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 ($R_1$) and HIV-1 mono-infection ($R_2$) 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 $R_1$ and $R_2$, 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.