Abstract
The present paper deals with the problem of a predator-prey model incorporating a prey refuge with disease in the prey-population. We assume the predator population will prefer only infected population for their diet as those are more vulnerable. Dynamical behaviours such as boundedness, permanence, local and global stabilities are addressed. We have also studied the effect of discrete time delay on the model. The length of delay preserving the stability is also estimated. Computer simulations are carried out to illustrate our analytical findings.
Highlights
The dynamic relationship between predator and their prey has long been and will continue to be one of the dominant topics in both applied mathematics and theoretical ecology due to its universal existence and importance
Most of the studies mainly focused on parasite infection in prey population only [6,7,8,9]
The dynamics of predator-prey system with infection in prey population is an important study from modelling point of view
Summary
The dynamic relationship between predator and their prey has long been and will continue to be one of the dominant topics in both applied mathematics and theoretical ecology due to its universal existence and importance. The dynamics of predator-prey system with infection in prey population is an important study from modelling point of view. The research of the hiding behaviour of preys has been incorporated as a new ingredient of prey-predator models and its consequences on the dynamics of prey-predator interactions can be recognized as one of the major issues in both applied mathematics and theoretical ecology. Prey populations often access to areas where they are safe from their predators Such refugia are usually playing two significant roles, serving both to reduce the chance of extinction due to predation and to damp preypredator oscillations. Hassel [13] showed that adding a large refuge to a model, which exhibited divergent oscillations in the absence of refuge, replaced the oscillatory behaviour with a stable equilibrium These mathematical models and a number of experiments indicate that refuge have a stabilizing effect on predator-prey interactions.
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