Presentation Information
[MS13-06]A Class of Kawasaki Disease Model considering Vascular Endothelial Cell Injury and Time Delays
*Wanbiao Ma1 (1. University of Science and Technology Beijing (China))
Keywords:
Kawasaki disease,Delayed differential equation model,Forward/backward bifurcation,Basic reproduction number
Kawasaki disease (KD) was first discovered by Japanese physician Tomoaki Kawasaki in 1967 and is an acute febrile and rash disease that commonly occurs in infants and young children. It is accompanied by systemic vasculitis and belongs to the autoimmune vasculitis syndrome, with coronary artery abnormalities being the most serious complication. We will construct a delayed differential equation model to describe the dynamical problems related to the acute infection phase of KD based on the interaction among normal endothelial cells, endothelial growth factors, adhesion/chemokines, and inflammatory factors in the lesion area of KD patients. Theoretical analysis reveals that due to the promoting effect of endothelial growth factor on endothelial cell proliferation, the model can exhibit forward/backward bifurcation of the equilibria and Hopf bifurcation. 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.