Abstract
Normally, chemical pesticides kill not only pests but also their natural enemies. In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. The effects of key parameters including killing efficiency rate, pulse period, the maximum birth effort per unit of time of natural enemy, and maturation time of prey on the threshold values are discussed in more detail. By comparing the two threshold values of mature prey-extinction, we provide the fact that the second control tactic is more effective than the first control method.
Highlights
The outbreak of pest often triggers serious ecological and economic problems
R1∗, R1 the effect of two > R1∗; this result indicates that if natural enemies were born at the same time as spraying insecticide, the side-effects of pesticides on the natural enemy population are very strong
When using integrated pest management as an approach to control insect pests, one must be committed to a long-term strategy
Summary
The outbreak of pest often triggers serious ecological and economic problems. In recent years, the management of pest has increasingly become the focus of attention. It is necessary to account for these differences, and the dynamics of mathematical models with stage-structured prey-predator model has been widely studied [5–11] in recent years. Time delay and stage-structured systems are introduced into predator-prey models, which greatly enriches biologic background. Tang and Chen study an age-structured model with density-dependent birth pulse in [16] and Xiang et al [17] have considered a delayed Lotka-Volterra model with birth pulse and impulsive effect at different moment on the prey. The qualitative analysis of impulsive differential equations at different moments has been widely investigated in many works [21–23]. Following the practical pest management, we firstly propose the predator-prey model with pulse at the same time. We assumed that the birth pulse and pest control tactics occur at different time. Discussing and comparing the mature prey-extinction of the two models, we get some new effective pest management
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