Abstract
A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest-extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest-extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation.
Highlights
Since the beginning of recorded history, outbreaks of pests have plagued humanity, coming in direct competition with people for life-sustaining food
The most effective strategy for controlling pests may be to combine methods in an approach known as integrated pest management IPM that emphasizes preventing pest damage
It is necessary to introduce the pollution model to model the process of pest-control problems and study its dynamics, and this is different from the previous pest-control model which assumed that pests were reduced proportionally by spraying pesticides
Summary
Since the beginning of recorded history, outbreaks of pests have plagued humanity, coming in direct competition with people for life-sustaining food. This fact urges us to consider the effect of pollution time delay on the extinction and permanence of population in a polluted environment With this in mind, it is necessary to introduce the pollution model to model the process of pest-control problems and study its dynamics, and this is different from the previous pest-control model which assumed that pests were reduced proportionally by spraying pesticides. By using pollution model and impulsive delay differential equation, Liu et al 19 constructed, and investigated, a pest-control model with age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. Based on all the above points, in this paper, we propose and investigate a pest-control model with a constant periodic pesticide input and natural enemies release at different fixed moment, in which the effects of impulsive pesticide input in the environment and in the organism are considered. A brief discussion is given to conclude this work
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