Journal of Applied Mathematics (Jan 2020)

Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

  • Dahlia Khaled Bahlool,
  • Huda Abdul Satar,
  • Hiba Abdullah Ibrahim

DOI
https://doi.org/10.1155/2020/5373817
Journal volume & issue
Vol. 2020

Abstract

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In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.