Modeling of KSHV/HHV-8 and HIV-1 Co-Dynamics in Vivo

Human immunodeficiency virus kind 1 (HIV-1) compromises the immune system by infecting and damaging CD4+ T cells. Infection can progress to the ultimate stage, acquired immune deficiency syndrome (AIDS), if HIV-1 therapy is not received. People living with HIV/AIDS are more vulnerable to infections that they otherwise wouldn't develop. Opportunistic infections or malignancies are the terms used to describe them. Kaposi sarcoma (KS) is an AIDSrelated malignancy caused by Kaposi's sarcoma-associated herpesvirus (KSHV) (also known as human herpesvirus 8 (HHV-8)). HIV-1 and KSHV co-infection cases has been shown in several studies. Using a system of ODEs, we develop a new mathematical model to study the co-dynamics of HIV-1 and KSHV in vivo. The model includes interactions between healthy CD4+ T cells, HIV-1-infected CD4+ T cells, HIV-1 particles, healthy B cells, KSHV-infected B cells, and KSHV particles. By analyzing the boundedness and nonnegativity of the solutions, we prove the mathematical well-posedness and biological compatibility of the model. The existence and stability of the model's steady states are established by four threshold values that we identify. We prove that steady states are globally asymptotically stable by using Lyapunov's method and LaSalle's invariance principle. Numerical simulations are used to display the results. For both basic reproduction ratios of HIV-1 mono-infection (R1) and KSHV mono-infection (R2), sensitivity analysis is carried out. A comparison between HIV-1 or KSHV mono-infections and co-infections with HIV-1 and KSHV is given. Empirical evidence indicates that co-infection results in higher KSHV and HIV-1 concentrations compared to mono-infection cases. This result is in line with a number of findings found in the literature.