Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that infect the susceptible CD4+T cells. It is known that HIV and HTLV-I have in common a way of transmission through direct contact with certain body fluids related to infected individuals. Therefore, it is not surprising that a mono-infected person with one of these viruses can be co-infected with the other virus. In the literature, a great number of mathematical models has been presented to describe the within-host dynamics of HIV or HTLV-I mono-infection. However, the within-host dynamics of HIV/HTLV-I co-infection has not been modeled. In this paper, we develop a new within-host HIV/HTLV-I co-infection model. The model includes the impact of Cytotoxic T lymphocytes (CTLs) immune response, which is important to control the progression of viral co-infection. The model describes the interaction between susceptible CD4+T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. We first show the nonnegativity and boundedness of the model’s solutions and then we calculate all possible equilibria. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle’s invariance principle. We have presented numerical simulations to illustrate the effectiveness of our main results. In addition, we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa.

中文翻译：

---

HIV/HTLV-I合并感染的建模与稳定性分析

人类免疫缺陷病毒 (HIV) 和人类 T 淋巴细胞病毒 I 型 (HTLV-I) 是感染易感 CD 的两种逆转录病毒4+T细胞。众所周知，HIV 和 HTLV-I 具有共同的传播方式，即通过直接接触与感染者相关的某些体液进行传播。因此，感染其中一种病毒的单一感染者可以与另一种病毒共同感染也就不足为奇了。在文献中，已经提出了大量的数学模型来描述 HIV 或 HTLV-I 单一感染的宿主内动态。然而，尚未对 HIV/HTLV-I 共感染的宿主内动态进行建模。在本文中，我们开发了一种新的宿主内 HIV/HTLV-I 共感染模型。该模型包括细胞毒性 T 淋巴细胞 (CTL) 免疫反应的影响，这对于控制病毒共感染的进展很重要。该模型描述了易感 CD 之间的相互作用4+T 细胞、沉默的 HIV 感染细胞、活跃的 HIV 感染细胞、沉默的 HTLV 感染细胞、表达税的 HTLV 感染细胞、游离 HIV 颗粒、HIV 特异性 CTL 和 HTLV 特异性 CTL。我们首先展示模型解的非负性和有界性，然后计算所有可能的平衡。我们推导出控制模型所有平衡的存在和稳定性的阈值参数。我们利用 Lyapunov 函数和 LaSalle 不变原理证明了所有均衡的全局渐近稳定性。我们提出了数值模拟来说明我们的主要结果的有效性。此外，我们讨论了 HTLV-I 感染对 HIV 感染患者的影响，反之亦然。