Population dynamics of plateau pika under lethal control and contraception control

• Published in: Advances in difference equations Vol. 2012; no. 1; pp. 1 - 13
• Main Authors: Liu, Hanwu, Jin, Zhen, Chen, Yuming, Zhang, Fengqin
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 08.03.2012; Springer Nature B.V; BioMed Central Ltd
• Subjects: Analysis; Asymptotic properties; Classification; Computer simulation; Control equipment; Difference and Functional Equations; Functional Analysis; Mathematical models; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Pests; Reproduction; Strategy; mathematical model; lethal control; contraception control; plateau pika; seasonal breeding
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2012-29

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.