Prey-predator interaction models were studied, where the predator feeds prefer entially on the most numerous prey type. This implies a kind of switching on the part of the predator towards prey which is in abundance. In chapter two we studied an eco-epidemiological model where prey is infected by a disease and predators feed preferentially on infected prey. We found that harvesting effort played an important role in controlling the disease. Chapter three also presents an eco-epidemiological model, for which we assumed that prey are infected by a fatal disease and after consuming infected prey the predator will eventually die. In chapter four we examined a model where transmission of the disease be tween infected and uninfected prey is nonlinear. In chapter five we investigated an advance time delay model where small prey suppresses their breeding tem porarily due to fear of the predation and restart breeding when the predation pressure lessens. In all models we determined equilibrium points of the systems and investigated dynamic behaviour around equilibrium points, by choosing suit able bifurcation could occur. Numerical simulations were carried out to support analytical results.