Effect of delay on a predator-prey model with parasitic infection

In the paper an eco-epidemic system with delay and parasitic infection in the prey is investigated. The conditions for asymptotic stability of steady states are derived and the length of the delay preserving the stability is also estimated. Further, the criterion for existence of Hopf-type small amplitude periodic oscillations of the predator and prey biomass is derived. Numerical results indicate that the delay does not affect the stability of the system in the process but makes all populations oscillate more intensively. In addition, the results show that the recovery makes the levels of the infected prey and the predator become lower but makes the sound prey higher in limit time.