Study On A Pest Management Model With Residual And Delayed Effects Of Pesticides

With the development of agricultural economy,many countries pay more and more attention to the control of pests.How to control pests more effectively has already become an issue in the department of agriculture.At present,chemical control and biological control are two commonly methods to control pests.Long-term single use of the same pesticide will cause pests resistance to pesticide.In this paper,the pests are divided into susceptible pests which are susceptible to pesticides and resistant pests which are resistant to pesticides.We assume that the pesticides have residual effect and delayed response on the pests.A continuous exponential function with time is introduced as the pesticide function,and the pest management models with residual and delayed effects of pesticides and resistance development are established and studied.In the first chapter,the preliminary knowledge needed for our research is given.In the second chapter,the model of pest management with resistance development under chemical control is studied.We assume that the pest population satisfy the Logistic growth.Considering the pesticides have residual and delayed effects on pests,a pest management model with resistance development is established by introducing pesticide function.Then the pest eradication threshold R0(n,T)is obtained by analysis method.Numerical simulations are used to analyze the effects of various factors on the development of pest resistance and the pest eradication threshold.Further analysis shows that with the increase of the spraying times.R0(n,T)will be greater than 1 eventually,that is,with the growth of resistance,the pests will outbreak eventually.In order to control pests,the pesticides switching strategy based on R0(n,T)is given.In the third chapter,on the basis of the second chapter,biological control is introduced.Firstly,an integrated pest management model with impulse at fixed-time is established considering the residual and delayed effects of pesticides and pest resistance development to pesticide.The pest eradication threshold R01(n,T)related to chemical and biological control is obtained by analytical methods and comparison theorem of impulsive differential equations.The results show that the integrated pest management is more effective than any single control,and simultaneously,the three-dimensional graphs and contour lines of R01(n,T)with the change of two parameters are given.In order to eradicate pests,two pest management strategies are given in this chapter:the first is to switch pesticides according to the pest eradication threshold R01(n,T),and the second is to dynamically change the amount of the released natural enemies.Secondly,in order to analyze the effect of each parameter on R01(n,T),sensitivity analysis of each parameter about R01(n,T)is carried out.Studies have shown that parameters r,T,? always play key roles in pests management.When pesticides are sprayed less frequently,parameters related to pesticides have strong effects on pests control.The increase of killing rate and delayed response rate promotes the pest control.However,when spraying pesticides more frequently,with the development of resistance to pesticides,the effect of pesticides on pests will be weaken,continuing to spray pesticides can not be effectively control pests.The study shows that the increase of r,T,a1,c1,c2 causes an increase of R01(n,T)and the increase of m1,a2,m2,? causes a decrease in R01(n,T).Finally,in order to reduce the frequency of spraying pesticides,pesticides are sprayed only when the pest population density reaches economic threshold.Based on periodic releases of natural enemies,a state-dependent integrated pest management model with economic threshold is established.The results show that the frequency of spraying pesticides needed to control pests below the economic injury level depends on the amount of natural enemies.If pests are resistant to pesticides,it necessitates that pesticides should be sprayed more frequently and at shorter intervals.