题目：Global Dynamics of a Kawasaki Disease Vascular Endothelial Cell Injury Model with Backward Bifurcation and Hopf Bifurcation

主讲人：马万彪 教授

时间：2024年12月17日（星期二）14:30

地点：腾讯会议（325-533-788）

主办单位：理学院

主讲人简介：

马万彪，现任北京科技大学数理学院应用数学系教授、博士生导师，1997年在日本静冈大学获博士学位，曾访问/任职于内蒙古师范大学、京都大学、大阪府立大学、静冈大学等。主要从事泛函微分方程稳定性及其在传染病学、免疫学、微生物连续培等交叉科学领域的应用研究。 在科学通报、数学学报、数学年刊、数学物理学报、系统科学与数学、应用数学学报、J. Math. Anal. Appl.、Tohoku Math. J.、SIAM J. Appl. Math.、Nonl. Anal.、Bull. Math. Biology.、Math. Biosci. Eng.、Discrete Contin. Dyn. Syst.-B、J. Comput. Appl. Math.、Int. J. Biomath.、Japan J. Indust. Appl. Math.、Int. J. Bifurcat. Chaos、J. Dyn. Diff. Eqs.、Nonlinearity、Chaos、Stud. Appl. Math.、Brief. Bioinform.等杂志合作发表论文200余篇。 联合编辑SCI杂志专辑2期，联合出版译著一部（时滞微分方程:泛函微分方程引论，科学出版社）。主持国家留学回国基金、北京市自然科学基金与国家自然科学基金项目7项，获省部级科学技术进步一等奖一项。现任中国数学会生物数学专业委员会常务委员、Int. J. Biomath.编委，曾任中国数学会理事、中国数学会生物数学专业委员会副主任兼秘书长。

摘要：

Kawasaki disease (KD) is an acute, febrile, systemic vasculitis that mainly affects children under five years of age. In this talk, we consider a class of 5-dimensional ordinary differential equation model describing the vascular endothelial cell injury in the lesion area of KD. This model exhibits forward/backward bifurcation. It is shown that the vascular injury-free equilibrium is locally asymptotically stable if the basic reproduction number R0 < 1. Further, we obtain two types of sufficient conditions for the global asymptotic stability of the vascular injury-free equilibrium, which can be applied to both the forward and backward bifurcation cases. In addition, the local and global asymptotic stability of the vascular injury equilibria and the presence of Hopf bifurcation are studied. It is also shown that the model is permanent if the basic reproduction number R0 > 1, and some explicit analytic expressions of ultimate lower bounds of the solutions of the model are given. Our results suggest that the control of vascular injury in the lesion area of KD is not only correlated with the basic reproduction number R0, but also with the growth rate of normal vascular endothelial cells promoted by the vascular endothelial growth factor.