The Optimal Profit Analysis Of The Pest Control Model Based On The Execution Threshold

Many important applications in life sciences,agriculture and medicine can be described and characterized by impulsive semi-dynamic systems.For example,in an integrated pest management(IPM)strategy,control actions are taken when the pest population reaches the economic threshold.Such control strategy can be described by the state-dependent impulsive model.In recent years,many scholars have stud-ied a variety of integrated pest management models based on economic threshold.The existence and stability of pest eradication periodic solutions and the effects of integrated control strategies on the critical conditions of stability are analyzed.However,these works are based on an assumption that whether the implementation of pest control is only depend on pests population density.In real life,a more realistic case is that whether the control action applied should rely on the combination of pest density and its growth rate.Therefore,in the present paper we propose a novel pest control and resources management model,i.e.a state-ratio dependent pest control model which the action threshold is the weighted sum of pest density and its growth rate is formulated.Assuming that the growth of pest population follows the laws of Logistic growth without control measures,the basic dynamics related to the occurrence of impulsive perturbations have been first addressed,and the critical conditions at which the system experience pest control are given.When the system degenerates into a general state-dependent impulse model,the analytical solutions,periodic solutions and periodic expressions are given.The purpose of pest control is to reduce the losses caused by pests and improve the farmers'income.Therefore,this paper introduces the profit function according to the yield and price of crops and the cost of pest control.The aim of this paper is to find the optimal control strategy for maximizing farmers' income.Chapter 3 of this paper considers the chemical control of pests under two different impulsive conditions with single pesticide application and multiple pesticide applications be-fore harvesting time.The optimal threshold and dosage are given for different cases respectively.By using analytical techniques and numerical investigations,the suffi-cient conditions for the existence of optimal action threshold and pesticide dosage under one time impulsive chemical control are given and verified.In the period-is impulsive control,under the assumption that the pests population reaches the threshold four times,we use numerical investigate to verify the existence conditions of the maximum benefit,the optimal threshold and the optimal pesticide dosage.In addition,the effects of the number of pesticide applications on the existences of the optimal threshold and the maximum profit are discussed.Finally,some biological implications concerning the pest control have been discussed.