【学术预告】数学与统计学院学术预告三则

报告题目1：Discrete boundary value problems with the mean curvature operator

报 告 人：周展

报告时间：11月25日（周六）08:30开始

报告地点：数学楼315会议室

报告摘要：In this talk, we will introduce some results on the positive solutions for some nonlinear discrete Dirichlet boundary value problems with the mean curvature operator by using critical point theory. First, some sufficient conditions on the existence of infinitely many positive solutions are given. We show that, the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. Then, the existence of at least two positive solutions is established when the nonlinear term is not oscillatory both at the origin and at infinity. Examples are also given to illustrate our main results at last.

报告人简介：周展，博士、二级教授、博士生导师，教育部“长江学者和创新团队发展计划”创新团队带头人，享受国务院政府特殊津贴专家，广州市“优秀专家”，中国数学会理事。现任广州大学应用数学研究中心执行主任。先后主持长江学者和创新团队发展计划2项、国家自然科学基金7项、教育部优秀青年教师资助计划、高等学校博士点基金等科研项目多项。近年来在《J. Differential Equations》《J. Dynam. Diff. Eqn.》《J. Geom. Anal.》《Nonlinearity》《Physica D》和《中国科学》(英文版)等重要刊物发表高水平科研论文100多篇，先后获得广东省自然科学一等奖(第三)、湖南省科技进步一等奖(第五)、湖南省自然科学优秀论文一等奖、第五届“秦元勋数学奖”、广东省高等学校“千百十人才培养工程”第六批先进个人。

报告题目2：Dynamics of a reaction-diffusion dengue disease model with spatial heterogeneity and general incidence

报 告 人：赵洪涌

报告时间：11月25日（周六）10:30开始

报告地点：数学楼315会议室

报告摘要：In this talk,we formulate a reaction-diffusion dengue disease model with spatial heterogeneity and general incidence. The global existence and ultimate boundedness of solutions are discussed, and threshold dynamics of the model with respect to the basic reproduction numberR0 are analyzed. In the case where the model is spatially homogeneous, the global asymptotic stability of the endemic equilibrium is proved whenR0>1 by constructing a Lyapunov functional and employing the LaSalle’s invariance principle. Furthermore, we establish the asymptotic profiles and monotonicity ofR0 with respect to heterogeneous diffusion rates. Numerically, the proposed model is applied to dengue transmission. We analyze the sensitivity ofR0 to model parameters, and explore the impacts of temperature and diffusion rates onR0 and disease dynamics, which provide valuable information for formulating targeted measures for the dengue prevention and control.

报告人简介：赵洪涌,南京航空航天大学教授，博士生导师,九三学社社员。长期从事生物系统动力学、传染病动力学分析与控制、时滞微分方程动力学等研究。江苏省高校“青蓝工程”优秀青年骨干教师和中青年学术带头人。2014年至2022年，连续九年入选爱思唯尔中国高被引学者榜单。国家科技部重大项目和江苏省高校重大项目会评专家，国家自然科学基金和江苏省自然科学基金通讯评议专家；主持完成和在研国家自然科学基金四项。在国际SCI杂志上发表学术论文一百余篇，被SCI刊物引用二千余次。现为中国数学会生物数学专委会常务理事，江苏省生物数学学会副理事长。

报告题目3：Global dynamics of a stochastic SIRS epidemic model with Beddington-DeAngelis incidence rate

报 告 人：邱志鹏

报告时间：11月25日（周六）12:30开始

报告地点：数学楼315会议室

报告摘要：In this paper, a stochastic SIRS compartmental model is fomulated to investigate the transmission dynamics of infectious diseases. The model incorporates the Beddington-DeAngelis incidence rate and vaccination. For the deterministic model, the basic reproduction number R0 is derived, and the global dynamics is analyzed using the Lyapunov function in terms of R0. The results show that the basic reproduction number completely determines the global dynamics of the deterministic system. For the stochastic model, a new technique is adopted by introducing a Lyapunov exponent λ. Then, the persistence and extinction of infectious diseases are completely determined by λ. If λ < 0, then the disease will die out with probability one, while the epidemic becomes strongly stochastically permanent if λ > 0. To further substantiate ourfindings, numerical simulations are conducted to validate and extend the theoretical results.

报告人简介：邱志鹏，南京理工大学数学与统计学院教授、博士生导师、江阴校区基础教学与实验中心主任。主要从事常微分方程、动力系统与生物数学的研究工作，正在或完成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60余篇，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。