A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection |
| |
| Authors: | Hasim A Obaid Rachid Ouifki |
| |
| Institution: | 1. Department of Mathematics and Applied Mathematics, University of the Western Cape, Bellville, South Africa.;2. DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, South Africa. |
| |
| Abstract: | We design and analyze an unconditionally convergent nonstandard finite-difference method to study transmission dynamics of a mathematical model of HIV-TB co-infection. 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 positivity of the solution which is one of the essential requirements when modelling epidemic diseases. Furthermore, we show that the numerical method is unconditionally stable. Competitive numerical results confirming theoretical investigations are provided. Comparisons are also made with other conventional approaches that are routinely used to solve these types of problems. |
| |
| Keywords: | HIV-TB co-infection dynamical systems nonstandard finite difference methods convergence and stability analysis |
|
