Discretization of an eco-epidemiological model and its dynamic consistency

Abstract

In this paper, we discretize a continuous-time eco-epidemiological model by non-standard finite difference (NSFD) scheme as well as standard Euler forward scheme. Dynamical properties of both the systems are explored and compared with their continuous-time model. We show that the solution of NSFD system remains positive for all positive initial values. Fixed points and their local stability properties are shown to be identical with that of the continuous model, indicating its dynamic consistency. Dynamics of the Euler model, however, depend on the step–size and therefore dynamically inconsistent. Solutions in this latter method may be negative and allows numerical instabilities, leading to chaos. Extensive numerical simulations have been performed to validate the theoretical results.

Keywords:

• Predator-prey-parasites model
• non-standard finite-difference scheme
• Euler forward scheme
• dynamic consistency
• stability
• chaos

AMS Subject Classifications:

• 92B05
• 92D25
• 92D40

Notes

No potential conflict of interest was reported by the authors.