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 lowresistance 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, anautoimmune disease, is a systemic vasculitis mainly affecting children younger than 5 years old. Dueto 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 infarctionor even die a sudden death. Unfortunately, at present, the pathogenesis of KD remains unknownand 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 believethat KD is caused by the cross reaction of external infection and organ tissue composition, herebytriggering disorder of the immune system and producing a variety of cytokines. On the basis ofconsidering the cytokines such as vascular endothelial cells, inflammatory factors, adhesion factorsand chemokines, endothelial cell growth factors, put forward a kind of dynamic model of pathogenesisof KD by the theory of ordinary differential equation. It is found that the dynamic model can showcomplex dynamic behavior, such as the forward and backward bifurcation of the equilibria. This articlereveals the possible complexity of KD infection, and provides a theoretical references for the researchof pathogenic mechanism and clinical treatment of KD.

Keywords

• kawasaki disease (kd)
• systemic vasculitis
• differential equation model
• backward bifurcation
• stability