# 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

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topHasim 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 -

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