Stability analysis of a diffusive HTLV-2 and HIV-1 co-infection model

Co-infections between human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 2 (HTLV-2) are more common, particularly among injection drug users and individuals engaging in sexual activity. This is because these viruses share similar modes of transmission. Mathematical models are essential for understanding the dynamics of both single and multiple viral infections in the within-host environment. The development of mathematical models for HTLV-2 mono-infection or its co-infection with HIV-1 has been largely neglected. This paper formulates a new within-host HTLV-2 and HIV-1 co-infection mode. The model comprises eight compartments: healthy CD4+ T cells, latently HIV-1-infected CD4+ T cells, actively HIV-1-infected CD4+ T cells, free HIV-1 particles, healthy CD8+ T cells, latently HTLV-2-infected CD8+ T cells, actively HTLV-2-infected CD8+ T cells, and HIV-1-specific B cells. Recent research suggests that immune cells, infected cells and viruses may disperse from regions of higher density to those with lower density. By taking into account the spatial mobility of both cells and viruses, we formulate the co-infection model with diffusion as a system of nonlinear partial differential equations. First, the model’s well-posedness is examined by demonstrating the existence of global solutions and boundedness. We identify the model’s steady states and thresholds and derive the threshold conditions for each steady state’s existence and global asymptotic stability. The global stability of all steady states is examined using proper Lyapunov functions and LaSalle’s invariance principle. The theoretical results gained are illustrated through a series of numerical simulations. Sensitivity analysis of the basic reproduction ratios of HTLV-2 mono-infection (R1) and HIV-1 mono-infection (R2) is carried out in order to obtain a better understanding of the effective parameters for co-infection with HIV-1 and HTLV-2. This study examines the influence of the B-cell response on the dynamics of HIV-1 and HTLV-2 co-infection. The findings indicate that the B-cell response plays a crucial role in controlling and limiting the progression of HIV-1. The differences between co-infections of HIV-1 and HTLV-2 and single infections of each virus are discussed. Our findings align with previous research indicating that HTLV-2 does not influence the progression of HIV-1 disease in HIV-1-infected patients. Furthermore, in patients infected with HTLV-2, HIV-1 may contribute to the development of malignant CD8+ T-lymphoproliferative diseases.