Dynamic interactions between HIV-1 and cancer: hopf bifurcation and stability in a dual time-delay mathematical model

The objective of this paper is to extend an existing mathematical model of HIV-associated cancer by incorporating two critical time delays: one between viral entry into a cell and the onset of latency and the other between cell infection and the start of viral production. By performing a Hopf bifurcation analysis, we examined four different scenarios to gain insight into how these delays contribute to oscillatory behaviors and periodic solutions in cell populations. The results of numerical simulations demonstrate the impact of these delays on the stability of healthy and infected cells and highlight the importance of infected T cells in the progression of AIDS-related complications.