A Non-Standard Finite Difference Discretization Scheme Applied to a Malaria Model

Abstract

In this research work, a dynamically consistent non-standard finite difference (NSFD) scheme is developed to solve a continuous-time model of malaria transmission with herbal medicine as control strategy. We compared results from NSFD scheme with the standard finite difference methods (4th order Runge-kutta and forward Euler methods). The numerical investigation showed that the proposed NSFD method remains consistent, preserves the positivity of solutions and converges to true equilibrium points of the continuous model independent of the step size h.