报告人：郭松柏，北京建筑大学

报告时间：2024年6月7日16:00

报告地点：东校区第三教学楼3201

报告人简介：

郭松柏博士，北京建筑大学教授、硕士生导师，美国Math Review评论员，德国zbMATHOpen评论员。主要研究泛函微分/差分方程持久性与稳定性理论、生物动力系统等。在J. Dyn. Differ. Equ.，Chaos，Acta Math.Appl. Sin.-E.，Math. Comput. Simulat.，Discrete Contin. Dyn. Syst.-Ser. B等学术期刊上发表论文50余篇，其中SCI源刊30余篇。主持完成了国家自然科学基金青年项目、中国博士后科学基金面上项目、北京市教委面上资助等课题，10余次参加国际学术会议并作报告。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。

报告摘要:

A time-delayed virus dynamic model is first proposed with generalmonotonic incidence βf(x,v), nonlinear cytotoxic T lymphocyte(CTL) elimination function pyg₁(z), nonlinear CTLstimulation function cyg₂(z), and immune impairmentnyz, which is not necessarily dissipative. Under some general assumptions,the general monotonic incidence function βf(x,v) can cover somecommon forms such as the bilinear incidence, the saturation incidence, theHolling types II and III functional response, the Beddington—DeAngelisfunctional response, and Crowley—Martin functional response. It is worthmentioning that g₁(z) and g₂(z)can take different functions, and the CTL stimulation function cyg₂(z)can include some monotone functions and non-monotone functions. In addition, wepoint out that the function f_v(x,0) is increasing (butnot necessarily strictly) in x>0 for the general monotonic incidence f(x,v),but some papers defaulted that this function was strictly increasing. Finally,the necessary and sufficient conditions for global stability of all equilibriaof the model are obtained by constructing appropriate Lyapunov functionals witha thorough detailed analysis. The main results of this presentation alsoimprove or extend some existing results.