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

作     者：Ke GUO Wan-biao MA 

作者机构：School of Mathematics and Physics University of Science and Technology Beijing 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报(英文版))

年 卷 期：2024年

核心收录：

学科分类：1002[医学-临床医学] 07[理学] 070104[理学-应用数学] 100202[医学-儿科学] 0701[理学-数学] 10[医学] 

基　　金：supported by the National Natural Science Foundation of China (12201038) the Project funded by China Postdoctoral Science Foundation (2022TQ0026) the Fundamental Research Funds for the Central Universities (FRF-TP-22-102A1) the Beijing Natural Science Foundation (1202019) 

摘      要：Kawasaki disease（KD） is an acute, febrile, systemic vasculitis that mainly affects children under five years of age. In this paper, we propose and study 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, and some explicit analytic expressions of ultimate lower bounds of the solutions of the model are *** 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.