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Numerical and bifurcation analyses for a population model of HIV chemotherapy

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

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).

Suggested Citation

  • Gumel, A.B. & Twizell, E.H. & Yu, P., 2000. "Numerical and bifurcation analyses for a population model of HIV chemotherapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 169-181.
    • Handle: RePEc:eee:matcom:v:54:y:2000:i:1:p:169-181
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    References listed on IDEAS

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    1. David D. Ho & Avidan U. Neumann & Alan S. Perelson & Wen Chen & John M. Leonard & Martin Markowitz, 1995. "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection," Working Papers 95-01-002, Santa Fe Institute.
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