The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis

Abstract

Fever is a extremely common symptom in infants and young children. Due to the low resistance of infants and young, long-term fever may cause damage to the child’s body. Clinically, some children with long-term fever was eventually diagnosed with Kawasaki disease (KD). KD, an autoimmune disease, is a systemic vasculitis mainly affecting children younger than 5 years old. Due to the delayed therapy and diagnosis, coronary artery abnormalities (CAAs) develop in children with KD, and leads to a high risk of acquired heart disease. Later, patients may have myocardial infarction or even die a sudden death. Unfortunately, at present, the pathogenesis of KD remains unknown and KD lacks of specific and sensitive biomarkers, thus bringing difficulties to diagnosis and therapy. Therefore it is a highly focused topic to research on the mechanism of KD. Some scholars believe that KD is caused by the cross reaction of external infection and organ tissue composition, hereby triggering disorder of the immune system and producing a variety of cytokines. On the basis of considering the cytokines such as vascular endothelial cells, inflammatory factors, adhesion factors and chemokines, endothelial cell growth factors, put forward a kind of dynamic model of pathogenesis of KD by the theory of ordinary differential equation. It is found that the dynamic model can show complex dynamic behavior, such as the forward and backward bifurcation of the equilibria. This article reveals the possible complexity of KD infection, and provides a theoretical references for the research of pathogenic mechanism and clinical treatment of KD.