To study the interaction of parasitoids and their insect hosts in laboratory environment, we propose a mathematical model incorporating impulsive resource inputs, stage-structure, maturation times and negative binomial distribution of parasitoid attacks. According to the adaptability of the insect host to the environment, we obtain conditions under which the system is uniformly permanent in two cases, which guarantee that the host and its parasitoid can coexist. By applying fixed point theory, we show existence of the positive periodic solution where the host and its parasitoid can coexist, and also obtain the conditions that ensure the existence of the parasitoid-extinction periodic solution. Our numerical analysis confirms and extends our theoretical results. The simulations show that when the total amount of resource is fixed, a smaller amount of recourse inputs with a shorter period of impulsive delivery results in smaller oscillation amplitude in the insect host population. However, the development of parasitoid population is not affected by the resource management strategy. It is also demonstrated that larger maturation times, either the host's or the parasitoid's, lead to the decline of the parasitoid population. But larger parasitoid's maturation time does accelerate the host's population growth. These are helpful for us to acquire a deeper knowledge of the host–parasitoid interaction in laboratory environment.

为了研究实验室环境中的寄生虫及其昆虫宿主之间的相互作用，我们提出了一个数学模型，该模型包含了脉冲资源输入，阶段结构，成熟时间和寄生虫攻击的负二项式分布。根据昆虫寄主对环境的适应性，我们获得了在两种情况下该系统均一不变的条件，这保证了该寄主及其寄生体可以共存。通过不动点理论，我们证明了正周期解的存在，在该周期解中宿主及其寄生生物可以共存，并且获得了确保寄生灭绝周期解存在的条件。我们的数值分析证实并扩展了我们的理论结果。仿真表明，当资源总量固定不变时，较少的脉冲输入和较短的脉冲传递时间会导致昆虫寄主种群的振荡幅度较小。但是，类寄生虫种群的发展不受资源管理策略的影响。还证明了，较大的成熟时间，无论是宿主的还是寄生体的，都会导致寄生体种群的减少。但是，较大的寄生虫的成熟时间确实会加速宿主种群的增长。这些有助于我们更深入地了解实验室环境中宿主与寄生虫的相互作用。还证明了较大的成熟时间，无论是宿主的还是寄生的，都会导致寄生种群的减少。但是，较大的寄生虫的成熟时间确实会加速宿主种群的增长。这些有助于我们更深入地了解实验室环境中宿主与寄生虫的相互作用。还证明了较大的成熟时间，无论是宿主的还是寄生的，都会导致寄生种群的减少。但是，较大的寄生虫的成熟时间确实会加速宿主种群的增长。这些有助于我们更深入地了解实验室环境中宿主与寄生虫的相互作用。