Gumel, A. B.; Mickens, R. E.; Corbett, B. D. A non-standard finite-difference scheme for a model of HIV transmission and control. (English) Zbl 1036.65057 J. Comput. Methods Sci. Eng. 3, No. 1, 91-98 (2003). Summary: An implicitly-derived explicit non-standard finite-difference scheme constructed and used to solve a deterministic nonlinear 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. Cited in 3 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 92-08 Computational methods for problems pertaining to biology 65L12 Finite difference and finite volume methods for ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 92D30 Epidemiology Keywords:HIV transmission and control; Runge-Kutta method; nonstandard finite difference schemes HIV mathematical models PDFBibTeX XMLCite \textit{A. B. Gumel} et al., J. Comput. Methods Sci. Eng. 3, No. 1, 91--98 (2003; Zbl 1036.65057)