Purity Ngina, Rachel Waema Mbogo, Livingstone S Luboobi
{"title":"细胞毒性T淋巴细胞对HIV感染的体内动态影响。","authors":"Purity Ngina, Rachel Waema Mbogo, Livingstone S Luboobi","doi":"10.1155/2017/2124789","DOIUrl":null,"url":null,"abstract":"<p><p>The <i>in vivo</i> dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having <i>R</i><sub>0</sub> < 1. Lastly, the biological dynamics of HIV <i>in vivo</i> infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.</p>","PeriodicalId":14433,"journal":{"name":"International Scholarly Research Notices","volume":"2017 ","pages":"2124789"},"PeriodicalIF":0.0000,"publicationDate":"2017-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2017/2124789","citationCount":"3","resultStr":"{\"title\":\"The <i>In Vivo</i> Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells.\",\"authors\":\"Purity Ngina, Rachel Waema Mbogo, Livingstone S Luboobi\",\"doi\":\"10.1155/2017/2124789\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The <i>in vivo</i> dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having <i>R</i><sub>0</sub> < 1. Lastly, the biological dynamics of HIV <i>in vivo</i> infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.</p>\",\"PeriodicalId\":14433,\"journal\":{\"name\":\"International Scholarly Research Notices\",\"volume\":\"2017 \",\"pages\":\"2124789\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2017/2124789\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Scholarly Research Notices\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2017/2124789\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2017/1/1 0:00:00\",\"PubModel\":\"eCollection\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Scholarly Research Notices","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2017/2124789","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/1/1 0:00:00","PubModel":"eCollection","JCR":"","JCRName":"","Score":null,"Total":0}
The In Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells.
The in vivo dynamics of HIV infection, the infection mechanism, the cell types infected, and the role played by the cytotoxic cells are poorly understood. This paper uses mathematical modelling as a tool to investigate and analyze the immune system dynamics in the presence of HIV infection. We formulate a six-dimensional model of nonlinear ordinary differential equations derived from known biological interaction mechanisms between the immune cells and the HIV virions. The existence and uniqueness as well as positivity and boundedness of the solutions to the differential equations are proved. Furthermore, the disease-free reproduction number is derived and the local asymptotic stability of the model investigated. In addition, numerical analysis is carried out to illustrate the importance of having R0 < 1. Lastly, the biological dynamics of HIV in vivo infection are graphically represented. The results indicate that, at acute infection, the cytotoxic T-cells play a paramount role in reducing HIV viral replication. In addition, the results emphasize the importance of developing controls, interventions, and management policies that when implemented would lead to viral suppression during acute infection.