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RECOVERY OF INFECTED PREY PREVENT LIMIT CYCLE OSCILLATIONS IN SIS PREY-PREDATOR
MODEL
K. Agnihotri
a, N. Juneja
ba Shaheed Bhagat Singh State Technical Campus, Ferozepur, 152004, Punjab, India
b Dev Samaj Post Graduate College For Women, Ferozepur, 152002, Punjab, India
ABSTRACT
The present paper deals with a predator-prey system in which only the prey population is infected with some disease. Consequently the prey population is divided into two categories i.e. the susceptible prey and infected prey. Recovery of the infected prey species is also incorporated. It is assumed that the predator consumes the infected prey only. Predator functional response is assumed to be Holling type II and the disease transmission in prey follows the simple mass action law. Condition for the existence and local as well as global stability of all the feasible equilibrium points are obtained. The conditions for Hopf bifurcation around non zero equilibrium point is also derived. The calculations and numerical simulations shows that the recovery of infected prey species plays a crucial role in creating or removing the limit cycle oscillations and may be used as biological control for the persistence of infected prey-predator dynamics.