Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control

Abstract

A general predator-prey model with disease in the prey and double impulsive control is proposed and investigated for the purpose of integrated pest management. By using the Floquet theory, the comparison theorem of impulsive differential equations, and the persistence theory of dynamical systems, we obtain that if threshold value 0 < 1, then the susceptible pest eradication periodic solution is globally asymptotically stable and if 0 > 1, then the model is permanent. The numerical examples not only illustrate the theoretical results, but also show that when the model is permanent, then it may possess a unique globally attractive -periodic solution.