A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection

作者：Obaid Hasim A; Ouifki Rachid; Patidar Kailash C^*

来源：Journal of Difference Equations and Applications, 2017, 23(6): 1105-1132.

DOI：10.1080/10236198.2017.1318859

• HIV-TB co-infection
• dynamical systems
• nonstandard finite difference methods
• convergence and stability analysis

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.

• 出版日期2017