Study of Dynamical Behavior of a Delayed Stage-Structured Predator-Prey Model with Disease in Prey

Abstract

The present paper deals with the dynamics of a stage-structured predator-prey model, with a ratio-dependent functional response including gestational delay in the predator. The prey is carrying an infection which affects the predator adversely. The boundedness of solutions and the stability of equilibrium points have been investigated. There is a Hopf-bifurcation arising out of the variation in the time-delay parameter. Numerical simulations of phase-plane diagrams, and bifurcation diagrams illustrate the dependence of the system on the delay -time. The effect of the disease transmission from prey to predator has also been illustrated through simulations.

Keywords

• stage structured prey-predator model with delay
• boundedness and permanence
• extinction criterion
• stability analysis
• hopf bifurcation
• global stability
• numerical simulation