Table of Contents
Journal of Nonlinear Dynamics
Volume 2015, Article ID 948728, 13 pages
http://dx.doi.org/10.1155/2015/948728
Research Article

Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control

1Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
2Shibpur Sri Ramkrishna Vidyalaya, 92 Kshetra Banerjee Lane, Shibpur, Howrah 711102, India
3Department of Mathematics, Abhedananda Mahavidyalaya, Sainthia, West Bengal 731234, India
4Department of Mathematics, Sundarban Hazi Desarat College, Pathankhali, West Bengal 743611, India

Received 31 May 2015; Accepted 12 November 2015

Academic Editor: Ivo Petras

Copyright © 2015 Swapan Kumar Nandi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A prey-predator model system is developed; specifically the disease is considered into the prey population. Here the prey population is taken as pest and the predators consume the selected pest. Moreover, we assume that the prey species is infected with a viral disease forming into susceptible and two-stage infected classes, and the early stage of infected prey is more vulnerable to predation by the predator. Also, it is assumed that the later stage of infected pests is not eaten by the predator. Different equilibria of the system are investigated and their stability analysis and Hopf bifurcation of the system around the interior equilibriums are discussed. A modified model has been constructed by considering some alternative source of food for the predator population and the dynamical behavior of the modified model has been investigated. We have demonstrated the analytical results by numerical analysis by taking some simulated set of parameter values.