Open Access Open Access  Restricted Access Subscription or Fee Access

Stability and Hopf bifurcation of a Holling type II Predator-Prey Model with disease in the prey

M. Sambath, C. Gokila


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.


Tilapia, Pelican, Stability, Lyapunov function, Hopf bifurcation.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.