Global attractivity and permanence of a stage-structured pest management SI model with time delay and diseased pest impulsive transmission

2008 ◽  
Vol 38 (3) ◽  
pp. 658-668 ◽  
Author(s):  
Jianjun Jiao ◽  
Xinzhu Meng ◽  
Lansun Chen
Keyword(s):  
Time Delay ◽  
Pest Management ◽  
Global Attractivity ◽  
Si Model

GLOBAL ATTRACTIVITY AND PERMANENCE OF A STAGE-STRUCTURED PEST MANAGEMENT SI MODEL WITH TIME DELAY AND DISEASED PESTS IMPULSIVE TRANSMISSION

2007 ◽  
Vol 10 (04) ◽  
pp. 479-494
Author(s):  
JIANJUN JIAO ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Pest Management ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Uniformly Ultimately Bounded ◽  
All Solutions ◽  
Si Model

In this work, we consider a stage-structured pest management SI model with time delay and diseased pests impulsive transmission. Sufficient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.

DYNAMIC COMPLEXITIES OF HOLLING TYPE II FUNCTIONAL RESPONSE PREDATOR–PREY SYSTEM WITH DIGEST DELAY AND IMPULSIVE HARVESTING ON THE PREY

2009 ◽  
Vol 02 (02) ◽  
pp. 229-242 ◽  
Author(s):  
JIANWEN JIA ◽  
HUI CAO
Keyword(s):  
Time Delay ◽  
Functional Response ◽  
Impulsive Differential Equation ◽  
Global Attractivity ◽  
Sufficient Condition ◽  
Type Ii ◽  
Predator Prey ◽  
Prey System ◽  
Impulsive Harvesting ◽  
Type Ii Functional Response

In this paper, we introduce and study Holling type II functional response predator–prey system with digest delay and impulsive harvesting on the prey, which contains with periodically pulsed on the prey and time delay on the predator. We investigate the existence and global attractivity of the predator-extinction periodic solutions of the system. By using the theory on delay functional and impulsive differential equation, we obtain the sufficient condition with time delay and impulsive perturbations for the permanence of the system.

scholarly journals A STAGE-STRUCTURED PREDATOR-PREY SI MODEL WITH DISEASE IN THE PREY AND IMPULSIVE EFFECTS

2013 ◽  
Vol 18 (4) ◽  
pp. 505-528 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Tonghua Zhang
Keyword(s):  
Pest Management ◽  
Analytical Techniques ◽  
Stage Structure ◽  
Threshold Level ◽  
Pest Population ◽  
Predator Prey ◽  
Impulsive Delay Differential Equations ◽  
Si Model ◽  
Impulsive Delay ◽  
Delay Differential

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.

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