Copyright © 2009 Bing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Many existing pest control models, which control pests by releasing natural
enemies, neglect the effect that natural enemies may get killed. From this point
of view, we formulate a pest control model with stage structure for the pest with
constant maturation time delay (through-stage time delay) and periodic releasing
natural enemies and natural enemies killed at different fixed time and perform a
systematic mathematical and ecological study. By using the comparison theorem
and analysis method, we obtain the conditions for the global attractivity of the
pest-eradication periodic solution and permanence of the system. We also present
a pest management strategy in which the pest population is kept under the economic
threshold level (ETL) when the pest population is uniformly permanent. We
show that maturation time delay, impulsive releasing, and killing natural enemies can
bring great effects on the dynamics of the system. Numerical simulations confirm
our theoretical results.