Abstract
The present paper deals with the problem of a ratio-dependent 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, local and global stability are addressed. We have also studied the effect of discrete time delay on the model. 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 ecology and mathematical ecology due to its universal existence and importance
We have investigated the dynamical behaviour of a ratio-dependent predator-prey systems with infection in prey population, and the effect of refuge in the infected prey
It is reasonable to assume that the effect of the infected prey on the predator population will not be instantaneous, but mediated by some discrete time lag τ required for incubation
Summary
The dynamic relationship between predator and their prey has long been and will continue to be one of the dominant topics in both ecology and mathematical 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. Such refugia are usually playing two significant role, serving both to reduce the chance of extinction due to predation and to damp prey-predator oscillations These are a potentially important means of increasing species richness in natural communities and of stabilizing population sizes, biomass and productivity. Hassel [12] 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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