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Search Results: 1 - 10 of 13682 matches for " Yakui Xue "
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Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent  [PDF]
Tiantian Li, Yakui Xue
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.410A2011

In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any \"\" Besides, the SEIQR model with nonlinear incidence rate is studied, and the \"\" that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the \"\" will effect changing trends of \"\"\"\" in system (1), which is obvious in simulations. Here, we take \"\" as an example to explain that.

The Stability of Highly Pathogenic Avian Influenza Epidemic Model with Saturated Contact Rate  [PDF]
Shuqin Che, Yakui Xue, Likang Ma
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.521313
Abstract: In this paper we present a highly pathogenic Avian influenza epidemic model with saturated contact rate. According to study of the dynamics, we calculated the basic reproduction number of the model. Through the analysis of this model, we have the following conclusion: if R0 ≤ 1, there is only one disease-free equilibrium which is globally stable, the disease will die; if R0 > 1, there is only one endemic equilibrium which is globally stable, disease will be popular.
Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
Yakui Xue,Junfeng Wang
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/647853
Abstract: An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay
Yakui Xue,Xiaoqing Wang
Discrete Dynamics in Nature and Society , 2012, DOI: 10.1155/2012/252437
Abstract: A predator-prey system with disease in the predator is investigated, where the discrete delay is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when crosses some critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.
The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays
Yakui Xue,Xiafeng Duan
Discrete Dynamics in Nature and Society , 2011, DOI: 10.1155/2011/509871
Abstract: We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.
Global Stability of a SLIT TB Model with Staged Progression
Yakui Xue,Xiaohong Wang
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/571469
Abstract: Because the latent period and the infectious period of tuberculosis (TB) are very long, it is not reasonable to consider the time as constant. So this paper formulates a mathematical model that divides the latent period and the infectious period into n-stages. For a general n-stage stage progression (SP) model with bilinear incidence, we analyze its dynamic behavior. First, we give the basic reproduction number . Moreover, if , the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If , the unique endemic equilibrium is globally asymptotically stable and the disease persists at the endemic equilibrium.
The Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence
Juping Zhang,Zhen Jin,Yakui Xue,Youwen Li
Discrete Dynamics in Nature and Society , 2009, DOI: 10.1155/2009/490437
Abstract: An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number ??? is defined. It is proved that the infection-free periodic solution is global asymptotically stable if ???<1. The infection-free periodic solution is unstable and the disease is uniform persistent if ???>1. Our theoretical results are confirmed by numerical simulations. 1. Introduction Every year billions of population suffer or die of various infectious disease. Mathematical models have become important tools in analyzing the spread and control of infectious diseases. Differential equation models have been used to study the dynamics of many diseases in wild animal population. Birth is one of the very important dynamic factors. Many models have invariably assumed that the host animals are born throughout the year, whereas it is often the case that births are seasonal or occur in regular pulse, such as the blue whale, polar bear, Orinoco crocodile, Yangtse alligator, and Giant panda. The dynamic factors of the population usually impact the spread of epidemic. Therefore, it is more reasonable to describe the natural phenomenon by means of the impulsive differential equation [1, 2]. Roberts and Kao established an SI epidemic model with pulse birth, and they found the periodic solutions and determined the criteria for their stability [3]. In view of animal life histories which exhibit enormous diversity, some authors studied the model with stage structure and pulse birth for the dynamics in some species [4–6]. Vaccination is an effective way to control the transmission of a disease. Mathematical modeling can contribute to the design and assessment of the vaccination strategies. Many infectious diseases always take on strongly infectivity during a period of the year; therefore, seasonal preventing is an effective and practicable way to control infectious disease [7]. Nokes and Swinton studied the control of childhood viral infections by pulse vaccination [8]. Jin studied the global stability of the disease-free periodic solution for SIR and SIRS models with pulse vaccination [9]. Stone et al. presented a theoretical examination of the pulse vaccination policy in the SIR epidemic model [10]. They found a disease-free periodic solution and studied the local stability of this solution. Fuhrman et al. studied asymptotic behavior of an SI epidemic model with pulse removal [11]. d'Onofrio studied the use of pulse vaccination strategy to eradicate infectious disease for SIR and SEIR epidemic models [12–15]. Shi
Complex dynamics of a Holling-type IV predator-prey model
Lei Zhang,Weiming Wang,Yakui Xue,Zhen Jin
Quantitative Biology , 2008,
Abstract: In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation in the spatial domain. Based on the stability and bifurcation analysis, we obtain spiral pattern formation via numerical simulation. Additionally, we study the model with colored noise and external periodic forcing. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species, and resonant response. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics.
Spatiotemporal pattern formation of Beddington-DeAngelis-type predator-prey model
Weiming Wang,Lei Zhang,Yakui Xue,Zhen Jin
Quantitative Biology , 2008,
Abstract: In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we give the spatial pattern formation via numerical simulation, i.e., the evolution process of the model near the coexistence equilibrium point. We find that for the model we consider, pure Turing instability gives birth to the spotted pattern, pure Hopf instability gives birth to the spiral wave pattern, and both Hopf and Turing instability give birth to stripe-like pattern. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
Removal Hg0 from Flue Gas with Modified VTSS by KBr and KI  [PDF]
Yingjie Shi, Yakui Li
Journal of Materials Science and Chemical Engineering (MSCE) , 2015, DOI: 10.4236/msce.2015.312010

Vanadium titanium steel slag (VTSS) containing transition metal can promote the adsorption of Hg0. The method of KBr and KI impregnation was applied to modify VTSS and the properties of the adsorbents were tested. The Hg0 removal tests were carried out with a fixed bed under different conditions. The results showed that the Hg0 adsorption capacity increase with the increasing temperature. The efficiency was highest with KI(3)/VTSS at 20C and adsorption capacity was 163.4 ug/g after 3 h. The highest Hg0 removal efficiency were 90.6% for KI(3)/VTSS, 73.5% for KBr(10)/VTSS/ VTSS at 120C, respectively.

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