Effect of delay on globally stable prey-predator system

The present paper deals with an eco-epidemiological prey-predator model with delay. It is assumed that infection floats in predator species only. Both the susceptible and infected predator species are subjected to harvesting at different harvesting rates. Differential predation rates for susceptible and infected predators are considered. It is shown that the time delay can even destabilize the otherwise globally stable non-zero equilibrium state. It is observed that coexistence of all the three species is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and central manifold arguments, stability of bifurcating periodic orbits is determined. Numerical simulations have been carried out to justify the theoretical results obtained.