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Journal of Biological Physics

, Volume 37, Issue 1, pp 91–106 | Cite as

Global stability and persistence in LG–Holling type II diseased predator ecosystems

  • Sahabuddin Sarwardi
  • Mainul Haque
  • Ezio VenturinoEmail author
Original Paper

Abstract

A Leslie–Gower–Holling type II model is modified to introduce a contagious disease in the predator population, assuming that disease cannot propagate to the prey. All the system’s equilibria are determined and the behaviour of the system near them is investigated. The main mathematical issues are global stability and bifurcations for some of the equilibria, together with sufficient conditions for persistence of the ecosystem. Counterintuitive results on the role played by intraspecific competition are highlighted.

Keywords

Ecoepidemiology Population models Epidemic models Boundedness Persistence Local stability Global stability Lyapunov function Hopf bifurcation 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Sahabuddin Sarwardi
    • 1
  • Mainul Haque
    • 2
  • Ezio Venturino
    • 3
    Email author
  1. 1.Department of MathematicsAliah UniversityKolkataIndia
  2. 2.School of Mathematical ScienceUniversity of NottinghamNottinghamUK
  3. 3.Dipartimento di Matematica “Giuseppe Peano”Università di TorinoTurinItaly

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