The Local Bifurcation of an Eco-Epidemiological Model in the Presence of Stage- Structured with Refuge

  • Entsar Matlop Kafi University of Baghdad
  • Azhar A. Majeed
Keywords: Prey- predator, Eco-epidemiological, SI epidemic disease function, Local bifurcation. model, Refuge, Stag- structure, Lyapunove

Abstract

In this paper, we establish the conditions of the occurrence of the local bifurcations, such as saddle node, transcritical and pitchfork, of all equilibrium points of an eco-epidemiological model consisting of a prey-predator model with SI (susceptible-infected) epidemic diseases in prey population only and a refuge-stage structure in the predators. It is observed that there is a transcritical bifurcation near the axial and free predator equilibrium points, near disease-free equilibrium point is a saddle-node bifurcation and near positive (coexistence) equilibrium point is a saddle-node bifurcation, a transcritical bifurcation and a pitchfork bifurcation. Further investigations for Hopf bifurcation near coexistence equilibrium point are carried out. Finally, numerical simulations are used to illustrate the occurrence of the local bifurcations of this model.  

Published
2020-08-28
How to Cite
Kafi, E. M., & Majeed, A. A. (2020). The Local Bifurcation of an Eco-Epidemiological Model in the Presence of Stage- Structured with Refuge. Iraqi Journal of Science, 61(8), 2087-2105. https://doi.org/10.24996/ijs.2020.61.8.24
Section
Mathematics