Dynamics and stability analysis of a fractional order Kawasaki disease vascular endothelial cell injury model

Kawasaki disease (KD) is a common childhood systemic vasculitis that primarily affects the coronary arteries. In this paper, a nonlinear fractional-order model is proposed for endothelial cell injury in KD. The model uses five compartments, a generalised functional response, and memory effects to describe the progression of cell injury. We apply power-rescaling to maintain dimensional consistency in our fractional-order framework. Then, the positivity and boundedness of the solutions are demonstrated. Later, we derive the basic reproduction number R0 and carry out sensitivity analysis to identify the parameters. Also, we analyse the local and global stability of the equilibrium points. Finally, we perform numerical simulations using the Adams-type predictor-corrector method. These simulations show how the fractional order affects the progression of cell injury. By incorporating the memory effect, we observe a better description of cell injury dynamics. This work offers new insights into the progression of KD.