Premium
Dynamics of a predator–prey model with disease in the predator
Author(s) -
Pal Pallav Jyoti,
Haque Mainul,
Mandal Prashanta Kumar
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2988
Subject(s) - predator , mathematics , predation , center manifold , stability (learning theory) , hopf bifurcation , functional response , manifold (fluid mechanics) , bifurcation , ecology , biology , physics , nonlinear system , computer science , mechanical engineering , quantum mechanics , machine learning , engineering
The present investigation deals with a predator–prey model with disease that spreads among the predator species only. The predator species is split out into two groups—the susceptible predator and the infected predator both of which feeds on prey species. The stability and bifurcation analyses are carried out and discussed at length. On the basis of the normal form theory and center manifold reduction, the explicit formulae are derived to determine stability and direction of Hopf bifurcating periodic solution. An extensive quantitative analysis has been performed in order to validate the applicability of our model under consideration. Copyright © 2013 John Wiley & Sons, Ltd.