Title: Disappearance of limit cycle oscillations in a predator-prey model: role of mortality due to predation of infected prey

Authors: Krishna Pada Das; Subhabrata Ghosh; Somnath Maiti

Addresses: Department of Mathematics, Mahadevananda Mahavidyalaya, Monirampore P.O.-Barrackpore, Kol-120, India ' Department of Botany, Mahadevananda Mahavidyalaya, Monirampore P.O.-Barrackpore, Kol-120, India ' Department of Mathematics, The LNM Institute of Information Technology, Jaipur, Rajasthan, 302031, India

Abstract: This present work establishes an eco-epidemiological model by three elements, namely a susceptible prey, an infected prey and predator. In this situation, the prey population shows its migratory nature. In real life situation, it is observed that a predator dies due to predation of an infected prey or it can even survive after consumption of an infected one. We have found specific conditions under the influence of predational effects for the stability of the system around the coexistence of steady state. Hopf-bifurcation and persistence conditions are also worked out. We simultaneously observe that with an increase in the degree of infection, the system loses its stability and indicate limit cycle oscillation. We have observed that the oscillatory coexistence of the species disappears and the system reaches its steady state position regulated by the conversion efficiency of the predator. Finally, we perform extensive numerical simulations to establish our analytical approach.

Keywords: disease in prey; Malthus growth; non positive restricted parameter; stability; Hopf-bifurcation; permanence.

DOI: 10.1504/IJDSDE.2019.101219

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.3, pp.262 - 285

Received: 10 Sep 2017
Accepted: 08 Mar 2018
Published online: 29 Jul 2019 *

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