A stage-structured predator-prey si model with disease in the prey and impulsive effects

    Tongqian Zhang Info
    Xinzhu Meng Info
    Yi Song Info
    Tonghua Zhang Info

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.

Keywords:

age-structured population, delay, impulsive differential equation, global asymptotic stability, predator-prey model

How to Cite

Zhang, T., Meng, X., Song, Y., & Zhang, T. (2013). A stage-structured predator-prey si model with disease in the prey and impulsive effects. Mathematical Modelling and Analysis, 18(4), 505-528. https://doi.org/10.3846/13926292.2013.840866

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September 1, 2013
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2013-09-01

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How to Cite

Zhang, T., Meng, X., Song, Y., & Zhang, T. (2013). A stage-structured predator-prey si model with disease in the prey and impulsive effects. Mathematical Modelling and Analysis, 18(4), 505-528. https://doi.org/10.3846/13926292.2013.840866

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