  In this paper, an attempt is made to understand the dynamics of a
three-dimensional discrete fractional-order eco-epidemiological model with
Holling type II functional response. We first discretize a fractional-order
predator-prey-parasite system with piecewise constant arguments and then
explore the system dynamics. Analytical conditions for the local stability of
different fixed points have been determined using the Jury criterion. Several
examples are given to substantiate the analytical results. Our analysis shows
that stability of the discrete fractional order system strongly depends on the
step-size and the fractional order. More specifically, the critical value of
the step-size, where the switching of stability occurs, decreases as the order
of the fractional derivative decreases. Simulation results explore that the
discrete fractional-order system may also exhibit complex dynamics, like chaos,
for higher step-size.
