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In this work, the control of brown planthopper, a major pest of rice, when a biological control agent (Cyrtorhinus lividipennis) and a pathogen (Beauveria bassiana) are utilized is investigated mathematically. An impulsive mathematical model accounted for the population densities of susceptible brown planthoppers (brown planthoppers that are susceptible to Beauveria bassiana), infected brown planthoppers (brown planthoppers that are infected by Beauveria bassiana), and Cyrtorhinus lividipennis (a natural enemy of brown planthopper) is developed. We analyze the model in terms of its stability and permanence so that we obtain the conditions that differentiate dynamic behaviors exhibited by the model. To illustrate our theoretical results, computer simulations are also presented.

Dynamical modeling of the control of brown planthoppers by Beauveria bassiana and Cyrtorhinus lividipennis