Abstract
This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion.
Highlights
Large-scale pest outbreak may bring serious ecological and economic problems to our society
Cotton bollworm outbreaks have caused severe losses of cotton in Xinjiang, Henan, Shandong, Hebei provinces of China in the past two decades; outbreaks of large-scale locusts, which feed on leaves, stems of crops, can cause serious ecological disaster
We further developed impulsive delayed models with staged structure, and investigated a high-dimensional delayed pest management SI model with impulsive natural enemies and diseased pest transmission at different fixed moments
Summary
Large-scale pest outbreak may bring serious ecological and economic problems to our society. Twodimensional delayed stage-structured models with impulsive effect at one fixed impulsive moment have been investigated in [5, 16]. We aim to propose a pest control SI model which is stagestructured for both the pest and the predator by introducing a constant periodic releasing animal enemies and infective pests at two different fixed moments. We propose a high-dimensional delayed predator-prey model with two stage structures and two different fixed moment impulse effects. Meng and Chen introduced a stage-structured SI ecoepidemiological model with time delay and impulsive controlling [14]. We formulate the following delayed pest management SI model with stage structure for both the pests and the predators, and the effects of constant natural enemies and diseased pests impulsive input periodically at two different fixed moments: dSj(t) dt.
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