An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

Hasim A. Obaid; Rachid Ouifki; Kailash C. Patidar

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 2, page 357-372
  • ISSN: 1641-876X

Abstract

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We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.

How to cite

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Hasim A. Obaid, Rachid Ouifki, and Kailash C. Patidar. "An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection." International Journal of Applied Mathematics and Computer Science 23.2 (2013): 357-372. <http://eudml.org/doc/256684>.

@article{HasimA2013,
abstract = {We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.},
author = {Hasim A. Obaid, Rachid Ouifki, Kailash C. Patidar},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {HIV infection; dynamical systems; nonstandard finite difference methods; equilibria; stability},
language = {eng},
number = {2},
pages = {357-372},
title = {An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection},
url = {http://eudml.org/doc/256684},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Hasim A. Obaid
AU - Rachid Ouifki
AU - Kailash C. Patidar
TI - An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 2
SP - 357
EP - 372
AB - We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
LA - eng
KW - HIV infection; dynamical systems; nonstandard finite difference methods; equilibria; stability
UR - http://eudml.org/doc/256684
ER -

References

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