In this paper,we study a kind of the delayed SEIQR infectious disease model withthe quarantine and latent, and get the threshold value which determines the globaldynamics and the outcome of the disease. The model has a disease-free equilibriumwhich is unstable when the basic reproduction number is greater than unity.At thesame time, it has a unique endemic equilibrium when the basic reproduction numberis greater than unity. According to the mathematical dynamics analysis, we showthat disease-free equilibrium and endemic equilibrium are locallyasymptotically stable byusing Hurwitz criterion and they are globally asymptotically stable by using suitableLyapunov functions for any Besides,the SEIQR model with nonlinear incidence rate is studied, and thethat the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify theconclusions that will be useful for us to control the spread of infectious diseases.Meanwhile, thewill effect changing trends ofin system (1),which is obvious in simulations. Here, we takeas an example to explain that.

Vanadium titanium steel slag (VTSS)
containing transition metal can promote the adsorption of Hg^{0}. The method of
KBr and KI impregnation was applied to modify VTSS and the properties of the
adsorbents were tested. The Hg^{0} removal tests were carried out with a fixed bed
under different conditions. The results showed that the Hg^{0} 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.

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

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 R_{0} ≤ 1, there is only one disease-free equilibrium which is globally stable, the disease will die; if R_{0} > 1, there is only one endemic equilibrium which is globally stable, disease will be popular.

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.

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.

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.

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.

Abstract:
In this study, the magnetism and electronic structure of LaTiO$_3$ bilayers along both the ($001$) and ($111$) orientations are calculated using the density functional theory. The band insulator LaScO$_3$ is chosen as the barrier layer and substrate to obtain the isolating LaTiO$_3$ bilayer. For both the ($001$)- and ($111$)-oriented cases, LaTiO$_3$ demonstrates the G-type antiferromagnetism as the ground state, similar to the bulk material. However, the electronic structure is significantly changed. The occupied bands of Ti are much narrower in the ($111$) case, giving a nearly flat band. As a result, the exchange coupling between nearest-neighbor Ti ions are reformed in these superlattices, which will affect the N\'{e}el temperature significantly.

Abstract:
The solid-phase extraction and capillary gas chromatography was introduced for determining 13 organochlorine pesticide residues including alpha-benzene hexachloride (BHC), betaBHC, gamma-BHC, delta-BHC, p,p'-dichloro-diphenyl-dichloroethylene (pp'-DDE), p,p'-dichloro-di-phenyl-dichloroethane (pp'-DDD), o,p'-dichloro-diphenyl-trichloroethane (op'-DDT), pp'-DDT, heptachlor (HEPT), aldrin, heptachlor epoxide (HCE), dieldrin and endrin in Scutellaria baicalensis, Salvia miltiorrhiza, Belamcanda chinensis, Paeoniae lactiflora, Angelica dahurica, Arisaema erubescens, Fructus arctii, Anemarrhena asphodeloides and Platycodon grandiflorum. The organochlorine pesticides were extracted from herbs with mixed solvents of acetone and n-hexane by ultrasonic and cleaned up by Florisil solid-phase extraction column. Then, the extract was separated by capillary column (30 m x 0.25 mm i.d. x 0.25 microm) and detected by electrochemical detector. The carrier gas was N2 (99.999%) with the flow rate of 1.4 mL/min. The split ratio was 1:2.2. The injector temperature was 220 degrees C and the detector temperature was 330 degrees C. The column temperature was increased by the rate of 20 degrees C/min from 100 degrees C to 190 degrees C (hold for 1. 0 min), then to 235 degrees C by the rate of 4 degrees C/min and hold for 7 min at 235 degrees C. The good linearities were obtained for 13 organochlorine pesticides. The detection limits were between 0.064-0.61 microg/L. The average recoveries were between 87.3%-102.3% and relative standard deviations of 1.3%-6.8%. The method is effective, fast and accurate.