微分方程與動(dòng)力系統(tǒng)研討會(huì)

報(bào)告時(shí)間：2024年11月16日（星期六）

活動(dòng)地點(diǎn)： 南校區(qū)會(huì)議中心121會(huì)議室

時(shí)間	活動(dòng)主題
8：30-12：00	與6位專家進(jìn)行學(xué)術(shù)研討
時(shí)間	主持人	專家	報(bào)告題目
14:00-14:40	吳事良	蔣衛(wèi)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(guó)	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(xì)胞與免疫細(xì)胞相互作用的簡(jiǎn)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(bào)告題目1：Steady-state bifurcation and spike pattern in the Klausmeier-Gray-Scott model with non-diffusive plants

報(bào)告人：蔣衛(wèi)華 教授 哈爾濱工業(yè)大學(xué)

報(bào)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(gè)人簡(jiǎn)介：蔣衛(wèi)華,哈爾濱工業(yè)大學(xué)長(zhǎng)聘教授，博士生導(dǎo)師。黑龍江省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)常務(wù)理事，美國(guó)數(shù)學(xué)會(huì)《Math.Review》評(píng)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(yīng)用的研究，在規(guī)范型的公式化以及從高余維分支研究角度揭示復(fù)雜模式的存在性和穩(wěn)定性方面有一些特色工作。主持和參與多項(xiàng)國(guó)家自然科學(xué)基金及省部級(jí)基金項(xiàng)目，主要工作發(fā)表在國(guó)內(nèi)外諸如科學(xué)通報(bào)，JDE, IMA J. Appl. Math.，DCDS, JDDE，JMB，Physica D等重要學(xué)術(shù)期刊上，出版專著一部

報(bào)告題目2：Dynamics of a class of reaction diffusion equation with memory effect

報(bào)告人：王春程 教授 哈爾濱工業(yè)大學(xué)

報(bào)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(bào)告人簡(jiǎn)介：王春程，哈爾濱工業(yè)大學(xué)數(shù)學(xué)學(xué)院，教授。2000-2004年大連理工大學(xué)學(xué)習(xí)，2010年畢業(yè)于哈工大，獲博士學(xué)位。主要研究方向：泛函微分方程、動(dòng)力系統(tǒng)、分支理論、生物數(shù)學(xué)。在JDE、JDDE、DCDS等刊物發(fā)表論文20余篇，主持和參與多項(xiàng)國(guó)家基金。

報(bào)告題目3：Viral dynamics with immune chemokines

報(bào)告人：舒洪英 教授 陜西師范大學(xué)

報(bào)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(bào)告人簡(jiǎn)介：舒洪英，2010年獲哈爾濱工業(yè)大學(xué)博士學(xué)位。2008年在加拿大阿爾伯塔大學(xué)留學(xué)兩年，2011年至2014年先后在加拿大新不倫瑞克大學(xué)、加拿大瑞爾森大學(xué)和約克大學(xué)任AARMS博士后研究員。2014年至2018年任職同濟(jì)大學(xué)特聘研究員，博士生導(dǎo)師。2018年至今任陜西師范大學(xué)特聘教授，博士生導(dǎo)師。2016年獲上海市浦江人才計(jì)劃，2017年獲陜西省百人計(jì)劃。先后主持2項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目，1項(xiàng)青年項(xiàng)目，1項(xiàng)上海市自然科學(xué)基金項(xiàng)目，1項(xiàng)加拿大科研基金項(xiàng)目。主要研究微分動(dòng)力系統(tǒng)及其在生物數(shù)學(xué)上的應(yīng)用，發(fā)表SCI收錄論文40余篇，分別發(fā)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(guó)數(shù)學(xué)學(xué)會(huì)MR評(píng)論員、歐洲數(shù)學(xué)學(xué)會(huì)zbMATH評(píng)論員。

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

報(bào)告人：徐瑞 教授 山西大學(xué)

報(bào)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(bào)告人簡(jiǎn)介：徐 瑞：2005年英國(guó)Dundee大學(xué)數(shù)學(xué)生物學(xué)專業(yè)獲哲學(xué)博士學(xué)位；現(xiàn)任山西大學(xué)復(fù)雜系統(tǒng)研究所教授、博士生導(dǎo)師。主要從事傳染病動(dòng)力學(xué)研究。擔(dān)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(guó)家自然科學(xué)基金面上項(xiàng)目5項(xiàng)；科學(xué)出版社出版學(xué)術(shù)專著5部；在國(guó)際學(xué)術(shù)期刊發(fā)表SCI論文180余篇。入選2021、2022和2023年愛(ài)思唯爾“中國(guó)高被引學(xué)者”榜單；入選由美國(guó)斯坦福大學(xué)和愛(ài)思唯爾出版集團(tuán)聯(lián)合發(fā)布的2023和2024年度全球前2%頂尖科學(xué)家榜單。

報(bào)告題目5：腫瘤細(xì)胞與免疫細(xì)胞相互作用的簡(jiǎn)單模型分析研究

報(bào)告人：李建全 教授 西京學(xué)院

報(bào)告摘要: 本報(bào)告在描述兩類腫瘤細(xì)胞和免疫細(xì)胞相互作用的簡(jiǎn)單模型基礎(chǔ)上，通過(guò)定性和定量分析其動(dòng)力學(xué)性態(tài)，闡述腫瘤細(xì)胞與免疫細(xì)胞作用過(guò)程的復(fù)雜性，研究腫瘤抗原作用和腫瘤生長(zhǎng)率對(duì)腫瘤發(fā)展的影響，并就腫瘤休眠、免疫逃逸和惡性發(fā)展等臨床現(xiàn)象進(jìn)行討論，為控制腫瘤的發(fā)展提供一定的理論依據(jù)。

報(bào)告人簡(jiǎn)介：李建全，現(xiàn)為西京學(xué)院教授。曾先后任職于空軍工程大學(xué)和陜西科技大學(xué)，長(zhǎng)期從事種群生態(tài)動(dòng)力學(xué)、傳染病動(dòng)力學(xué)、病毒動(dòng)力學(xué)和腫瘤免疫動(dòng)力學(xué)的數(shù)學(xué)建模與研究，發(fā)表相關(guān)學(xué)術(shù)論文120 余篇，其中被SCI 收錄50余篇。所參與的研究項(xiàng)目分別于2002 年和2006 年獲教育部高等學(xué)?？茖W(xué)技術(shù)獎(jiǎng)自然科學(xué)二等獎(jiǎng)。曾主持國(guó)家博士后科學(xué)基金一項(xiàng)，主持國(guó)家自然科學(xué)基金項(xiàng)目三項(xiàng)，參與兩項(xiàng)國(guó)家十二五重大專項(xiàng)研究項(xiàng)目。博士學(xué)位論文獲西安交通大學(xué)和陜西省優(yōu)秀博士學(xué)位論文。

報(bào)告題目6：Dynamics of a vector-borne disease model with spatial heterogeneity and advection

報(bào)告人：趙洪涌 教授 南京航空航天大學(xué)

報(bào)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(bào)告人簡(jiǎn)介：四川大學(xué)博士，南京大學(xué)博士后.現(xiàn)為南京航空航天大學(xué)二級(jí)教授，博士生導(dǎo)師,九三學(xué)社社員.長(zhǎng)期從事生物系統(tǒng)動(dòng)力學(xué)、傳染病動(dòng)力學(xué)分析與控制、時(shí)滯微分方程動(dòng)力學(xué)等研究.江蘇省高?！扒嗨{(lán)工程”優(yōu)秀青年骨干教師和中青年學(xué)術(shù)帶頭人. 2014年至2023年，連續(xù)十年入選愛(ài)思唯爾中國(guó)高被引學(xué)者榜單.主持省和國(guó)家自然科學(xué)基金面上項(xiàng)目多項(xiàng). 獲省自然科學(xué)優(yōu)秀論文二等獎(jiǎng)一項(xiàng)、省教育科學(xué)研究成果二等獎(jiǎng)一項(xiàng). 2016年入選南京航空航天大學(xué)年度人物.國(guó)家科技部重大項(xiàng)目和江蘇省高校重大項(xiàng)目會(huì)評(píng)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(guó)際重要期刊上發(fā)表學(xué)術(shù)論文一百四十余篇，被SCI刊物引用三千余次.現(xiàn)為中國(guó)數(shù)學(xué)會(huì)生物數(shù)學(xué)專委會(huì)常務(wù)理事，江蘇省生物數(shù)學(xué)學(xué)會(huì)副理事長(zhǎng).

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院