微分方程與動力系統研討會

報告時間：2024年11月16日（星期六）

活動地點： 南校區會議中心121會議室

時間	活動主題
8：30-12：00	與6位專家進行學術研討
時間	主持人	專家	報告題目
14:00-14:40	吳事良	蔣衛華	Steady-state bifurcation and spike pattern in the Klausmeier-Gray-Scott model with non-diffusive plants
14:40-15:20		王春程	Dynamics of a class of reaction diffusion equation with memory effect
15:20-16:00		舒洪英	Viral dynamics with immune chemokines
16：00-16：10	休息
16：10-16：50	白振國	徐瑞	Vaccination strategies of multi-strain cholera transmission with hyperinfectious vibrios: mathematical modelling, analysis and data fitting
16：50-17：30		李建全	腫瘤細胞與免疫細胞相互作用的簡單模 型分析研究
17：30-18：10		趙洪涌	Dynamics of a vector-borne disease model with spatial heterogeneity and advection

報告題目1：Steady-state bifurcation and spike pattern in the Klausmeier-Gray-Scott model with non-diffusive plants

報告人：蔣衛華 教授 哈爾濱工業大學

報告摘要: 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.

個人簡介：蔣衛華,哈爾濱工業大學長聘教授，博士生導師。黑龍江省工業與應用數學學會常務理事，美國數學會《Math.Review》評論員。 主要從事泛函微分方程和偏泛函微分方程的分支理論及應用的研究，在規范型的公式化以及從高余維分支研究角度揭示復雜模式的存在性和穩定性方面有一些特色工作。主持和參與多項國家自然科學基金及省部級基金項目，主要工作發表在國內外諸如科學通報，JDE, IMA J. Appl. Math.，DCDS, JDDE，JMB，Physica D等重要學術期刊上，出版專著一部

報告題目2：Dynamics of a class of reaction diffusion equation with memory effect

報告人：王春程 教授 哈爾濱工業大學

報告摘要: 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.

報告人簡介：王春程，哈爾濱工業大學數學學院，教授。2000-2004年大連理工大學學習，2010年畢業于哈工大，獲博士學位。主要研究方向：泛函微分方程、動力系統、分支理論、生物數學。在JDE、JDDE、DCDS等刊物發表論文20余篇，主持和參與多項國家基金。

報告題目3：Viral dynamics with immune chemokines

報告人：舒洪英 教授 陜西師范大學

報告摘要: 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.

報告人簡介：舒洪英，2010年獲哈爾濱工業大學博士學位。2008年在加拿大阿爾伯塔大學留學兩年，2011年至2014年先后在加拿大新不倫瑞克大學、加拿大瑞爾森大學和約克大學任AARMS博士后研究員。2014年至2018年任職同濟大學特聘研究員，博士生導師。2018年至今任陜西師范大學特聘教授，博士生導師。2016年獲上海市浦江人才計劃，2017年獲陜西省百人計劃。先后主持2項國家自然科學基金面上項目，1項青年項目，1項上海市自然科學基金項目，1項加拿大科研基金項目。主要研究微分動力系統及其在生物數學上的應用，發表SCI收錄論文40余篇，分別發表在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。任美國數學學會MR評論員、歐洲數學學會zbMATH評論員。

報告題目4：Vaccination strategies of multi-strain cholera transmission with hyperinfectious vibrios: mathematical modelling, analysis and data fitting

報告人：徐瑞 教授 山西大學

報告摘要: 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.

報告人簡介：徐 瑞：2005年英國Dundee大學數學生物學專業獲哲學博士學位；現任山西大學復雜系統研究所教授、博士生導師。主要從事傳染病動力學研究。擔任Elsevier出版社SCI期刊Mathematics and Computers in Simulation編委。先后主持完成和在研國家自然科學基金面上項目5項；科學出版社出版學術專著5部；在國際學術期刊發表SCI論文180余篇。入選2021、2022和2023年愛思唯爾“中國高被引學者”榜單；入選由美國斯坦福大學和愛思唯爾出版集團聯合發布的2023和2024年度全球前2%頂尖科學家榜單。

報告題目5：腫瘤細胞與免疫細胞相互作用的簡單模型分析研究

報告人：李建全 教授 西京學院

報告摘要: 本報告在描述兩類腫瘤細胞和免疫細胞相互作用的簡單模型基礎上，通過定性和定量分析其動力學性態，闡述腫瘤細胞與免疫細胞作用過程的復雜性，研究腫瘤抗原作用和腫瘤生長率對腫瘤發展的影響，并就腫瘤休眠、免疫逃逸和惡性發展等臨床現象進行討論，為控制腫瘤的發展提供一定的理論依據。

報告人簡介：李建全，現為西京學院教授。曾先后任職于空軍工程大學和陜西科技大學，長期從事種群生態動力學、傳染病動力學、病毒動力學和腫瘤免疫動力學的數學建模與研究，發表相關學術論文120 余篇，其中被SCI 收錄50余篇。所參與的研究項目分別于2002 年和2006 年獲教育部高等學校科學技術獎自然科學二等獎。曾主持國家博士后科學基金一項，主持國家自然科學基金項目三項，參與兩項國家十二五重大專項研究項目。博士學位論文獲西安交通大學和陜西省優秀博士學位論文。

報告題目6：Dynamics of a vector-borne disease model with spatial heterogeneity and advection

報告人：趙洪涌 教授 南京航空航天大學

報告摘要: 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.

報告人簡介：四川大學博士，南京大學博士后.現為南京航空航天大學二級教授，博士生導師,九三學社社員.長期從事生物系統動力學、傳染病動力學分析與控制、時滯微分方程動力學等研究.江蘇省高校“青藍工程”優秀青年骨干教師和中青年學術帶頭人. 2014年至2023年，連續十年入選愛思唯爾中國高被引學者榜單.主持省和國家自然科學基金面上項目多項. 獲省自然科學優秀論文二等獎一項、省教育科學研究成果二等獎一項. 2016年入選南京航空航天大學年度人物.國家科技部重大項目和江蘇省高校重大項目會評專家.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等國際重要期刊上發表學術論文一百四十余篇，被SCI刊物引用三千余次.現為中國數學會生物數學專委會常務理事，江蘇省生物數學學會副理事長.

主辦單位：數學與統計學院