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Mathematical Medicine and Biology Advance Access originally published online on November 17, 2008
Mathematical Medicine and Biology 2009 26(2):97-115; doi:10.1093/imammb/dqn025
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Pest management of a prey–predator model with sexual favoritism

Yongzhen Pei{dagger} and Yong Yang{ddagger}

School of Science, Tianjin Polytechnic University, Tianjin 300161, China

Changguo Li

Department of Basic Science of Institute of Military Traffic, Tianjin 300161, China

Lansun Chen

Department of Applied Mathematics, Dalian University of Technology, Dalian 116023, China

{dagger} Corresponding author. Email: peiyongzhen{at}sina.com

{ddagger} Email: yangy1619{at}163.com

Received on April 24, 2008. Revised on October 18, 2008. Accepted on October 22, 2008.

Although sex of prey is an important factor for the risk of predating, few articles consider the consequences of sexual favoritism and the corresponding effects on the impulsive predator–prey dynamics and its utility in biological control. This paper investigates the pest management strategy of a prey–predator system model with sexual favoritism. An impulsive differential equation which models the process of periodically releasing natural enemies and spraying pesticides at different fixed time for pest control is proposed and investigated. It is proved that the pest-eradication periodic solution is globally asymptotically stable under the assumption that the release amount of the predator is greater than some critical value. Permanent conditions are established under the assumption that the release amount of the predator is less than another critical value. In particular, two single control strategies are proposed. Furthermore, we compare three pest control strategies and find that if we choose narrow-spectrum pesticides that targeted to a specific pest's life cycle to kill the pest, then the combined strategy is preferable. Finally, the corresponding system with no sexual favoritism is investigated. The results indicate that we can release fewer amount of the predators to eliminate the preys with sexual favoritism than without and any strong sexual favoritism will drive the pest towards extinction. In view of the biological meaning, the sexual favoritism plays a more active role in suppressing insect pests.

Keywords: prey–predator system; impulsive control; sexual favoritism; extinction; permanence


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