Integrated Pest Management with a Mixed Birth Rate for Prey Species

Abstract X. Song and Z. Xiang [7] develop an impulsive differential equations model for a two-prey, one-predator model with stage structure for the predator. They demon-strate the conditions on the impulsive period for which a globally asymptotically stable pest-eradication periodic solution exists, as well as conditions on the im-pulsive period for which the prey species is permanently maintained under an economically acceptable threshold. We extend their model by including stage structure for both predator and prey and also by adding stochastic elements in the birth rate of the prey. As in [7], we find the conditions under which a globally asymptotically stable pest-eradication periodic solution exists.