应兰州大学数学与统计学院王宾国教授和张亮教授的邀请，北京建筑大学郭松柏副教授将于2025年11月26日-28日访问兰州大学，期间于11月26日举办线上专题学术报告。

报告题目：Lyapunov functionals for a general time-delayed virus dynamic model with different CTL responses

时 间：11月26日下午3:30.

地 点：榆中校区天山堂B407； 腾讯会议（238-367-266）

报告摘要：A time-delayed virus dynamic model is first proposed with general monotonic incidenceβf(x,v),nonlinear cytotoxic T lymphocyte (CTL) elimination functionpyg₁(z), nonlinear CTL stimulation functioncyg₂(z),and immune impairmentnyz, which is not necessarily dissipative. Under some general assumptions,the general monotonic incidence functionβf(x,v) can cover some common forms such as the bilinear incidence,the saturation incidence, the Holling types II and III functional response, the Beddington—DeAngelis functional response, and Crowley—Martin functional response. It is worth mentioning thatg₁(z) andg₂(z) can take different functions, and the CTL stimulation functioncyg₂(z) can include some monotone functions and non-monotone functions. In addition, we point out that the functionf_v(x,0) is increasing (but not necessarily strictly) inx>0for the general monotonic incidencef(x,v), but some papers defaulted that this function was strictly increasing. Finally, the necessary and sufficient conditions for global stability of all equilibria of the model are obtained by constructing appropriate Lyapunov functionals with a thorough detailed analysis. The main results of this presentation also improve or extend some existing results.

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报告人简介

郭松柏，男，汉族，博士，副教授,硕士生导师，美国Math Review评论员，德国zbMATH Open评论员。主要研究泛函微分/差分方程持久性与稳定性理论，生物动力系统。在“J. Dyn. Differ. Equ.、Chaos、Commun. Pur. Appl. Anal.、Discrete Contin. Dyn. Syst.-Ser. B、Bull. Math. Biol.”等学术期刊上已发表论文60余篇，其中SCI论文40余篇。主持完成了国家自然科学基金青年、中国博士后科学基金面上、北京市教委面上、中国科学院可靠性保障中心种子课题等资助项目,参加了3项国家自然科学基金面上项目。2020年入选北京建筑大学金字塔人才培养工程—建大英才。获得过2次研究生国家奖学金，博士学位论文“HIV病毒感染与微生物絮凝相关问题的全局动力学”获北京科技大学优秀博士学位论文。

甘肃应用数学中心

数学与统计学院

萃英学院

2026年11月25日