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Search Results: 1 - 10 of 13685 matches for " Yakui Xue "
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 Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.410A2011 Abstract: 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.
 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.
 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.
 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.
 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.
 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.
 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
 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.
 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.
 Journal of Materials Science and Chemical Engineering (MSCE) , 2015, DOI: 10.4236/msce.2015.312010 Abstract: 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 20。C 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 120。C, respectively.
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