Global stability analysis of within-host Zika virus-chikungunya virus co-infection with CTL immune responses

We formulate and analyse a mathematical model for the within-host co-infection dynamics of Zika virus (ZIKV) and chikungunya virus (CHIKV), incorporating latently infected cells and cytotoxic T lymphocyte (CTL) immune responses. We establish the nonnegativity and boundedness of solutions. Using the next-generation matrix method, we derive the basic reproduction numbers ($R_Z^L$) and ($R_C^L$) for the ZIKV and CHIKV submodels, respectively, and the overall reproduction number ($R_0^L=\max \{R_Z^L,R_C^L\}$). Invasion reproduction numbers, ($R_Z^{L,inv}$) and ($R_C^{L,inv}$), are derived to characterise the ability of either virus to invade an established infection. Global stability of the equilibria is established using Lyapunov functions. We investigate three therapeutic protocols: antiviral treatment blocking viral entry, treatment reducing viral production, and IL-2 therapy enhancing CTL responses. Sensitivity analysis of ($R_Z^L$) and ($R_C^L$) is performed, and numerical simulations support the stability results. Simulations indicate that combined antiviral and immune-based interventions suppress co-infection by reducing viral replication and enhancing immune-mediated clearance.