Ngina Purity, Mbogo Rachel Waema, Luboobi Livingstone S
Institute of Mathematical Sciences, Strathmore University, P.O. Box 59857, Nairobi 00200, Kenya.
Int Sch Res Notices. 2017 Nov 14;2017:2124789. doi: 10.1155/2017/2124789. eCollection 2017.
The 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 < 1. Lastly, the biological dynamics of HIV 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.
人们对艾滋病毒感染的动态、感染机制、被感染的细胞类型以及细胞毒性细胞所起的作用了解甚少。本文使用数学建模作为工具来研究和分析存在艾滋病毒感染时的免疫系统动态。我们根据免疫细胞与艾滋病毒粒子之间已知的生物相互作用机制，构建了一个六维非线性常微分方程模型。证明了微分方程解的存在性、唯一性以及正性和有界性。此外，推导了无病繁殖数并研究了模型的局部渐近稳定性。此外，进行了数值分析以说明(< 1)的重要性。最后，以图形方式表示了艾滋病毒感染的生物动态。结果表明，在急性感染时，细胞毒性T细胞在减少艾滋病毒病毒复制方面起着至关重要的作用。此外，结果强调了制定控制措施、干预措施和管理政策的重要性，这些措施实施后将在急性感染期间导致病毒抑制。
