A Non-Standard Finite-Difference Scheme for a Model of HIV Transmission and Control

A. B. Gumel, R. E. Mickens, B. D. Corbett

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

An implicitly-derived explicit non-standard finite-difference scheme will be constructed and used to solve a deterministic non-linear model for HIV transmission and control. The model monitors the populations of untreated susceptibles, vaccinated susceptibles (given prophylactic vaccines), untreated infecteds and treated infecteds as time (t) tends to infinity. Unlike the standard fourth-order Runge-Kutta method (RK4), which induces contrived numerical instabilities, the non-standard method will be seen to be free of numerical instabilities for all parameter values used in the numerical simulations.

Original languageEnglish (US)
Pages (from-to)91-98
Number of pages8
JournalJournal of Computational Methods in Sciences and Engineering
Volume3
Issue number1
DOIs
StatePublished - Jan 1 2003
Externally publishedYes

Keywords

  • HIV mathematical models
  • Nonstandard finite difference schemes
  • numerical integration

ASJC Scopus subject areas

  • Engineering(all)
  • Computer Science Applications
  • Computational Mathematics

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