{"title":"具有CTL免疫应答的肝脏和肝外组织中病毒向细胞传播的HCV模型的阈值动力学","authors":"Xinli Hu, Jianquan Li, Xiaomei Feng","doi":"10.1080/17513758.2020.1859632","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number <math><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub></math> and immune reproduction number <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub></math> are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when <math><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub><mo><</mo><mn>1</mn></math> , the virus will be cleared out eventually and the CTL immune response will also disappear; when <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub><mo><</mo><mn>1</mn><mo><</mo><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub></math> , the virus persists within the host, but the CTL immune response disappears eventually; when <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub><mo>></mo><mn>1</mn></math> , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"15 1","pages":"19-34"},"PeriodicalIF":1.8000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17513758.2020.1859632","citationCount":"6","resultStr":"{\"title\":\"Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue.\",\"authors\":\"Xinli Hu, Jianquan Li, Xiaomei Feng\",\"doi\":\"10.1080/17513758.2020.1859632\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number <math><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub></math> and immune reproduction number <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub></math> are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when <math><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub><mo><</mo><mn>1</mn></math> , the virus will be cleared out eventually and the CTL immune response will also disappear; when <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub><mo><</mo><mn>1</mn><mo><</mo><msub><mi>R</mi><mrow><mn>01</mn></mrow></msub></math> , the virus persists within the host, but the CTL immune response disappears eventually; when <math><msub><mi>R</mi><mrow><mn>02</mn></mrow></msub><mo>></mo><mn>1</mn></math> , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given.</p>\",\"PeriodicalId\":48809,\"journal\":{\"name\":\"Journal of Biological Dynamics\",\"volume\":\"15 1\",\"pages\":\"19-34\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/17513758.2020.1859632\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Biological Dynamics\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1080/17513758.2020.1859632\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Dynamics","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1080/17513758.2020.1859632","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECOLOGY","Score":null,"Total":0}
Threshold dynamics of a HCV model with virus to cell transmission in both liver with CTL immune response and the extrahepatic tissue.
In this paper, a deterministic model characterizing the within-host infection of Hepatitis C virus (HCV) in intrahepatic and extrahepatic tissues is presented. In addition, the model also includes the effect of the cytotoxic T lymphocyte (CTL) immunity described by a linear activation rate by infected cells. Firstly, the non-negativity and boundedness of solutions of the model are established. Secondly, the basic reproduction number and immune reproduction number are calculated, respectively. Three equilibria, namely, infection-free, CTL immune response-free and infected equilibrium with CTL immune response are discussed in terms of these two thresholds. Thirdly, the stability of these three equilibria is investigated theoretically as well as numerically. The results show that when , the virus will be cleared out eventually and the CTL immune response will also disappear; when , the virus persists within the host, but the CTL immune response disappears eventually; when , both of the virus and the CTL immune response persist within the host. Finally, a brief discussion will be given.
期刊介绍:
Journal of Biological Dynamics, an open access journal, publishes state of the art papers dealing with the analysis of dynamic models that arise from biological processes. The Journal focuses on dynamic phenomena at scales ranging from the level of individual organisms to that of populations, communities, and ecosystems in the fields of ecology and evolutionary biology, population dynamics, epidemiology, immunology, neuroscience, environmental science, and animal behavior. Papers in other areas are acceptable at the editors’ discretion. In addition to papers that analyze original mathematical models and develop new theories and analytic methods, the Journal welcomes papers that connect mathematical modeling and analysis to experimental and observational data. The Journal also publishes short notes, expository and review articles, book reviews and a section on open problems.