ON A PREY–PREDATOR–PATHOGEN MODEL WITH PREY PREFERENCE: A THEORETICAL STUDY

Abstract

In the present paper, we study a prey–predator–pathogen model where the prey population suffer from an SI epidemic. The predator is assumed to exercise preferential predation. The prey preference mechanism ranges from predation only on the susceptible or only on the infective to proportional predation on both the prey types. The formulation maintains the native Holling type-II functional response in one hand and invokes prey switching on the other. We first describe stability and persistence results for the model without preference, which highlights the significance of some system parameters namely, predator mortality rate and predation pressure on the susceptible in shaping the system dynamics. Then we investigate the model with the preference mechanism, which shows the importance of the preference parameter (α) in controlling the stability and existence criteria of component populations. Our study reveals the existence of preference parameter ranges that (i) guarantees stable species coexistence (ii) exhibits rich dynamics in the form of oscillatory phenomena, point attractors and limit cycle attractors and (iii) causes possible extinction of the predators together with the susceptible prey. The ecological meaning of the corresponding ranges is also elaborated.