## 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). Although the Gauss-Seidel-type method to be developed in this paper is implicit by construction, it enables the various sub-populations of the model to be monitored explicitly as time t tends to infinity. Furthermore, the method will be seen to be more competitive (in terms of numerical stability) than some well-known methods in the literature. The method is used to determine the impact of the chemotherapy treatment by comparing the population sizes at equilibrium of the treated and untreated infecteds.

Original language | English (US) |
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Pages (from-to) | 169-181 |

Number of pages | 13 |

Journal | Mathematics and Computers in Simulation |

Volume | 54 |

Issue number | 1-3 |

DOIs | |

State | Published - Nov 30 2000 |

Externally published | Yes |

## Keywords

- Bifurcation
- Chemotherapy
- Critical points
- Finite-difference

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics