Numerical and bifurcation analyses for a population model of HIV chemotherapy

A.B. Gumel, E.H. Twizell and P. Yu

Mathematics and Computers in Simulation (MATCOM), 2000, vol. 54, issue 1, 169-181

Abstract: 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).

Keywords: Finite-difference; Chemotherapy; Critical points; Bifurcation (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:54:y:2000:i:1:p:169-181

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