题目1：Calculation of random transmission indicators in an epidemic model with isolation measures

主讲人：刘桂荣 教授

时间：2026年11月8日（星期日）9:00-10:00

地点：理学院308会议室

主办单位：理学院

主讲人简介：

刘桂荣，山西大学数学与统计学院教授，博士生导师，中国数学会常务理事，中国数学会生物数学专业委员会委员。2007年毕业于山西大学，获博士学位。主要从事微分方程与生物数学方向的研究工作。主持国家自然科学基金5项、人社部留学回国人员科技活动择优资助项目1项、山西省重点研发计划项目1项；主持省级教改项目2项；以第一完成人获得山西省教学成果一等奖2项和山西省科学技术奖二等奖1项；作为课程负责人，常微分方程获批省级一流课程。获全国高校教师教学创新大赛三等奖、山西省中青年教师教学基本功竞赛三等奖。

摘要：

We construct a continuous-time Markov chain epidemic model with testing and isolation measures, and analyze some random transmission indicators of infectious diseases, including extinction time, final size, exact reproduction number of a given individual, the population transmission number, the maximum number of infectious individuals and the time to reach this maximum. By using first-step analysis, Laplace transforms and probability generating function, we provide matrix equations and algorithmic schemes for computing the moments of various random transmission indicators. Finally, the algorithmic schemes are applied to real COVID-19 data.

题目2：Dynamics of SIRS epidemic model in heterogeneous hypernetworks

主讲人：张菊平 教授

时间：2026年11月8日（星期日）10:00-11:00

地点：理学院308会议室

主办单位：理学院

主讲人简介：

张菊平，山西大学教授，博士生导师，山西省三晋英才，复杂系统与数据科学教育部重点实验室副主任，中国数学会生物数学专业委员会委员，美国《数学评论》评论员，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，JTB，Chaos等期刊发表论文50余篇，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，获山西省科学技术奖（自然科学类）一等奖2项。

摘要：

In this talk, the complex epidemic behavior of higher-order interactions is investigated by considering heterogeneous hypernetworks with collective contagion mechanisms, and the epidemic model is established in hypernetworks. First, we propose a mean-field model in heterogeneous hypernetworks based on hyperdegree, and conduct analyses of this model. For general heterogeneous hypernetworks, we determine the epidemic threshold for disease spread and the threshold for the emergence of backward bifurcation, performing comprehensive dynamical analyses. Specifically, in a heterogeneous hypernetwork where the hyperedge size does not exceed 4, the existence of endemic equilibria is examined, and conditions for the system possessing a varying number of endemic equilibria are provided. By analyzing the model, we identify three types of bifurcations and two distinct bistable phenomena. Finally, theoretical predictions are confirmed through numerical simulations.