Study of a discretized fractional-order eco-epidemiological model with prey infection

Abstract

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.

A comprehensive review article on fractional models involving ecology and eco-epidemiology

“…The Adams-Bashforth predictor corrector and a mathematical numerical technique dependent on the Lagrange polynomial has been employed in this manuscript. Mondal et al, [75] have discretized the proposed fractional-order model with piecewise constant argument. This paper used the Jury criterion for determining local stability of the discrete fractional-order system.…”

“…The authors have examined the possibility for finding new dynamical phase portraits with singular and non-singular arbitrary order operator and demonstrate the dynamical phase portraits at various values of arbitrary order. Mondal et al, [75] have taken initiative to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. At first, a fractional-order predator-prey-parasite system with piecewise constant arguments has been discretized.…”

Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

“…In ecological systems, fractional order models have also been used to understand the dynamics of interacting populations [6,7,8,9,10,11,12,13,14]. Lots of researchers are also showing interest to study the dynamics of discretized fractional-order systems and able to find more complex behaviors depending on both the step-size and fractional-order [15,16]. The major reason of using fractional derivatives is that it has the unique property of capturing the history of the variable, that is, it has memory [17,18].…”