Modeling virus-stimulated proliferation of CD4 T-cell, cell-to-cell transmission and viral loss in HIV infection dynamics.

Human immunodeficiency virus (HIV) can persist in infected individuals despite prolonged antiretroviral therapy and it may spread through two modes: virus-to-cell and cell-to-cell transmissions. Understanding viral infection dynamics is pivotal for elucidating HIV pathogenesis. In this study, we incorporate the loss term of virions, and both virus-to-cell and cell-to-cell infection modes into a within-host HIV model, which also takes into consideration the proliferation of healthy target cells stimulated by free viruses. By constructing suitable Lyapunov function and applying geometric methods, we establish global stability results of the infection free equilibrium and the infection persistent equilibrium, respectively. Our findings highlight the crucial role of the basic reproduction number in the threshold dynamics. Moreover, we use the loss rate of virions as the bifurcation parameter to investigate stability switches of the positive equilibrium, local Hopf bifurcation, and its global continuation. Numerical simulations validate our theoretical results, revealing rich viral dynamics including backward bifurcation, saddle-node bifurcation, and bistability phenomenon in the sense that the infection free equilibrium and a limit cycle are both locally asymptotically stable. These insights contribute to a deeper understanding of HIV dynamics and inform the development of effective therapeutic strategies.