Analysis of a Prey-predator Model with Disease in Prey  

作　　者：LI JIAN-JUN GAO WEN-JIE SUN PENG 

机构地区：[1]College of Science, Liaoning Technical University, Fuxin, Liaoning, 123000 [2]Institute of Mathematics, Jilin University, Changchun, 130012

出　　处：《Communications in Mathematical Research》2010年第1期27-40,共14页数学研究通讯（英文版）

基　　金：The NSF (10771085) of China;the Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education;the 985 program of Jilin University

摘　　要：In this paper, a system of reaction-diffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the nonconstant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steadystate solution under some conditions.In this paper, a system of reaction-diffusion equations arising in ecoepidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the nonconstant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steadystate solution under some conditions.

关 键 词：ECO-EPIDEMIOLOGY BIFURCATION non-constant positive steady solution 

分 类 号：S853.21[农业科学—临床兽医学] Q141[农业科学—兽医学]