一个阶段时滞结构的生态-流行病模型的害虫综合防治策略  

Strategy for Integrated Pest Management on the Eco-epidemiology Model of Delayed Stage Structure

作　　者：祝光湖[1] 陈兰荪[1,2] 

机构地区：[1]福建师范大学闽南科技学院,福建泉州362332 [2]中国科学院数学与系统科学研究院,北京100080

出　　处：《重庆文理学院学报（自然科学版）》2008年第6期1-5,共5页Journal of Chongqing University of Arts and Sciences

基　　金：国家自然科学基金(10771179)

摘　　要：分析一个阶段结构的捕食者-食饵(天敌-害虫)模型,利用人工周期定量地投放有病的害虫和天敌去治理害虫.通过脉冲微分方程理论,证明了周期投放量p和q满足β2q(exp(mT)-1)/(exp(d4T)-1)(exp((m+d4)T)-1)+β1p/(exp(d3T)-1)>be-d1τ时,害虫幼虫及成虫将灭绝,而病虫和天敌的密度驱于一个稳定的水平,并进一步证明了当周期投放量p和q满足be-d1τ-d2E<β2q(exp(mT)-1)/(exp(d4T)-1)(exp((m+d4)T)-1)+β1p/(exp(d3T)-1)>be-d1τ时,害虫的密度将在经济受害损失允许水平之下并与天敌共存.Abstract： This paper deals with a stage structure predator - prey （ natural enemy - pest） model . It obtains an integrated pest management strategy by periodically releasing the infected pest and the natural predators. By using the theory of impulsive differential equation, we prove that the larva and imago will perish when the periodic releasing amount p and q satisfy β2q（exp（mT）-1/（exp（d4T）-1）exp（（m＋d4）T）-1）＋β1p/exp（d3T）-1〉be^-d1τ.Then we prove that when be^-d1τ-d2E〈β2q（exp（mT）-1/（exp（d4T）-1）exp（（m＋d4）T）-1）＋β1p/exp（d3T）-1〉be^-d1τ, the pest population is below the economic threshold level and it may coexist with the predator population.

关 键 词：阶段时滞结构 生态-流行病模型 综合防治 脉冲效应 全局吸引 

分 类 号：O175.14[理学—数学]