Within-host dynamics of HTLV-2 and HIV-1 co-infection with delay

This paper formulates a mathematical model for the co-infection of HTLV-2 and HIV-1 with latent reservoirs, four types of distributed-time delays and HIV-1-specific B cells. We establish that the solutions remain bounded and nonnegative, identify the system's steady states, and derive sufficient conditions ensuring both their existence and global asymptotic stability. The system's global stability is confirmed using Lyapunov's method. We provide numerical simulations to support the stability results. Sensitivity analysis of basic reproduction numbers of HTLV-2 mono-infection (R1) and HIV-1 mono-infection (R2) is conducted. We examine how time delays influence the interaction between HIV-1 and HTLV-2. Including delay terms in the model reflects the influence of antiviral treatments, which help decrease R1 and R2, thus limiting the spread of infection. This highlights the potential for designing therapies that prolong delay period. Incorporating such delays improves model precision and supports more effective evaluation of treatment strategies.

本文针对伴随潜伏库、四类分布时滞以及人类免疫缺陷病毒1型（HIV-1）特异性B细胞的人类T淋巴细胞病毒2型（HTLV-2）与HIV-1共感染场景，构建了数学模型。本文证明模型解始终保持有界且非负，确定了系统的稳态，并推导了保证其存在性与全局渐近稳定性的充分条件。本文采用李雅普诺夫（Lyapunov）方法验证了系统的全局稳定性。本文通过数值仿真对稳定性相关结论进行了验证。针对HTLV-2单一感染（R1）与HIV-1单一感染（R2）的基本再生数，本文开展了敏感性分析。本文探讨了时滞对HIV-1与HTLV-2之间相互作用的影响机制。模型中引入时滞项可体现抗病毒治疗的作用效果：抗病毒治疗能够降低R1与R2的数值，进而限制病毒的传播范围。这一发现凸显了通过延长时滞周期设计治疗方案的潜在可行性。引入此类时滞项能够提升模型的精准度，助力更高效地评估各类治疗策略。