{"title":"具有时滞的两种群疟疾模型的稳定性和Hopf分支","authors":"E. Agyingi, T. Wiandt, M. Ngwa","doi":"10.1080/23737867.2017.1296383","DOIUrl":null,"url":null,"abstract":"We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.","PeriodicalId":37222,"journal":{"name":"Letters in Biomathematics","volume":"4 1","pages":"59 - 76"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23737867.2017.1296383","citationCount":"3","resultStr":"{\"title\":\"Stability and Hopf bifurcation of a two species malaria model with time delays\",\"authors\":\"E. Agyingi, T. Wiandt, M. Ngwa\",\"doi\":\"10.1080/23737867.2017.1296383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.\",\"PeriodicalId\":37222,\"journal\":{\"name\":\"Letters in Biomathematics\",\"volume\":\"4 1\",\"pages\":\"59 - 76\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/23737867.2017.1296383\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Biomathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23737867.2017.1296383\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Biomathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23737867.2017.1296383","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Stability and Hopf bifurcation of a two species malaria model with time delays
We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.
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