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Analysis and optimization based on a sex pheromone and pesticide pest model with gestation delay

Sex pheromone, aiming at mating disruption (MD), being species specific and leaving no toxic residues in the produce grown, offers an attractive alternative to conventional pesticides. In this paper, by incorporating the gestation delay and sex pheromone, we explore the impact of MD control on the dynamic behaviors of pest system. Firstly, the boundness, stability and bifurcation of system are deliberated. Secondly, an optimal control problem based on sex pheromone and pesticide is transformed into an equivalent optimal parameter selection problem by introducing the constrain violation function. Additionally, the gradients of the cost function with respect to the dose of sex pheromone and the killing rate are given. Furthermore, simulations are executed to validate the validity of our method. Meanwhile, our results indicate that gestation delay increases the extinction risk of the population and liberating sex pheromone destroys the stability of equilibrium states.