Modelling the Effects of Pest Control with Development of Pesticide Resistance

In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive differential systems and analytical methods,the sufficient condition for the global attractiveness of the susceptible pest eradication periodic solution is given.Combined with numerical simulations,the effects of spraying frequency of pesticides on critical threshold conditions for eradicating susceptible pests are discussed.The results confirm that it is not that the more frequently the pesticides are sprayed,the better the result of the pest control is.Two control strategies for eradicating susceptible pests are proposed:switching pesticides and releasing natural enemies elastically.Finally,the parameters in the critical threshold are analyzed from the following two aspects:(1)The key factors affecting pest control are determined by parameter sensitivity analyses.The results indicate that the correlation of the critical threshold concerning the killing efficiency rate and the decay rate of pesticides to susceptible pests varies due to the resistance development of susceptible pests.(2)Three-dimensional graphs and contours of susceptible pest eradication critical threshold with two parameters are simulated,and the effects of the main parameters on the critical threshold are analyzed.

An SI integrated pest management model with pesticide resistance to susceptible pests

In this paper,epidemnic diseases among pests are assumed to occur,so pests are divided into susceptible pests and infected pests,and only susceptible pests are harmful to crops.Considering spraying pesticides and releasing of natural enermies and infected pests to control pests,as well as the long-term application of the same pesticide to induce resistance,an integrated pest management with pesticide resistance is established.The pollution emission model is introduced to model the action process of pesticides,which well reflects its residual and delay effects.By using comparison theorem of impulsive differential equation and analysis method,the threshold condition for eradication of susceptible pests is obtained.Then we analyze the frequency of spraying pesticide on the success of pests control.It shows that it is not that the more frequently pesticides are applied,the better the result of the susceptible pests control is.From the sensitivity analysis,the key factors on the threshold are obtained.Finally,the strategies to control susceptible pests are given,including switching pesticides and releasing infected pests and natural enemies elastically.