<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematics and Applied Mathematics University of the Western Cape, Bellville 7535, South Africa

DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis Stellenbosch University, Stellenbosch 7600, South Africa

Department of Mathematics and Applied Mathematics University of the Western Cape, Private Bag X17, Bellville 7535, South Africa

International Journal of Applied Mathematics and Computer Science

We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of...

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

Publié en ligne: 28 juin 2013

Pages: 357 - 372

DOI: https://doi.org/10.2478/amcs-2013-0027

This content is open access.