The dynamics of pest control pollution model with age structure and time delay

In this paper, by using pollution model and impulsive delay differential equation, we investigate the dynamics of a pest control model with age structure for pest by introducing a constant periodic pesticide input and releasing natural enemies at different fixed moment. We assume only the pests are affected by pesticide. We show that there exists a global attractive pest-extinction periodic solution when the periodic natural enemies release amount μ1 and pesticide input amount μ2 are larger than some critical value. Further, the condition for the permanence of the system is also given. By numerical analyses, we also show that constant maturation time delay, pulse pesticide input and pulse releasing of the natural enemies can bring obvious effects on the dynamics of system. We believe that the results will provide reliable tactic basis for the practical pest management.