Dynamic consistent non-standard numerical scheme for a dengue disease transmission model

This work deals with the relationship between a dengue disease transmission model and numerical methods for its computer simulations, viewed as discrete dynamical systems. Dynamic consistency is defined with respect to particular properties of a system and generally these properties will vary from one system to another. Here, this concept means that discretization scheme preserves correct number and stability of the equilibria, the positivity and the boundedness of the solutions for the corresponding continuous-time model. Using discrete-time analogue of Lyapunov functions, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number independent of the time step size h, which is consistent with the corresponding continuous system. Finally, numerical simulations are presented to illustrate our theoretical results.