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

Authors

  • Entsar Matlop Kafi University of Baghdad
  • Azhar A. Majeed

DOI:

https://doi.org/10.24996/ijs.2020.61.8.24

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.  

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Published

2020-08-28

Issue

Section

Mathematics

How to Cite

The Local Bifurcation of an Eco-Epidemiological Model in the Presence of Stage- Structured with Refuge. (2020). Iraqi Journal of Science, 61(8), 2087-2105. https://doi.org/10.24996/ijs.2020.61.8.24

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