Abstract In this paper, the analysis of an HIV-1 epidemic model is presented by incorporating a distributed intracellular delay. The delay term represents the latent period between the time that the target cells are contacted by the virus and the time the virions penetrated into the cells. To understand the analysis of our proposed model, the Rouths–Hurwiz criterion and general theory of delay differential equations are used. It is shown that the infection free equilibrium and the chronic-infection equilibrium are locally as well as globally asymptotically stable, under some conditions on the basic reproductive number R 0 {R_{0}} . Furthermore, the obtained results show that the value of R 0 {R_{0}} can be decreased by increasing the delay. Therefore, any drugs that can prolong the latent period will help to control the HIV-1 infection.

中文翻译：

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HIV-1感染模型延迟积分微分方程的稳定性分析

摘要 在本文中，通过结合分布式细胞内延迟来分析 HIV-1 流行模型。延迟项表示靶细胞与病毒接触的时间与病毒粒子渗透到细胞的时间之间的潜伏期。为了理解我们提出的模型的分析，使用了 Rouths-Hurwiz 准则和延迟微分方程的一般理论。结果表明，在基本再生数R 0 {R_{0}} 的某些条件下，无感染平衡和慢性感染平衡是局部和全局渐近稳定的。此外，获得的结果表明，可以通过增加延迟来减小R 0 {R_{0}} 的值。因此，任何可以延长潜伏期的药物都有助于控制 HIV-1 感染。