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Darti, Isnani
Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Gorontalo
Social Sciences

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Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey Panigoro, Hasan S.; Suryanto, Agus; Kusumahwinahyu, Wuryansari Muharini; Darti, Isnani
Communication in Biomathematical Sciences Vol 2, No 2 (2019)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2363.045 KB) | DOI: 10.5614/cbms.2019.2.2.4

Abstract

In this paper, a dynamical analysis of a fractional-order predator-prey model with infectious diseases in prey is performed. First, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. We also show that the model has at most five equilibrium points, namely the origin, the infected prey and predator extinction point, the infected prey extinction point, the predator extinction point, and the co-existence point. For the first four equilibrium points, we show that the local stability properties of the fractional-order system are the same as the first-order system, but for the co-existence point, we have different local stability properties.We also present the global stability of each equilibrium points except for the origin point. We observe an interesting phenomenon, namely the occurrence of Hopf bifurcation around the co-existence equilibrium point driven by the order of fractional derivative. Moreover, we show some numerical simulations based on a predictor-corrector scheme to illustrate the result of our dynamical analysis.
Co-Authors Hasan S. Panigoro Kusumahwinahyu, Wuryansari Muharini Suryanto, Agus