Abstract

AbstractThis paper concerns a predator–prey system with migrating and refuging prey with disease infection. Analysis of the model regarding stability has been performed. The effect of time delay on the above system is also studied. By assuming the time delay a bifurcation parameter, the stability of the positive equilibrium, and Hopf-bifurcation is studied. Further, the directions of Hopf-bifurcation and the stability of bifurcated periodic solutions are calculated using the famous normal form theory, Riesz representation theorem and central manifold theorem. This is not a case study, hence real data is not available. However, to verify our theoretical predictions, some numerical simulations are also included.KeywordsPredator–prey modelStabilityHopf-bifurcationMigration RefugeDelay

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