{"title":"Dynamics of a non-autonomous Kawasaki disease model with endothelial cell injury and general functional responses","authors":"Ke Guo , Wanbiao Ma , Conghui Xu , Fuxiang Li","doi":"10.1016/j.aml.2025.109659","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>></mo><mn>1</mn></mrow></math></span>. If the model is transformed into the autonomous case, then <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> is the basic reproduction number of the model. In addition, some sufficient conditions for inflammatory cytokines to be cleared are obtained.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109659"},"PeriodicalIF":2.9000,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925002095","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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 . If the model is transformed into the autonomous case, then is the basic reproduction number of the model. In addition, some sufficient conditions for inflammatory cytokines to be cleared are obtained.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.