Effect of insecticide on the population dynamics of brown planthoppers and Cyrtorhinus lividipennis: a modeling approach

Abstract

In this paper, we investigate the effect of insecticide on the population dynamics of brown planthoppers (a major insect pest of rice) and Cyrtorhinus lividipennis (one of the natural enemies of brown planthoppers) by developing an impulsive mathematical model, and we analyze the model theoretically and numerically. The conditions on the parameters of the model for which the stability and permanence of the system can be ensured are derived. Computer simulations are also presented to confirm our theoretical results. The results show that with an appropriate amount and period between two consecutive applications of insecticide, the population of brown planthoppers could be maintained below a certain level, while Cyrtorhinus lividipennis could also survive.