{"title":"对具有两个不同感染阶段的结核病模型的数学分析","authors":"A. H. Permatasari, R. H. S. Utomo","doi":"10.14710/jfma.v5i2.15723","DOIUrl":null,"url":null,"abstract":"Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"77 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION\",\"authors\":\"A. H. Permatasari, R. H. S. Utomo\",\"doi\":\"10.14710/jfma.v5i2.15723\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.\",\"PeriodicalId\":359074,\"journal\":{\"name\":\"Journal of Fundamental Mathematics and Applications (JFMA)\",\"volume\":\"77 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fundamental Mathematics and Applications (JFMA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14710/jfma.v5i2.15723\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fundamental Mathematics and Applications (JFMA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14710/jfma.v5i2.15723","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION
Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.
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