Diseased prey predator model with general Holling type interactions

• Published in: Applied mathematics and computation Vol. 226; pp. 83 - 100
• Main Authors: Sahoo, Banshidhar, Poria, Swarup
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.01.2014
• Subjects: Bifurcation; Bifurcations; Disease; Food chain; General Holling; Hopf point; Mathematical analysis; Mathematical models; Oscillations; Packages; Permanence; Predators; Stability; Bifurcation; Hopf point; Stability; Disease; Permanence; General Holling
• ISSN: 0096-3003; 1873-5649; 0096-3003
• DOI: 10.1016/j.amc.2013.10.013

Choice of interaction function is one of the most important parts for modelling a food chain. Many models have been proposed as a diseased-prey predator model with Holling type-I or type-II or type-III interactions, but there is no model with general Holling type interactions. In this paper, we study a diseased prey–predator model with general Holling type interactions. Local stability conditions of equilibrium points are derived. We obtain the permanence and impermanence conditions of the system. The conditions for global stability of the system are also derived. The system exhibits limit cycle, period-2, higher periodic oscillations and chaotic behaviour for different values of Holling parameters. One parameter bifurcation analysis is done with respect to general Holling parameters and infection rate. We utilize the MATCONT package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied. It is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions. Our results give an idea for constructing a realistic food chain model through proper choice of general Holling parameters.