创新企业种群成长动力学分析

以生物系统中种群动力学为主要理论依据,开发了创新种群成长动力学模型.方程组推导结果表明:创新种群的成长过程中存在一定的均衡条件.科研种群是创新创群的主要互动种群.创新种群和科研种群之间存在显著地激励机制,两类种群对创新资源的占用存在一定的比例关系.创新种群的增长收到多种环境因素的影响,政府部门、服务机构、科研种群的影响均不同.创新种群的总量平衡点受总体环境制约.创新种群的增量平衡点主要受科研种群影响.     

一类食物链模型的全局定性分析

文系统地研究了由一个食饵种群和两个捕食者种群所构成的食物链系统.结论表明：种群间的相互作用可以导致两个捕食者种群灭绝或一个捕食者种群灭绝,或者所有三个种群能以稳定的正平衡态或振动解的形式共存.利用MATLAB软件,该文提供了两个例子来模拟这些结论.     

马尔可夫骨架过程在种群动态学中的应用

本文借助于马尔可夫骨架过程（舱妒）方法研究了种群动态学中单种群种群数量的瞬时分布，并证明单种群种群数量在时刻t的瞬时分布是某一非负线性方程的最小非负解。     

基于年龄结构的种群系统的最优收获控制

研究一类带年龄结构的非线性种群系统的最优收获问题.建立单种群阶段结构模型,对成年、幼年种群同时捕获,得到了单种群阶段结构模型在正平衡点渐近稳定的充分条件;并给出了脉冲控制时间间隔的上界估计值.分别对其幼年种群和成年种群捕获问题,给出以最大捕获可持续均衡收获(M SY)为目标的最优捕获策略.     

脉冲输入毒素对具有阶段结构的单种群生存影响的研究

研究了一类小容量污染环境中脉冲输入毒素对具有阶段结构的单种群生存问题,分别找到了种群生存与灭绝的阈值,利用不等式放缩技巧,得到了种群灭绝和持久生存的充分条件.利用MATLAB数值仿真,验证了理论结果的正确性,分析了毒素输入量,毒素输入周期及种群成长时间对种群生存的影响.     

基于独立性的组织种群共生演化稳定性比较研究

运用Logistic模型对存在依存关系但相互独立性不同的组织种群共生演化稳定性进行了研究.发现种群独立性和种群间相互贡献度将对组织种群的共生稳定性将产生影响.     

污染环境中的非自治种群模型的生存分析

研究了环境污染对种群的长期影响.考虑到新生个体的出生对种群体内毒素的影响,以及死亡的种群个体将体内毒素带回环境,建立了一个非自治数学模型.主要运用比较定理得到了种群一致持续生存、弱持续生存以及绝灭的判据.     

污染环境中的Leslie系统

研究了环境污染对Leslie资源-消费者系统中消费者种群的长期影响．考虑到种群数量的变化对种群体内毒素浓度和环境毒素浓度的影响,建立了一个新的数学模型, 给出了消费者种群弱持续生存和绝灭的判据,并在一定条件下得到了弱持续生存与绝灭的阈值．     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

一类捕食者具有阶段结构的捕食——被捕食模型的全局性态分析

在假设捕食的受益是减少死亡下,建立了一类捕食种群具有阶段结构的捕食-被捕食模型,分析得到了不存在食饵种群情形下捕食者种群模型和食饵存在时捕食-被捕食模型的平衡点存在性和全局稳定性,并确定了决定模型动力学性态的捕食者种群基本再生数、捕食存在时的食饵种群净增长率以及食饵灭绝与否的捕食率阈值.     

Stability and periodic solutions for a model of bacterial resistance to antibiotics caused by mutations and plasmids

Bacterial resistance is one of the most prominent public health problems affecting the entire world population. Although some infectious diseases are no longer a problem as they were in the past, the acquisition of bacterial resistance continues to increase. In particular, antibiotics have been losing their effectiveness after decades of misuse and overuse, which has generated an emergency situation. In this work, we formulate and analyse a deterministic model for the population dynamics of susceptible and resistant bacteria to antibiotics, assuming that drug resistance is acquired through mutations and plasmid transmission. Qualitative analysis reveals the existence of a bacteria-free equilibrium, a resistant bacteria equilibrium, an a coexistence equilibrium and a limit cycle arising from Hopf bifurcation. The stability of the equilibria are given in terms of the growth rate of bacteria, the acquisition of resistance, as well as the elimination of bacteria due to the immune system and the action of antibiotics. Numerical simulations corroborate our analytical results, and illustrate the temporal dynamics of the susceptible and resistant bacteria.     

Mathematical analysis of a three-strain tuberculosis transmission model

In recent years, bacteria have become resistant to antibiotics, leading to a decline in the effectiveness of antibiotics in treating infectious diseases. A mathematical model for multi-strain tuberculosis transmission dynamics to assess the burden of drug-sensitive, multidrug-resistant and extensively drug-resistant tuberculosis is formulated and analyzed. Each single strain submodel is shown to exhibit backward bifurcation when the threshold parameter is less than unity. Both analytical and numerical results show that resistance to drugs increase with increase in drug use, that is, active tuberculosis treatment results in a reduction of drug sensitive and increase in multidrug-resistant tuberculosis. Furthermore, use of second line drugs results in a decrease of the multidrug-resistant and increase of extensively drug resistant tuberculosis as most cases of multidrug resistant tuberculosis occur as a result of inappropriate, misuse or mismanaged treatment. Both the analytic results and numerical simulations suggest that quarantine of extensively drug resistant TB cases in addition to treatment of other forms of TB may be able to reduce the spread of the epidemic in poor resource-settings.     

ECONOMIC MODELING OF THE PERSISTENCE OF ANTIMICROBIAL RESISTANCE

Abstract According to the dynamic relationship between antibiotic use and the incidence of multidrug‐resistant bacteria, the effectiveness of antibiotics is characterized as a natural resource exploited by antibiotic use. A major question is whether antibiotic effectiveness should be considered a renewable or an exhaustible resource. This paper presents a model combining epidemiological aspects of the decrease of resistance over time with an economic approach, modeling antimicrobial resistance as a negative externality of antibiotic use. The article concludes that the relative fitness of resistant bacteria is one driving factor for an estimation of the externality. If we, for instance, assume a low degree of relative fitness of resistant bacteria it is shown that resistance decreases fastest directly after antibiotic treatment. Accordingly, cycling of nonidentical drugs improves antibiotic effectiveness because cycling lowers the frequency of use of the individual antibiotic. In this case, antibiotic effectiveness must be characterized as a renewable resource in much the same way as a stock of fish in a lake. In contrast, if we assume a high degree of relative fitness of resistant bacteria, antibiotic effectiveness must be treated as an exhaustible resource because it is declined by every use of antibiotics.     

Conceptual Representations of Flu and Microbial Illness Held by Students,Teachers, and Medical Professionals

This study describes 5 th, 8th, and 11th‐grade students', teachers', and medical professionals' conceptions of flu and microbial illness. Participants constructed a concept map on “flu” and participated in a semi‐structured interview. The results showed that these groups of students, teachers and medical professionals held and structured their conceptions about microbes differently. A progression toward more accurate and complete knowledge existed across the groups but this trajectory was not always a predictable, linear developmental path from novice to expert. Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses. This knowledge was tightly linked to participants' prior experiences with colds and flu. There were typically large gaps in participants' (children and teachers) understandings of vaccines, immune system responses, treatments (including the mechanisms of pain medications and the functions of antibiotics), and transmission of non‐respiratory microbial illness. A common misconception held by students was the belief that antibiotics can cure viral infections.     

Modelling and solving fixed-bed adsorption

In this paper we develop a mathematical model for packed-bed adsorption of a single component, directed toward the purification of β-lactamic antibiotics. The model describes the removal of sorbates from an aqueous stream entering a bed packed with spherical sorbent particles. Then, assuming that the adsorption isotherm is linear, an exact solution for this model is found.     

Modeling basic aspects of bacterial resistance of <Emphasis Type="Italic">Mycobacterium tuberculosis</Emphasis> to antibiotics

In this work we study the effect of antibiotics treatment and the immune system in the development of Mycobacterium tuberculosis infection through the formulation and analysis of a nonlinear system of ordinary differential equations. The results are given in terms of forward and backward bifurcation and they reveal the importance of combining a suitable treatment with a good stimulation of the immune system.     

Announcing the Burtin graphic contest winners

The graphics contest announced in Volume 23, Issue 4, of CHANCE asked readers to create a display of a 1951 data set on antibiotic effectiveness. The three winners of the contest are Mark Nicolich, Brian Schmotzer, and Dibyojyoti Haldar. The winners’ graphs are different, yet communicate the same information—each compares the antibiotics and bacteria and succinctly summarizes the influence of the gram staining factor.     

Mathematical analysis of a model describing the number of antibiotic resistant bacteria in a polluted river

In France, 90% of surface water suffer from antibiotic pollution that increases the number of antibiotic resistant bacteria. The first indicator of water quality is revealed by the fish quality. According to the Le Conseil Supérieur de la Pêche, only 15% of rivers in France are considered in good condition, whereas 22% are in very bad condition. The bacterial resistance to antibiotics is a public health problem as it affects humans through drinking water; the treatment of water is costly. Mathematical modeling may estimate and predict the quantity of bacteria in rivers. In this paper, we investigate properties of the mathematical model estimating the number of bacteria in a river presented by Lawrence, Mummert and Somerville. Global analysis of equilibria is presented, using a Lyapunov function. Moreover, the existence of positive periodic solutions is proven. Copyright © 2013 John Wiley & Sons, Ltd.     

基于分层贝叶斯时空模型的雾霾天气过程计数分析

本文以北京市8个行政区(东城区、西城区、石景山区、海淀区、朝阳区、昌平区、顺义区、怀柔区)的PM2.5指数计算各区逐月雾霞天气过程计数频数为研究对象,选择考虑包括地表温度、相对湿度、平均风速、SO_2质量浓度和NO_2质量浓度在内的5个影响因素。本文定义雾霾天气过程,构建分层贝叶斯时空模型,在一个统计模型中对诸多影响因素进行分析,并从计数分析的角度对北京市雾霾天气现象的时空分布、影响因素进行深入讨论。通过分析得出,温度、湿度、污染物浓度对于雾霾天气过程发生具有促进作用,平均风速对于雾霾天气过程发生具有抑制作用。从时空角度分析,从时间维度上看雾霾天气过程的发生具有明显的季节性特征,冬季(1月、2月)以及3月雾霾天气过程发生次数最高,春季(4月、5月)发生次数最低,秋季发生次数略高于夏季。从空间维度上来看,中心城区(东城区、西城区、石景山、海淀区、朝阳区)雾霾天气过程发生次数明显高于郊区(顺义、昌平、怀柔),以东城区、西城区和朝阳区最为严重。