{"title":"HIV-1 感染在淋巴结传播初期的数学建模","authors":"N. Pertsev, G. Bocharov, K. Loginov","doi":"10.17537/2024.19.112","DOIUrl":null,"url":null,"abstract":"\n A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.\n","PeriodicalId":53525,"journal":{"name":"Mathematical Biology and Bioinformatics","volume":"20 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node\",\"authors\":\"N. Pertsev, G. Bocharov, K. Loginov\",\"doi\":\"10.17537/2024.19.112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.\\n\",\"PeriodicalId\":53525,\"journal\":{\"name\":\"Mathematical Biology and Bioinformatics\",\"volume\":\"20 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Biology and Bioinformatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17537/2024.19.112\",\"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":"Mathematical Biology and Bioinformatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17537/2024.19.112","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了一个数学模型,描述了 HIV-1 感染在感染者单个淋巴结中传播的初始阶段。模型变量为病毒颗粒、CD4+ T 淋巴细胞和抗原递呈细胞的数量。在建立模型时,使用了一个带有延迟的高维微分方程系统,并补充了初始数据。其中一些模型方程考虑到了病毒粒子和参与感染过程的细胞的中间发展阶段。在初始数据为非负的情况下,确定了模型解在半轴上的分量的存在性、唯一性和非负性。此外,还获得了被解释为淋巴结中不存在 HIV-1 感染的平衡状态的渐进稳定性条件。为了对模型进行数值求解,采用了半隐式欧拉方案。对淋巴结中 HIV-1 感染的衰减和感染者机体内感染开始全身扩散的条件进行了分析和数值计算。
Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node
A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.