Geometric approach to global asymptotic stability for the SEIRS models in epidemiology

In this paper, we present a more general criterion for the global asymptotic stability of equilibria for nonlinear autonomous differential equations based on the geometric criterion developed by Li and Muldowney. By applying this criterion, we obtain some results for the global asymptotic stability of SEIRS models with constant recruitment and varying total population size. Based on these results, we give a complete affirmative answer to Liu–Hethcote–Levin conjecture. Furthermore, an affirmative answer to Li–Graef–Wang–Karsai’s problem for SEIR model with permanent immunity and varying total population size is given.     

A Direct Experimental Evidence of Collective Electron Resonance Mechanism of Surface Enhanced Infrared Spectroscopy (Seirs)

Abstract

We report here the preliminary results of the surface enhanced transmission infrared spectra of CH₃(CH₂)₇Azo(CH₂)₃COOH monolayers on CaF₂ substrate which was coated by silver island films with different size and distribution. The larger enhancement of absorbance of v(C=O) in COOH residing between silver island gap and small enhancement of absorbance of vibration mode of COO^? located on the silver islands are observed. It give us a direct experimental evidence of the collective electron resonance mechanism of surface enhance infrared spectroscopy (SEIRS), i.e. the decrease of the electromagnetic (EM) coupling reduces the enhancement factor of SEIRS.     

Global dynamics of a class of SEIRS epidemic models in a periodic environment

In this paper, we study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number R₀ which is defined through the spectral radius of a linear integral operator. If R₀<1, then the disease free periodic solution is globally asymptotically stable and if R₀>1, then the disease persists. Our results really improve the results in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology Bull. Math. Biol. 69 (8) (2007) 2537-2559] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given.     

Analysis of an Age Structured SEIRS Epidemic Model with Varying Total Population Size and Vaccination

This article focuses on the study of an age structured SEIRS epidemic model with a vaccinationprogram when the total population size is not kept at constant.We first give the explicit expression of thereproduction number R(ψ,(?)) in the presence of vaccine ((?) is the exponent of growth of total population),andshow that the infection-free steady state is linearly stable if R(ψ,(?))<1 and unstable if R(ψ,(?))>1,then weapply the theoretical results to vaccination policies to determine the optimal age or ages at which an individualshould be vaccinated.It is shown that the optimal strategy can be either one- or two-age strategies.     

基于随机与异质网络共存的SEIRS传染病模型

讨论了随机与异质网络共存的SEIRS传染病模型,通过正平衡点的存在性给出基本再生数R_0=((1-η)Aλ+ηβ)/μ.结果表明,当R_01时,无病平衡点(1,0,0,0)局部稳定;当R_01时,无病平衡点(1,0,0,0)不稳定,此时系统存在唯一的地方病平衡点,并且一致持续存在.最后通过数值仿真,验证了理论结果的正确性.     

基于SEIRS的建设工程质量风险传递模型及仿真研究

工程建设过程、从业人员专业水平和信息存在较为突出的碎片化现象,导致了工程质量风险的传递。为揭示平行承发包模式下建设工程质量风险的传递效应和放大效应,利用传染病模型中的动力学原理,综合考虑工程质量风险传递的影响因素,构建了SEIRS的建设工程质量风险传递模型。仿真研究结果表明,建设工程在质量风险传递过程中存在阈值;质量风险传递阈值h1时,在质量风险传递阻碍因素的作用下,风险逐步衰减直至消失;质量风险传递阈值h<1时,在质量风险传递促进因素的作用下,风险会稳定存在于建设工程中,甚至危害工程的整体质量。研究结论为政府实现由直接监管向间接监管、由事前监管向事中事后监管的转变等提供理论支撑。     

一类SEIRS型流行病的细胞自动机模型

本文通过分析SEIRS类流行病，建立了该类疾病的二维概率细胞自动机模型。在二维中，每个细胞的状态代表易感者，潜伏者，患者，恢复者（或免疫者）和死亡者五个部分个体之一。我们研究了两种情况下，即对潜伏者和患者隔离与不隔离将对疾病转播的影响。经研究我们发现，如果不隔离疾病将持续流行，而及时的隔离则将会减缓疾病的流行。本模型给出了对具体疾病利用细胞自动进行仿真的算法。我们发现当恢复者的失去免疫力大于时，疾病潜伏者和患者的密度序列将在正平衡点附近振荡。最后，我们用计算机对模型进行了仿真。     

SEIRS型传染病模型的全局稳定性

In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.     

On Some SEIRS Epidemic Models

We discuss a few variations of the SEIRS epidemic model. How basic dynamical properties of the models can be derived by using some tools of the computer algebra system Mathematica is shown, and how invariant surfaces of the system can be found by using computer algebra system Singular is explained. Some numerical simulations are presented as well.