICS-wall, which uses a graphite polystyrene plate as the insulating layer, shows better tensile properties than the wall with an ordinary polystyrene plate. The tensile strength and bearing capacity of the wall can be improved effectively by strengthening the triangle truss connection and shortening the vertical distances of the triangle truss. The compression capacity of the wall is mainly determined by the compression capacity of concrete, and the bonding strength between the wall and the insulating plate is the main influencing factor of the shearing capacity of the wall. According to the tensile strength and corrosion resistance tests of Austenitic stainless steel, the bearing capacity of the triangle truss does not decrease after corrosion, indicating good corrosion resistance.