微分方程与动力系统研讨会

微分方程与动力系统研讨会

报告时间：2024年11月16日（星期六）

活动地点： 南校区会议中心121会议室

报告题目1：Steady-state bifurcation and spike pattern in the Klausmeier-Gray-Scott model with non-diffusive plants

报告人：蒋卫华 教授 哈尔滨工业大学

报告摘要: We first established the critical conditions for instability of the constant steady state in general coupled ODE-PDE activator-inhibitor systems. In addition, the local structure of the nonconstant steady state and the condition to determine the local bifurcation direction were obtained. Secondly, for the Klausmeier-Gray-Scott model with non-diffusive plants, the steady-state bifurcation was subcritical and the nonconstant steady-state bifurcation solutions were unstable. Finally, we investigated the spatial pattern of the model with slowly diffusive plants to understand the formation of the spike pattern of the model with non-diffusive plants.

个人简介：蒋卫华,哈尔滨工业大学长聘教授，博士生导师。黑龙江省工业与应用数学学会常务理事，美国数学会《Math.Review》评论员。 主要从事泛函微分方程和偏泛函微分方程的分支理论及应用的研究，在规范型的公式化以及从高余维分支研究角度揭示复杂模式的存在性和稳定性方面有一些特色工作。主持和参与多项国家自然科学基金及省部级基金项目，主要工作发表在国内外诸如科学通报，JDE, IMA J. Appl. Math.，DCDS, JDDE，JMB，Physica D等重要学术期刊上，出版专著一部

报告题目2：Dynamics of a class of reaction diffusion equation with memory effect

报告人：王春程 教授 哈尔滨工业大学

报告摘要: In this talk, I will present a class of delayed diffusive models, where time delays are involved in diffusion terms. Such models involves population models and heat conduction models with memory effect, and viscoelastic fluid models. The theory of linear and nonlinear equation are studied, including the semigroup properties of solution operator, distribution of eigenvalues, normal form theory and global boundedness of the solutions. These are joint works with Yanhui Fan, Xuanyu Liu and Junping Shi.

报告人简介：王春程，哈尔滨工业大学数学欧博官网，教授。2000-2004年大连理工大学学习，2010年毕业于哈工大，获博士学位。主要研究方向：泛函微分方程、动力系统、分支理论、生物数学。在JDE、JDDE、DCDS等刊物发表论文20余篇，主持和参与多项国家基金。

报告题目3：Viral dynamics with immune chemokines

报告人：舒洪英 教授 陕西师范大学

报告摘要: We study a viral infection model incorporating both cell-to-cell infection and immune chemokines. Based on experimental results in the literature, we make a standing assumption that the cytotoxic T lymphocytes (CTL) will move toward the location with more infected cells, while the diffusion rate of CTL is a decreasing function of the density of infected cells. We first establish the global existence and ultimate boundedness of the solution via a priori energy estimates. We then define the basic reproduction number of viral infection R0 and prove that the infection-free steady state E0 is globally asymptotically stable if R0 < 1. When R0 > 1, then E0 becomes unstable, and another basic reproduction number of CTL response R1 becomes the dynamic threshold in the sense that if R1 < 1, then the CTL-inactivated steady state E1 is globally asymptotically stable; and if R1 > 1, then the immune response is uniform persistent and, under an additional technical condition the CTL-activated steady state E2 is globally asymptotically stable. To establish the global stability results, we need to prove point dissipativity, obtain uniform persistence, construct suitable Lyapunov functions, and apply the LaSalle invariance principle.

报告人简介：舒洪英，2010年获哈尔滨工业大学博士学位。2008年在加拿大阿尔伯塔大学留学两年，2011年至2014年先后在加拿大新不伦瑞克大学、加拿大瑞尔森大学和约克大学任AARMS博士后研究员。2014年至2018年任职同济大学特聘研究员，博士生导师。2018年至今任陕西师范大学特聘教授，博士生导师。2016年获上海市浦江人才计划，2017年获陕西省百人计划。先后主持2项国家自然科学基金面上项目，1项青年项目，1项上海市自然科学基金项目，1项加拿大科研基金项目。主要研究微分动力系统及其在生物数学上的应用，发表SCI收录论文40余篇，分别发表在J. Math. Pures Appl., SIAM Journal of Applied Mathematics, Journal of Differential Equations, Nonlinearity, Journal of Dynamics and Differential Equations, Journal of Mathematical Biology，Bulletin of Mathematical Biology 和Journal of Theoretical Biology等SCI期刊上。任美国数学学会MR评论员、欧洲数学学会zbMATH评论员。

报告题目4：Vaccination strategies of multi-strain cholera transmission with hyperinfectious vibrios: mathematical modelling, analysis and data fitting

报告人：徐瑞 教授 山西大学

报告摘要: In this work, 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.

报告人简介：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180余篇。入选2021、2022和2023年爱思唯尔“中国高被引学者”榜单；入选由美国斯坦福大学和爱思唯尔出版集团联合发布的2023和2024年度全球前2%顶尖科学家榜单。

报告题目5：肿瘤细胞与免疫细胞相互作用的简单模型分析研究

报告人：李建全 教授 西京欧博官网

报告摘要: 本报告在描述两类肿瘤细胞和免疫细胞相互作用的简单模型基础上，通过定性和定量分析其动力学性态，阐述肿瘤细胞与免疫细胞作用过程的复杂性，研究肿瘤抗原作用和肿瘤生长率对肿瘤发展的影响，并就肿瘤休眠、免疫逃逸和恶性发展等临床现象进行讨论，为控制肿瘤的发展提供一定的理论依据。

报告人简介：李建全，现为西京欧博官网教授。曾先后任职于空军工程大学和陕西科技大学，长期从事种群生态动力学、传染病动力学、病毒动力学和肿瘤免疫动力学的数学建模与研究，发表相关学术论文120 余篇，其中被SCI 收录50余篇。所参与的研究项目分别于2002 年和2006 年获教育部高等学校科学技术奖自然科学二等奖。曾主持国家博士后科学基金一项，主持国家自然科学基金项目三项，参与两项国家十二五重大专项研究项目。博士学位论文获西安交通大学和陕西省优秀博士学位论文。

报告题目6：Dynamics of a vector-borne disease model with spatial heterogeneity and advection

报告人：赵洪涌 教授 南京航空航天大学

报告摘要: In this talk, we formulate and analyze a reaction-diffusion-advection vector-borne disease model with spatial heterogeneity. We find the aggregation phenomenon of endemic equilibrium and classify possible dynamics for the model, including the asymptotic profiles and monotonicity of basic reproduction ratio R_0 with respect to the diffusion and advection rates of infected hosts and vectors. More importantly, we obtain some crucial and interesting phenomena by classifying the level set of R_0. Specifically, there exist unique critical surfaces to separate the dynamics, namely, the disease-free equilibrium is stable on one side of the surface and unstable on the other side. The resulting aggregation phenomenon shows that the infected individuals will aggregate in the downstream end if their advection rates are sufficiently large relative to dispersal. To the best of our knowledge, the conclusions of the paper complement the results of vector-borne disease in non-advective environments for the first time and provide new perspectives for the investigation and control of the disease.

报告人简介：四川大学博士，南京大学博士后.现为南京航空航天大学二级教授，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2023年，连续十年入选爱思唯尔中国高被引学者榜单.主持省和国家自然科学基金面上项目多项. 获省自然科学优秀论文二等奖一项、省教育科学研究成果二等奖一项. 2016年入选南京航空航天大学年度人物.国家科技部重大项目和江苏省高校重大项目会评专家.在Journal of Differential Equations、Journal of Dynamics and Differential Equations、Journal of Mathematical Biology、Journal of Theoretical Biology、Bulletin of Mathematical Biology、 Mathematical Biosciences、Journal of Nonlinear Science、Information Sciences、Chaos等国际重要期刊上发表学术论文一百四十余篇，被SCI刊物引用三千余次.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.

主办单位：数学与统计欧博官网