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

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.