An application of nonstandard finite-difference scheme for solving autonomous and non-autonomous mathematical model for Wolbachia-carrying mosquito population dynamics

Abstract

The use of Wolbachia bacterium has been proposed as an alternative strategy against Dengue, Zika and Chikungunya. This requires that Wolbachia-carrying mosquitoes should persist in the population. A number of mathematical models has been developed and analysed to understand Wolbachia-carrying mosquito population dynamics. However, their analytical solutions are not easily derived and therefore, a numerical approach is required. In this paper, we develop a nonstandard finite difference scheme (NSFDS) for autonomous and non-autonomous mathematical models of Wolbachia-carrying mosquito population. The dynamical properties of discrete systems are then analysed. We also perform numerical simulations of the scheme and compare to other traditional methods. We found that the discrete system preserves properties of the continuous models such as equilibrium points and stability.