Numerical and bifurcation analyses for a population model of HIV chemotherapy

A competitive implicit finite-difference method will be developed and used for the solution of a non-linear mathematical model associated with the administration of highly-active chemotherapy to an HIV-infected population aimed at delaying progression to disease. The model, which assumes a non-constant transmission probability, exhibits two steady states; a trivial steady state (HIV-infection-free population) and a non-trivial steady state (population with HIV infection). Detailed stability and bifurcation analyses will reveal that whilst the trivial steady state only undergoes a static bifurcation (single zero singularity), the non-trivial steady state can not only exhibit static and dynamic (Hopf) bifurcations, but also a combination of two types of bifurcation (a double zero singularity).