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Stability and Hopf bifurcation of a Holling type II Predator-Prey Model with disease in the prey
Abstract
A predator-prey model with disease on the prey and Holling type II functional response for both infected and susceptible prey is proposed and analyzed based on the mathematical features. First we discussed the boundedness and all feasible equilibrium of the given system. By using the Routh-Hurwitz Criteria and appropriate Lyapunov functions, the local and global stability analysis are examined. Conditions for persistence of the system are derived. The existence of Hopf bifurcation is investigated by analyzing the distribution of eigenvalues at the positive equilibrium point. Moreover we use the normal form method and center manifold theorem to investigate the direction of the Hopf bifurcation and stability of the bifurcating limit cycle. To check our theoretical findings, some numerical results are work out.
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