Modelling approach for biological control of insect pest by releasing infected pest

Abstract

Models of biological control have a long history of theoretical development that have focused on the interactions between a predator and a prey. Here we have extended the classical epidemic model to include a continuous and impulsive pest control strategies by releasing the infected pests bred in laboratory. For the continuous model, the results imply that the susceptible pest goes to extinct if the threshold condition R 0 < 1. While R 0 > 1, the positive equilibrium of continuous model is globally asymptotically stable. Similarly, the threshold condition which guarantees the global stability of the susceptible pest-eradication periodic solution is obtained for the model with impulsive control strategy. Consequently, based on the results obtained in this paper, the control strategies which maintain the pests below an acceptably low level are discussed by controlling the release rate and impulsive period. Finally, the biological implications of the results and the efficiency of two control strategies are also discussed.