学术报告一

报告题目：传染病异质性接触的动力学建模与分析

报 告 人：靳祯 教授（山西大学）

负 责 人：王稳地 教授

报告时间：2024年12月14日（星期六）上午9:00-9:40

报告地点：数学大楼103报告厅

参加人员：教师、研究生、本科生

摘 要：群体水平传染病的传播大多数依赖于个体接触，但因为各种原因导致接触的异质性，传统的方法主要基于复杂网络度的来揭示异质性接触对传播的影响，其动力学模型是依赖于度的非线性方程组。本报告主要想把接触连续化思想，建立基于随机参数分布的动力学模型，在期望意义下导出了非线性动力学模型，进而给出模型的最终规模等。

个人简介：靳祯，山西大学二级教授。现任教育部重点实验室主任，山西省数学会理事长，享受国务院政府特殊津贴。主要从事生物动力系统研究，先后主持国家自然基金项目10 项，其中国家基金重点项目2 项。曾获山西省科学技术奖（自然科学类）一等奖2项，教育部高等学校优秀成果二等奖奖（自然科学类）1项。

学术报告二

报告题目：Multi-strain cholera transmission with hyperinfectious vibrios: mathematical modelling, analysis and data fitting

报 告 人：徐瑞 教授（山西大学）

负 责 人：王稳地 教授

报告时间：2024年12月14日（星期六）上午9:40-10:20

报告地点：数学大楼103报告厅

参加人员：教师、研究生、本科生

摘 要：In this talk, we consider a multi-strain cholera model with hyperinfectious and hypoinfectious vibrios. First, the basic reproduction number is calculated by using the next generation matrix method. Second, the global stability of the endemic equilibrium of the model is established by constructing suitable Lyapunov function and using LaSalle’s invariance principle. Accordingly, it is shown that the model exhibits threshold dynamics in terms of the basic reproduction number, which determines whether cholera becomes endemic or not. Finally, the model is used to fit the real disease situation of the 2017 cholera outbreak in Yemen. Based on parameters determined by data fitting, the vaccination strategies are studied by numerical simulation.

个人简介：徐 瑞，2005年英国Dundee大学数学生物学专业获哲学博士学位；现任山西大学复杂系统研究所教授、博士生导师。主要从事传染病动力学研究。担任Elsevier出版社SCI期刊Mathematics and Computers in Simulation编委。先后主持完成和在研国家自然科学基金面上项目5项；科学出版社出版学术专著5部；在国际学术期刊发表SCI论文100余篇。入选2021、2022和2023年爱思唯尔“中国高被引学者”榜单。

学术报告三

报告题目：Stochastic switches of eutrophication and oligotrophication: Modeling extreme weather via non-Gaussian Lévy noise

报 告 人：原三领 教授（上海理工大学）

负 责 人：王稳地 教授

报告时间：2024年12月14日（星期六）上午10:40-11:20

报告地点：数学大楼103报告厅

参加人员：教师、研究生、本科生

摘 要：Disturbances related to extreme weather events, such as hurricanes, heavy precipitation events and droughts, are important drivers of evolution processes of a shallow lake ecosystem. A non-Gaussian α-stable Lévy process is esteemed as the most suitable model to describe such extreme events. This paper incorporates extreme weather via α-stable Lévy noise into a parameterized lake model for phosphorus dynamics. We obtain the stationary probability density function of phosphorus concentration and examine the pivotal roles of α-stable Lévy noise on phosphorus dynamics. The switches between the oligotrophic state and the eutrophic state can be induced by the noise intensity σ, skewness parameter β or stability index α. We calculate the mean first passage time (MFPT), also referred to as the mean switching time, from the oligotrophic state to the eutrophic state. We observe that the increased noise intensity, skewness parameter or stability index makes the mean switching time shorter, and thus accelerates the switching process and facilitates lake eutrophication. When the frequency of extreme weather events exceeds a critical value, the intensity of extreme events becomes the most key factor for promoting lake eutrophication. As an application, we analyze the available data of Lake Taihu (2014--2018) for monthly precipitation, phosphorus and Chlorophyll-a concentrations, and quantify the linkage among them using the Lévy-stable distribution. This study provides a fundamental framework to uncover the impact of any extreme climate event on aquatic nutrient status.

个人简介：原三领，上海理工大学教授，博士生导师，中国数学会生物数学专业委员会副主任。研究方向为：微分方程与动力系统、生物数学。曾先后主持多项国家自然科学基金面上项目和上海市项目的研究工作。研究内容涉及微分方程与动力系统、种群动力学、流行病动力学、海洋生态学以及生物化学工程等诸多领域，具有多学科交叉的特点。曾多次受邀到国内和国际多所高校进行合作研究和学术交流，在SIAM Journal on Applied Mathematics、Journal of Mathematical Biology、Journal of Differential Equations等国内外重要学术刊物上发表SCI论文100余篇。

学术报告四

报告题目：Quasi-stationary distributions for absorbed diffusions driven by a class of Markov processes

报 告 人：邱志鹏 教授（南京理工大学）

负 责 人：王稳地 教授

报告时间：2024年12月14日（星期六）上午11:20-12:00

报告地点：数学大楼103报告厅

参加人员：教师、研究生、本科生

摘 要：The talk is devoted to present the transient dynamics of diffusion processes driven by a class of Markov processes, which is absorbed by the absorption set in finite time with probability one. Our primary concern is to analyze quasi-stationary distributions (QSDs) which characterize the long term behavior before absorption. Due to the irreversibility of the absorbed diffusion processes in this paper, probability methods are used to analyze the sub-Markovian semigroup generated by the absorbed diffusion processes. We provide the Lyapunov type criteria for the existence, uniqueness of the quasi-stationary distribution and show the exponential convergence to this QSD in the weighted total variation distance. Finally, the criteria is applied to stochastic ecological systems subject to both demographic and environmental stochasticity, and sufficient conditions are given for the existence, uniqueness and convergence of the quasi-stationary distribution. This work is jointed with Yu Zhu.

个人简介：邱志鹏，南京理工大学数学与统计学院教授、博士生导师。主要从事常微分方程、动力系统与生物数学的研究工作，主持国家自然科学基金4项，国家自然科学基金国际合作基金1项，教育部留学回国基金1项，参加国家自然科学基金面上项目2项和江苏省自然科学基金青年项目1项，目前已在Bull. Math. Biol., Math. Biosci., J. Diff. Equs., SIAM J. Appl. Math., J. Math. Biol., J. Theor. Biol.等期刊上发表论文多篇，曾先后访问过美国Purdue大学、Florida大学，意大利Trento大学、加拿大York大学和Alberta大学。