| Title (题目): 随机环境种群系统 Speaker (报告人): 崔景安教授 北京建筑大学 Time (时间): 2016-04-16 (星期六) 8:30-9:10 Place (地点): 数学楼二楼报告厅 Abstract (摘要): We consider the effect of jump-diffusion random environmental perturbations on the permanence and extinction of a single-species dispersal periodic system in poor patchy environments with the possibility of species loss during their dispersion among patches. First, we prove that there is a unique global positive solution to the system with any initial positive value with probability 1, and we obtain the sufficient conditions that stochastically ensure the ultimate boundedness as well as the asymptotic polynomial growth of the population system. Next, we establish the sufficient conditions for the almost sure permanence in the mean, stochastic permanence, and extinction of the system. In particular, by constructing an appropriate integrating factor, we obtain the sufficient conditions for the almost sure weak permanence of the patch. The conditions obtained for permanence generalize the sufficient conditions established previously on the system without random environmental perturbations. Finally, we discuss the biological implications of the main results. Title (题目): 西尼罗河病毒扩散边沿及其基本再生数 Speaker (报告人): 林支桂教授 扬州大学 Time (时间): 2016-04-16 (星期六) 9:10-9:50 Place (地点): 数学楼二楼报告厅 Abstract (摘要): 我们用反应扩散方程组描述西尼罗河病毒的空间扩散，用自由边界表示病毒扩散的边沿。 为了检查空间特征对病毒扩散的影响，我们定义了四个基本再生数，分别对应于常微分方程组问题、具齐次Neumann问题，齐次Dirichlet问题和自由边界问题。 结果表明，在高风险区域，如果感染区域范围大或者扩散慢，病毒将蔓延；在低风险区域，小的初始感染病例，小的感染范围和大的扩散速率有利于病毒的消退。当病毒蔓延时我们证明了其空间扩散速度接近于一个常数。 Title (题目): Bogdanov-Takens Bifurcation of Codimension 3 in a Predator- Prey Model with Constant-Yield Predator Harvesting Speaker (报告人): 黄继才教授 华中师范大学 Time (时间): 2016-04-16 (星期六) 9:50-10:30 Place (地点): 数学楼二楼报告厅 Abstract (摘要): In this talk, we will give an analytical proof about the existence of Bogdanov-Takens bifurcation of codimension 3 in a predator-prey model with constant-yield predator harvesting, where the existence of a Bogdanov-Takens singularity (cusp) of codimension 3 was shown in (J. Huang, Y. Gong and S. Ruan, Discrete Contin. Dynam. Syst. B 18 (2013), 2101-2121). Numerical simulations of various bifurcation cases, including the existence of two limit cycles, the coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1, are presented to confirm the theoretical analysis. Title (题目): A discrete time analogue for coupling within-host and between-host dynamics in environmentally-driven infectious disease Speaker (报告人): 滕志东教授 新疆大学 Time (时间): 2016-04-16 (星期六) 10:50-11:30 Place (地点): 数学楼二楼报告厅 Abstract (摘要): In this talk, we propose a discrete time analogue for coupling within-host and between-host model in environmentally-driven infectious disease by using the nonstandard finite difference scheme. The model is divided into a fast time system and a slow time system by using the idea of limit equations. For the fast system, the positivity and boundedness of solutions, the basic reproduction number and the existence for infection-free and unique virus infectious equilibria are obtained, the threshold conditions on the local stability of equilibria are established. In the slow system, except for the positivity and boundedness of solutions, the existence for disease-free, unique endemic and two positive equilibria are obtained, the sufficient conditions on the local stability for disease-free and unique endemic equilibria are established. To return the coupling system, the local stability for the infection- and disease-free equilibrium, and virus infectious but disease-free equilibrium is established. The numerical examples show that a positive equilibrium is local stable and the other one is unstable when there are two positive equilibria. Title (题目): A nosocomial-pathogens-infections model with impulsive antibiotics treatment on multiple bacterias Speaker (报告人): 刘胜强教授 哈尔滨工业大学 Time (时间): 2016-04-16 (星期六) 14:00-14:40 Place (地点): 数学楼二楼报告厅 Abstract (摘要): A nosocomial-pathogens-infections model with impulsive antibiotics treatment on multiple bacteria and time-dependent drug efficacy is proposed in this paper. The purposes of this article are to investigate the efficacies of periodic input of antibiotic dosage on bacterial populations with impulsive drug effects and to preserve or restore antibiotic effectiveness. An impulsive system can be developed to describe the patients infected by the bacterial populations of both antibiotic-wild -type and antibiotic-resistant strains during the course of combination treatment. Two antibiotics are used to induce instantaneous antibiotic efficacies at fixed times and antibiotic concentrations decay exponentially. Using the theories of asymptotic periodic systems, uniform persistence theory of discrete dynamical systems and monotone dynamics, we establish sufficient conditions for treatment success as well as for treatment failure by using the basic reproduction ratio of periodic ompartment models. In particular, our results show that if any basic reproduction ratio for the patients infected by wild-type bacteria, resistant bacteria or those infected by both strains is larger than unity, then there will be persistent treatment failure for patients infected by resistant bacteria. This talk is based on a joint work with Dr Xia Wang and Dr Hongjian Guo. Title (题目): 一类交叉扩散传染病模型的分支结构及稳定性分析 Speaker (报告人): 王玮明教授 温州大学 Time (时间): 2016-04-16 (星期六) 14:40-15:20 Place (地点): 数学楼二楼报告厅 Abstract (摘要): 自从Shigesada等于1979年关于两竞争种群的交叉扩散系统的研究工作始, 交叉扩散系统得到了众多数学家和生物学家的广泛关注并取得了丰富的研究成果. 交错扩散的存在可使其常数稳态解失去原有的全局渐近稳定性, 产生非常数正稳态解. 在传染病模型中, 正稳态解(即地方病稳态解)具有十分重要的生物学意义, 从流行病学角度来看, 一个正解对应着易感者和感染者的共存稳态, 也就是说, 地方病的存在意味着疾病可能在整个区域上持续和蔓延. 因此对于传染病模型正稳态解的研究具有重要价值. 受Ducrot、Kuto以及李万同教授等工作的启示, 本报告将主要介绍我们近期关于空间异质性和交错扩散对传染病模型中地方病稳态解的影响机制的研究结果, 特别地, 将重点研究正稳态解的分支结构和渐近行为. Title (题目): 蚊媒传染病模型中的后向分支问题 Speaker (报告人): 万辉教授 南京师范大学 Time (时间): 2016-04-16 (星期六) 15:20-16:00 Place (地点): 数学楼二楼报告厅 Abstract (摘要): 蚊媒传染病是通过蚊子作为疾病的传播媒介, 将病原生物从宿主向人传播的疾病。主要蚊媒传染病有：疟疾、登革热、流行性乙型脑炎（乙脑）和西尼罗热等。我们在报告中将介绍几类不同蚊媒传染病的动力学模型，研究影响这些疾病传播的一些关键因素，并对这几类模型中出现的后向分支进行了分析。在某些参数条件下，相关模型都可能发生后向分支。而后向分支的发生，从传染病学角度看，有着重要含义。基本再生数小于1不再是控制疾病传播的阈值条件。疾病最终是否会流行与疾病流行的初始状态有着密切关系。对于疾病流行的初始状态人们需要给予更多关注。另外，后向分支还意味着，环境的细微改变，可能会带来疾病传播行为的根本变化。 Title (题目): 基于组合摄动的组合药物在疾病治疗中的应用 Speaker (报告人): 王瑞琦教授 上海大学 Time (时间): 2016-04-16 (星期六) 16:20-17:00 Place (地点): 数学楼二楼报告厅 Abstract (摘要): 组合药物在复杂疾病的治疗中发挥着重要的作用。该研究把疾病治疗中的组合药物转化为动力学中的摄动问题。 通过组合摄动对疾病系统动力学影响的研究，可以为组合药物的筛选以及优化的治疗策略提供理论支持。 | 