报告题目1：State feedback impulsive therapy to SIS model of animal infectious diseases

报告人：陈兰荪，研究员

报告时间：2019年4月22日（周一）8:00—10:00   

报告地点：威廉希尔学术报告厅

摘要： Controlling animal infectious diseases and its related infra microbes is of great significance to public health, since a lot of infectious diseases originate from animal epidemics and they often threaten human health. A state feedback impulsive model is constructed to depict the transmission and treatment of animal epidemics. Basing on the impulsive model, the existence of order-1 periodic solution and its stability are proved with a novel method. The theoretical results indicate that the impulsive treatment triggered by the number of infectious is an efficient approach to control animal infectious disease from breakout. Numerical simulation is presented to support the theoretical conclusion in the end.

报告题目2： State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate

报告人：陈兰荪，研究员

报告时间：2019年4月24日（周三）9:00—11:00   

报告地点：威廉希尔学术报告厅

摘要： The state-dependent pulse vaccination and therapeutic strategy are considered in the control of the disease. A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. /en for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a

unique order-1 homoclinic cycle, and by choosing p as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when p changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.

专家简介：陈兰荪，中国科学院数学与系统科学研究院数学研究所研究员, 博士生导师，中国数学会生物数学学会原理事长，国家有突出贡献专家，获政府特殊津贴。国际学术期刊 《International Journal of Biomathematics》(SCI检索)、《Communications in Mathematical Biology and Neuroscience》、《生物数学学报》等杂志主编。 《系统科学与数学》、《Differential Equations and Dynamical Systems》、《Journal of Biological Systems》、《应用生态学报》、《数学研究与评论》、《微分方程年刊》等刊物的常务编委或编委。早年从事常微分方程定性理论研究，在1979年得到“二次微分系统至少存在四个极限环”的结果，指出了前苏联著名数学家莫斯科大学董事长彼得罗夫斯基院士的“二次微分系统至多有三个极限环” 的结论是错误的，此结果在1980年获江苏省科技进步一等奖， 被许多国内、外专著所引用。从20世纪的 80 年代初开始从事生物数学研究，作为我国生物数学研究的开创者与组织者，组织了多次国际国内生物数学重要会议。在数员工态学模型、分子作用动力学模型以及传染病数学模型等方面有多的研究工作。在国内外刊物上发表论文 440 多篇，其中 300 多篇被SCI 检索，被 SCI 杂志总共引用次数为 2000 多次，单篇最高引用率 220 多次。撰写和主编了十余本专著和论文集，分别由世界科学出版社，科学出版社，美国数学会，四川科学技术出版社，四川教育出版社，美国数学理科学院研究所出版。

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2019年4月16日