Nonstandard Finite Difference Schemes for the Study of the Dynamics of the Babesiosis Disease

Abstract

In this paper, a discrete-time model for Babesiosis disease, given by means of nonstandard finite difference (NSFD) schemes, is first provided and analyzed. Mathematical analyses show that the provided NSFD schemes preserve the essential (qualitative) dynamical properties of the continuous-time model, namely, positivity and boundedness of the solutions, equilibria, and their stability properties. In particular, the global stability of the disease free equilibrium point is proved by using an appropriate Lyapunov function. As a relevant consequence, we get the dynamic consistency of NSFD schemes in relation to the continuous-time model. Numerical simulations are presented to support the validity of the established theoretical results.