具有阶段时滞结构的生态-流行病模型的生物防治策略

Biological Control Strategy of Eco-Epidemiology Model of Delayed Stage Structure

分析一个具有一般形式的疾病感染率和功能反应函数的阶段时滞结构的捕食者-食饵(天敌-害虫)模型,利用人工脉冲周期投放有病的害虫和天敌去控制害虫.通过脉冲方程理论,证明了当周期投放量达到一个临界点时,害虫将灭绝;并进一步证明了当投放量控制在一定范围之内时,害虫的密度将在农作物经济危害水平之下并与天敌共存.

A stage structure delayed predator - prey （ natural enemy - pest） model with a general form of incidence rate and response function was analyzed. We controlled the pest by periodically releasing the infected pest and the natural enemy. By using the theory of impulsive differential equation, we first proved that there exists a globally attractive pest - eradication periodic solution when the periodic releasing amount is larger than some critical value. Then, we further proved when the pest population is under the economic threshold level, it may coexist with the predator population.