报告题目1：Dynamics analysis of a reaction-diffusion-advection benthic-drift model with logistic growth

报告人：聂华

报告时间：2024年11月10日（周日）上午09:00开始

报告地点：数学楼315会议室

报告摘要：The purpose of this talk is to investigate the benthic-drift population model in open and closed advective environments, focusing on the logistic growth of benthic populations. We employ the theory of monotone dynamical systems to establish the threshold dynamics. In special, when the zero solution is linearly unstable, we first obtain upper and lower semi-continuous limits separately by monotonically iterating from upper and lower solutions; then using a part metric, we prove that these two limits are equal and continuous in order to construct a positive steady state. Furthermore, we conduct a quantitative analysis of the principal eigenvalue for a non-self-adjoint eigenvalue problem to study the impact of diffusion rate, advective rate, and population release rates on the dynamics. The results suggest that the diffusion rate and advection rate play distinct roles for different population release rates in open and closed advective environments, respectively.

报告人简介：聂华，教授、博士生导师，研究方向：反应扩散方程与空间生态种群模型。现任中国数学会生物数学专业委员会委员、中国数学会计算数学分会理事。2006年于陕西师范大学获得博士学位；入选教育部“新世纪优秀人才支持计划”和陕西省“青年科技新星”，获得陕西省杰出青年基金；多次赴美国明尼苏达大学、澳大利亚新英格兰大学、台湾清华大学合作研究与访问。已主持国家自然科学基金面上项目3项，主持完成省部级项目3项；已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“SIAM J. Appl. Dyn. Syst.”、“J. Differential Equations”、“J. Math. Biol.”、“Math. Biosci.”、“European J. Appl. Math.”、“Proc. London Math. Soc.”、“Sci. China Math.”等国内外知名刊物上发表学术论文70多篇。

报告题目2：Spatiotemporal Dynamics of a Structured Spruce Budworm Diffusive Model

报告人：舒洪英

报告时间：2024年11月10日（周日）上午10:00开始

报告地点：数学楼315会议室

报告摘要：We formulate and analyze a general reaction-diffusion equation with delay, inspired by age-structured spruce budworm population dynamics with spatial diffusion by matured individuals. The model has its particular feature for bistability due to the incorporation of a nonlinear birth function (Ricker’s function) and a Holling type function of predation by birds. Here we establish some results about the global dynamics, in particular, the stability of and global Hopf bifurcation from the spatially homogeneous steady state when the maturation delay is taken as a bifurcation parameter. We also use a degree theoretical argument to identify intervals for the diffusion rate when the model system has a spatially heterogeneous steady state.

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3：Dynamic analysis and optimal control of HIV/AIDS model considering the first 95% target

报告人：张菊平

报告时间：2024年11月10日（周日）上午11:00开始

报告地点：数学楼315会议室

报告摘要：Based on the level of awareness of the population, an HIV/AIDS model is developed, which focused on the first 95% plan developed by UNAIDS. The threshold R0 of model and the expressions of the disease-free equilibrium and the endemic equilibrium are calculated, proving the existence of backward bifurcation. Backward bifurcation is caused by the imperfect protection rate of susceptible population due to education. Using China’s actual data for parameter fitting, it is found that new HIV infections are on an upward trend. In response to this phenomenon, publicity and education, condoms, screening and treatment of infected populations are considered as control measures. It is concluded that publicity and education is the primary strategy. This measure can not only effectively reduce the number of infected populations, but also effectively increase the awareness rate of HIV-infected populations. It is recommended to use condoms and have fewer sexual partners during sexual contact. Numerical simulation verifies that early stage publicity and education are much more important than post-infection screening and treatment measures.

报告人简介：张菊平，山西大学教授，博士生导师，York University博士后，山西省“三晋英才”，主要从事传染病的数学建模、分析及复杂网络上传播动力学研究。在JMB，BMB，MBS，JTB等期刊发表论文50余篇，获山西省科学技术奖（自然科学类）一等奖2项，主持或完成国家自然科学基金4项，省部级项目6项，参与国家基金重点项目2项等。