{"title":"具有标准发病率的时滞疟疾模型的全局稳定性","authors":"Song-bai Guo, Min He, Jing-an Cui","doi":"10.1007/s10255-023-1042-y","DOIUrl":null,"url":null,"abstract":"<div><p>A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number <i>R</i><sub>0</sub>. Specifically, it shows that the disease-free equilibrium <i>E</i><sup>0</sup> is globally asymptotically stable (GAS) for <i>R</i><sub>0</sub> < 1, and globally attractive (GA) for <i>R</i><sub>0</sub> = 1, while the endemic equilibrium <i>E*</i> is GAS and <i>E</i><sup>0</sup> is unstable for <i>R</i><sub>0</sub> > 1. Especially, to obtain the global stability of the equilibrium <i>E*</i> for <i>R</i><sub>0</sub> > 1, the weak persistence of the model is proved by some analysis techniques.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"39 2","pages":"211 - 221"},"PeriodicalIF":0.9000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-023-1042-y.pdf","citationCount":"1","resultStr":"{\"title\":\"Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate\",\"authors\":\"Song-bai Guo, Min He, Jing-an Cui\",\"doi\":\"10.1007/s10255-023-1042-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number <i>R</i><sub>0</sub>. Specifically, it shows that the disease-free equilibrium <i>E</i><sup>0</sup> is globally asymptotically stable (GAS) for <i>R</i><sub>0</sub> < 1, and globally attractive (GA) for <i>R</i><sub>0</sub> = 1, while the endemic equilibrium <i>E*</i> is GAS and <i>E</i><sup>0</sup> is unstable for <i>R</i><sub>0</sub> > 1. Especially, to obtain the global stability of the equilibrium <i>E*</i> for <i>R</i><sub>0</sub> > 1, the weak persistence of the model is proved by some analysis techniques.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"39 2\",\"pages\":\"211 - 221\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10255-023-1042-y.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-023-1042-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-023-1042-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate
A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R0. Specifically, it shows that the disease-free equilibrium E0 is globally asymptotically stable (GAS) for R0 < 1, and globally attractive (GA) for R0 = 1, while the endemic equilibrium E* is GAS and E0 is unstable for R0 > 1. Especially, to obtain the global stability of the equilibrium E* for R0 > 1, the weak persistence of the model is proved by some analysis techniques.
期刊介绍：
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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