A Leslie-Gower Holling Type-II Predator-Prey Mathematical Model with Disease in Prey Population Incorporating a Prey Refuge  

作　　者：P. Mandal N. Das S. Pal 

机构地区：[1]Department of Mathematics, Hooghly Mohsin College, Chinsurah, Hooghly, India. [2]Department of Mathematics, Maulana Azad College, Kolkata, India. [3]Department of Mathematics, University of Kalyani, Nadia, lndia.

出　　处：《Journal of Mathematics and System Science》2016年第10期395-408,共14页数学和系统科学（英文版）

摘　　要：We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.

关 键 词：Predator and prey Disease transmission Prey refuge Stability Hopf-bifurcation. 

分 类 号：Q141[生物学—生态学] O141.4[生物学—普通生物学]