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

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 - 2003
Externally publishedYes

Fingerprint

Nonstandard Finite Difference Schemes
Numerical Instability
Vaccines
Runge Kutta methods
Vaccine
Deterministic Model
Runge-Kutta Methods
Nonlinear Model
Fourth Order
Monitor
Infinity
Tend
Numerical Simulation
Computer simulation
Model
Standards

Keywords

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

ASJC Scopus subject areas

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

Cite this

A Non-Standard Finite-Difference Scheme for a Model of HIV Transmission and Control. / Gumel, Abba; Mickens, R. E.; Corbett, B. D.

In: Journal of Computational Methods in Sciences and Engineering, Vol. 3, No. 1, 2003, p. 91-98.

Research output: Contribution to journalArticle

@article{e13d21c073cd4a53988644c25f286d6b,
title = "A Non-Standard Finite-Difference Scheme for a Model of HIV Transmission and Control",
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.",
keywords = "HIV mathematical models, Nonstandard finite difference schemes, numerical integration",
author = "Abba Gumel and Mickens, {R. E.} and Corbett, {B. D.}",
year = "2003",
doi = "10.3233/JCM-2003-3107",
language = "English (US)",
volume = "3",
pages = "91--98",
journal = "Journal of Computational Methods in Sciences and Engineering",
issn = "1472-7978",
publisher = "IOS Press",
number = "1",

}

TY - JOUR

T1 - A Non-Standard Finite-Difference Scheme for a Model of HIV Transmission and Control

AU - Gumel, Abba

AU - Mickens, R. E.

AU - Corbett, B. D.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - HIV mathematical models

KW - Nonstandard finite difference schemes

KW - numerical integration

UR - http://www.scopus.com/inward/record.url?scp=22344440721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22344440721&partnerID=8YFLogxK

U2 - 10.3233/JCM-2003-3107

DO - 10.3233/JCM-2003-3107

M3 - Article

VL - 3

SP - 91

EP - 98

JO - Journal of Computational Methods in Sciences and Engineering

JF - Journal of Computational Methods in Sciences and Engineering

SN - 1472-7978

IS - 1

ER -