Study On The Pest Control Model With Resistance Development Under Different Frequency Control Measures

Chemical pesticides are widely used in the countries all over the world and play an important role in the development of agricultural production.However,pesticides also cause pollution to soil,water and atmospheric environment,which in turn causes harm to human health.At the same time,the susceptible pests will develop resistance if we use the same pesticide frequently.Based on the above biological background,in this paper,a piecewise continuous negative exponential function is taken to simulate the action of the pesticide,the hybrid dynamic system is used to simulate the process of pest control considering the development of pest resistance to pesticides,and then pest control models with resistance development under different frequency control measures are established and studied.In the first chapter,it assumes that pests are divided into susceptible pests and infected pests,and that only susceptible pests cause damage to crops.We consider to control susceptible pests by spraying pesticides and releasing infected pests.Assuming that only susceptible pests are resistant to pesticides,a pest control model with resistance development is established with spraying pesticides more frequently than releasing infected pests.The sufficient condition of global attractiveness of susceptible pest eradication periodic solution is given by using the basic theories of impulsive differential system and analysis methods.Further,the effect of the frequency of spraying pesticides on the threshold of controlling the eradication of susceptible pest is analyzed by numerical simulations.It concludes that it is not true the more frequently the pesticides is sprayed,the better the pest control.Finally,the method of the releasing infected pests for the eradication of susceptible pests is determined.In the second chapter,natural enemies are introduced on the basis of the research in the first chapter,and an integrated pest control model with the resistance development under the different frequency of spraying pesticides and releasing infected pests and natural enemies is established.Firstly,the critical condition for eradicating susceptible pests is obtained,and the effects of the frequency of spraying pesticide on the threshold R01(h,TN)of susceptible pest eradication are analyzed when the decay rate ?1 and impulsive period TN are taken different values,respectively.Then the switching strategy of pesticides is given according to the threshold condition.Finally,the parameters in the threshold R01(h,TN)are analyzed:(1)we use the method of LHS to estimate PRCC.PRCC is an estimation method of the uncertain influence of input parameters on the value of output variables.It shows that the birth rate r,the death rate d1,d2 of infected pests and natural enemies and impulsive period TN are positive correlation with R01(h,TN),the releasing amount ?1,?2 of infected pests and natural enemies are negative correlation with R01(h,TN).With the increase of the frequency h of spraying pesticides,the correlation of the killing efficiency rate m1 of pesticides on susceptible pest and the decay rate ?1 with R01(h,TN)varies.Since the absolute value of PRCC of r,TN,?1,?2,is over 0.4,it shows that these four parameters have great effects on R01(h,TN)and play important roles in pest control;(2)we simulate the three-dimensional graph and the corresponding contour with the change of two parameters,analyze the effects of the change of parameters on the threshold,and obtain the key factors of controlling susceptible pests.