Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species

Mainul Haque, Sahabuddin Sarwardi, Simon Preston, Ezio Venturino

Research output: Journal PublicationArticlepeer-review

46 Citations (Scopus)

Abstract

We consider a system of delay differential equations modeling the predator-prey ecoepidemic dynamics with a transmissible disease in the predator population. The time lag in the delay terms represents the predator gestation period. We analyze essential mathematical features of the proposed model such as local and global stability and in addition study the bifurcations arising in some selected situations. Threshold values for a few parameters determining the feasibility and stability conditions of some equilibria are discovered and similarly a threshold is identified for the disease to die out. The parameter thresholds under which the system admits a Hopf bifurcation are investigated both in the presence of zero and non-zero time lag. Numerical simulations support our theoretical analysis.

Original languageEnglish
Pages (from-to)47-57
Number of pages11
JournalMathematical Biosciences
Volume234
Issue number1
DOIs
Publication statusPublished - Nov 2011
Externally publishedYes

Keywords

  • Delay
  • Ecoepidemic models
  • Global stability
  • Hopf-bifurcation
  • Local stability
  • Population models

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology (all)
  • Immunology and Microbiology (all)
  • Agricultural and Biological Sciences (all)
  • Applied Mathematics

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