关键词: 染病害虫, 最优脉冲控制, 时间缩放和时间平移, 梯度

Abstract:

In view of the side effects, the technique relying on diseased pest releases as a valuable non-chemical tool is getting much more essentiality in pest management. Inspired by Xiang (2009) and Bhattacharyya et al (2006), the present thesis firstly focuses on a susceptible and infected pest model for pest management, which possesses multiple dynamic behaviors but does not eradicate susceptible individuals. For eliminating the pests, human impulsive interventions are embroiled in this model. Then the sufficient conditions for the global asymptotic stability of the susceptible pest-eradication periodic solution are established by unlimited pulse interventions. However, the strategy driving susceptible pests to extinction is unadvisable from ecological and economical aspects since the appropriate amount of pests in the field is beneficial for conservation of natural enemies and maintaining the crop overcompensation after pest injury. Hence, three different optimal problems involving different pest control tactics are deliberated in order to diminish the susceptible population at the terminal time and keep this in balance with the cost of the intervention (control). Subsequently, by time scaling and translation transformation techniques, the gradients for the cost functional on durations, fractions of susceptible pests killed due to chemical sprays as well as the number of infected pest released at each impulsive intervention moment are computed, which are vital to capture the optimal control strategy for pest regulation. Finally, on the basis of simulations, the strategy of alternative integrated control at unfixed time is validated to be the most effective compared with the other two policies. In addition, by comparing our optimal strategy with pest-extinction one, it is revealed that our strategy is more desirable.

Key words: Infected pest, Optimal impulsive control, Time scaling and time translation, Gradients