Global stability properties of age‐dependent epidemic models with varying rates of recurrence

The purpose of this paper is to study the global stability properties of equilibria for age‐dependent epidemiological models in presence of recurrence phenomenon. In these systems, the recurrence rate depends on asymptomatic–infection–age. The models are appropriate for human herpes virus (HSV‐1 and HSV‐2) and varicella‐zoster virus. We derived explicit formulas for the basic reproductive number, which completely characterizes the global behaviour of solutions to the models: if the basic reproductive number is less than or equal to unity, the disease will die out; if the basic reproductive number is greater than unity, the disease will be persistent. Volterra‐type Lyapunov functions are constructed to establish the global asymptotic stability of the infection‐free and endemic steady states. Copyright © 2015 John Wiley & Sons, Ltd.     

Lumineszenzdatierung quartärer Sedimente

The purpose of this paper is to discuss briefly the basis, technique and efficiency of luminescence dating. Thermoluminescence and optically-stimulated luminescence are useful for dating of quaternary sediments. Contents: Sediment Dating, Thermoluminescence Dating, Thermoluminescence (TL), Dating Method, Sources of Error, Dosimetry, Dating Techniques, Optical Dating (OSL), Sediments, References.     

A stochastic model for a general load‐sharing system under overload condition

A load‐sharing parallel system functions if at least one unit in the system is functioning and the surviving units share the load. In most of research on load‐sharing system, the performance of the system has been studied only for the case when the lifetimes of components in the system follow exponential distributions. In this paper a load‐sharing parallel system is considered when the lifetimes of the units in the system are any continuous random variables. The reliability function of the system is derived and the problem of load allocation is also considered. Copyright © 2009 John Wiley & Sons, Ltd.     

基于游客年龄特征的旅游巴士定价研究

为旅游巴士设计合理的定价,对旅游公共交通的发展有着积极影响。通过对游客出行偏好的分析,考虑不同年龄阶段的游客在选择行为上有较大的差异,建立了上层以旅游巴士企业利润最大为目标,下层为多方式多人群弹性需求随机用户平衡的旅游巴士定价模型,并设计了改进粒子群算法求解问题。数值实验结果表明:1)年龄特征会影响最优定价策略,考虑游客年龄在选择行为上的差异得出的票价更优;2)舒适度敏感系数对定价有影响,且旅游巴士较常规公交,舒适度更好,一定程度上提高了旅游巴士企业的竞争力;3)改进粒子群算法较标准粒子群算法,有更好的求解性能和质量。     

Promoting number theory in high schools or birthday problem and number theory

The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges.     

Clustering with a constraining variable

Clustering can be treated as an optimization problem over a set of feasible clusterings. This paper deals with a clustering problem where the set of feasible clusterings is determined by constraining the function of values of a given (constraining) variable in each cluster. It can be shown that agglomerative clustering methods are not suitable for solving problems with constraining variables. For solving clustering problems of this type, local optimization procedures can be adapted. In the study of the influence of constraints on the clustering, a special coefficient is defined. The proposed procedures of clustering with constraining variables are illustrated by clustering the Slovene communes on the basis of the socioeconomic indicators.     

Dynamics of an age‐structured host‐vector model for malaria transmission

In this paper, we propose a host‐vector model for malaria transmission by incorporating infection age in the infected host population and nonlinear incidence for transmission from infectious vectors to susceptible hosts. One novelty of the model is that the recovered hosts only have temporary immunity and another is that successfully recovered infected hosts may become susceptible immediately. Firstly, the existence and local stability of equilibria is studied. Secondly, rigorous mathematical analyses on technical materials and necessary arguments, including asymptotic smoothness and uniform persistence of the system, are given. Thirdly, by applying the fluctuation lemma and the approach of Lyapunov functionals, the threshold dynamics of the model for a special case were established. Roughly speaking, the disease‐free equilibrium is globally asymptotically stable when the basic reproduction number is less than one and otherwise the endemic equilibrium is globally asymptotically stable when no reinfection occurs. It is shown that the infection age and nonlinear incidence not only impact on the basic reproduction number but also could affect the values of the endemic steady state. Numerical simulations were performed to support the theoretical results.     

Theory and approximation of solutions to a harvested Hierarchical age-structured population model

This article is concerned with theoretic analysis and numerical approximation of solutions to a hierarchical age-structured population model, in which the vital rates of an individual depend more on the number of older individuals. The well-posedness of the model is rigorously treated by means of fixed point principle, and an algorithm and convergence analysis are presented. An example is used to show the effectiveness of the numerical method.