%0 Journal Article
%T 基于潜伏感染和饱和发生率的HIV感染模型<br>An HIV Infection Model Based on Latent Infection and Saturated Incidence Rate
%A 宋世杰
%A 陈莺蓉
%A 李朋朔
%A 王艳
%J Advances in Applied Mathematics
%P 2900-2912
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.115308
%X 本文根据HIV在感染者体内的感染过程，考虑到T细胞的潜伏感染以及免疫应答，建立具有饱和发生率的HIV感染模型，来模拟感染过程中病毒颗粒和T细胞之间的相互关系。首先，依据模型求解得到唯一的未感染平衡点E<sub>0</sub>和感染平衡点E<sup>*</sup>，然后通过利用微分方程稳定性理论，得到模型在两类平衡点的局部渐近稳定性，随后在实际参数意义下对模型进行数值模拟，以此验证平衡点的稳定性。最后，通过模型比较，说明所建模型的合理性和正确性。<br />
In this paper, an HIV infection model with saturation incidence rate is developed based on the in-fection process of HIV in infected individuals, taking into account the latent infection of T cells and the immune response, to simulate the interrelationship between viral particles and T cells during the infection process. Firstly, the model is solved to obtain unique uninfected and infected equilib-ria <span>E</span><sub>0</sub> and infected equilibria <span>E</span><sup>*</sup> , and then the local asymptotic stability of the model at the two types of equilibria is obtained by using the stability theory of ordinary differential equation. The model is then numerically simulated in the sense of actual parameters to verify the stability of the equilibrium point. Finally, through the model comparison, the rationality and accuracy of the built model are explained.
%K HIV病毒，免疫应答，常微分方程，稳定性<br>HIV Virus
%K Immune Response
%K Ordinary Differential Equation
%K Stability
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=51827