Population dynamics of plateau pika under lethal control and contraception control

Advances in Difference Equations

Fengqin Zhang¹  Zhen Jin¹  Yuming Chen²  Hanwu Liu³ 

[1] College of Science, North University of China, Taiyuan, China;Department of Applied Mathematics, Yuncheng University, Yuncheng, China;Electromechanical Engineering College, North University of China, Taiyuan, China

关键词: contraception control;    lethal control;    seasonal breeding;    mathematical model;    plateau pika;   

DOI  :  10.1186/1687-1847-2012-29

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The overabundance of plateau pika brings a great damage to the alpine meadow. Rodenticide and sterilant have been used to control this mammalian pest. In this article, we proposed models to incorporate these controls and the seasonal cycle of breeding and non-breeding. It is shown that when the basic reproduction number is less than 1 then the trivial equilibrium is globally asymptotically stable; if the basic reproduction number is greater than 1 then the trivial equilibrium is unstable and there is a positive equilibrium which attracts all positive solutions. Then we study the effects of controls on the existence of the positive equilibrium and the population size. These theoretical results are supported by numerical simulations. We also propose the possible strategies to be implemented in practice. Mathematical Subject Classification: 39A30; 39A60; 92D25.

【 授权许可】

CC BY