Title: Role of harvesting in controlling chaos and disease propagation in predator-prey system with disease in prey

Authors: Prodip Roy; Krishna Pada Das; Partha Karmakar; Seema Sarkar (Mondal)

Addresses: Department of Mathematics, Mahadevananda Mahavidyalaya, Monirampore, Barrackpore, Kol-120, 700120, India ' Department of Mathematics, Mahadevananda Mahavidyalaya, Monirampore, Barrackpore, Kol-120, 700120, India ' Department of Mathematics, Muragachha Government College, Nadia, 741154, India ' Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, 713209, India

Abstract: The paper explores an eco-epidemiological model with harvesting in the species and the disease is circulating in the prey population. The curiosity of this paper is to consider the role of harvesting on chaotic dynamics. We perform the local and global stability analysis of the equilibrium points and the Hopf bifurcation analysis around the interior equilibrium point. Further we pay attention to the direction of Hopf Bifurcation. Our numerical simulations reveal that the three species eco-epidemiological system shows chaos in low level of infection. It is observed that when force of infection increases chaos becomes stable. We conclude that chaotic dynamics can be controlled by the harvesting parameter as well as the force of infection.We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to identify chaotic behaviour of the system.

Keywords: disease in prey; stable; permanence; impermanence; chaos; Lyapunov exponent.

DOI: 10.1504/IJDSDE.2019.101218

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.3, pp.234 - 261

Received: 11 Aug 2017
Accepted: 24 Feb 2018
Published online: 29 Jul 2019 *

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