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

Article type: Research Article

Authors: Gumel, A.B.^{a; 1} | Mickens, R.E.^{b; 2} | Corbett, B.D.^{a; 3}

Affiliations: [a] Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 | [b] Department of Physics, Clark Atlanta University, Atlanta, GA, 30314, USA

Note: [1] E-mail: gumelab@cc.umanitoba.ca.

Note: [2] E-mail: rohrs@math.gatech.edu.

Note: [3] E-mail: umcorbe1@cc.umanitoba.ca.

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: Nonstandard finite difference schemes, numerical integration, HIV mathematical models

Keywords: 65L07, 92-08, 92C50

DOI: 10.3233/JCM-2003-3107

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 1, pp. 91-98, 2003