Effect of partial immunity on transmission dynamics of dengue disease with optimal control

Dengue fever is one of the most dangerous vector‐borne diseases in the world in terms of death and economic cost. Hence, the modeling of dengue fever is of great significance to understand the dynamics of dengue. In this paper, we extend dengue disease transmission models by including transmit vaccinated class, in which a portion of recovered individual loses immunity and moves to the susceptibles with limited immunity and hence a less transmission probability. We obtain the threshold dynamics governed by the basic reproduction number R₀; it is shown that the disease‐free equilibrium is locally asymptotically stable if R₀ ≤ 1, and the system is uniformly persistence if R₀ > 1. We do sensitivity analysis in order to identify the key factors that greatly affect the dengue infection, and the partial rank correlation coefficient (PRCC) values for R₀ shows that the bitting rate is the most effective in lowering dengue new infections, and moreover, control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the public are highly suggested to control population size of mosquitoes and to use mosquito nets. By formulating the control objective, associated with the low infection and costs, we propose an optimal control question. By the application of optimal control theory, we analyze the existence of optimal control and obtain necessary conditions for optimal controls. Numerical simulations are carried out to show the effectiveness of control strategies; these simulations recommended that control measures such as protection from mosquito bites and mosquito eradication strategies effectively control and eradicate the dengue infections during the whole epidemic.     

ICF内爆靶丸能流分布三维数值仿真

针对惯性约束聚变(ICF)两区均匀模型中靶丸表面能流分布问题,采用三维离散视角因子方法进行模拟仿真。对辐照过程中出现腔壁自身遮挡的面元,利用四叉树结构进行快速剔除;实现了GPU上的靶丸能流分布的并行计算。基于该方法开发的三维仿真软件IRAD3D 1.0,其有效性通过与解析解的对比得到了验证。不同算例模型的仿真结果表明了软件具有通用性、高效性,给出了靶丸均匀性分析的应用实例。     

用PC机代替打点计时器计时

在匀变速直线运动的实验中，利用PC机的串行接口来记录运动小车通过测量点的时刻值，以此代替打点计时器计时。     

Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

Lipschitz局部严格伪压缩映象的迭代逼近

设Ｋ是一致光滑Ｂａｎａｃｈ空间Ｋ的非空子集，Ｔ：Ｋ→Ｘ是Ｌｉｐｓｃｈｉｔｚ局部严格伪压缩映象。本文给出一个迭代序列强收敛到Ｔ的唯一不动点，并给出一个涉及Ｌｉｐｓｃｈｉｔｚ局部强增殖映象Ｔ的非线性方程Ｔｘ＝ｆ的解的迭代逼近。     

空间l1(Xn)中的弱紧性

本文首先讨论空间l₁(X_n)中的弱收敛性，然后给出了l₁(X_n)中弱紧性的几种等价刻画，同时对l_p(X_n)（１＜ｐ＜∞）中的弱紧性也得到了类似的结果．     

Banach空间X的弱局部Zk性质

本文引入了Ｂａｎａｃｊ空间Ｘ的弱局部Ｚ_k性质和弱Ｚ_k性质，得出了：Ｂａｎａｃｈ空间Ｘ是Ｋ－ＮＵＣ空间的一个充分必要条件和Ｂａｎａｃｈ空间Ｘ是ＬＫ－ＮＵＣ空间的一个充分条件，并指出弱Ｚ_k性质蕴含弱Ｂａｎａｃｈ－Ｓａｋｓ性质．     

Strong convergence of projection-like methods in Hilbert spaces

Many mathematical and applied problems can be reduced to finding a common point of a system of convex sets. The aim of this paper is twofold: first, to present a unified framework for the study of all the projection-like methods, both parallel and serial (chaotic, mostremote set, cyclic order, barycentric, extrapolated, etc.); second, to establish strong convergence results for quite general sets of constraints (generalized Slater, generalized uniformly convex, made of affine varieties, complementary, etc.). This is done by introducing the concept of regular family. We proceed as follows: first, we present definitions, assumptions, theorems, and conclusions; thereafter, we prove them.     

认购证发行总数的估计

利用发行的认购证有编号１，２，……，Ｎ，，本文通过随机抽取的几个认购证号码，给出了认购证发行总数的最大似然估计，一致最小方差无偏估计和Ｂａｙｅｓ估计。