Dynamics of a non-autonomous Kawasaki disease model with endothelial cell injury and general functional responses

Patients with Kawasaki disease (KD) are exposed to various environmental factors during the onset and treatment of the disease, which result in the parameters of the KD model not remaining constant but fluctuating over time. Consequently, this paper constructs and studies a non-autonomous KD model with endothelial cell injury and general functional responses. We first obtain some explicit estimates of the ultimate lower bounds of any positive solution of the model through some elaborate mathematical analytical approaches, from which we deduce the model is permanent if $R^p>1$. If the model is transformed into the autonomous case, then $R^p$ is the basic reproduction number of the model. In addition, some sufficient conditions for inflammatory cytokines to be cleared are obtained.