Mathematical Study On The Pest Control Model With Pesticide Resistance Under The Influence Of Pesticide Function

Considering that the effect of pesticides is continuous exponential function and pests will develop resistance to pesticides under repeated use of the same pesticides over a long period of time and combining the actual biological background,a single pest control model and a two population integrated pest management model with pesticide resistance under the effect of pesticide function are established and studied based on the theoretical knowledge of the resistance of pests and the theoretical research of existing literature.In the first chapter,the preliminary knowledge needed for our research is given.In the second chapter,we investigate a single pest management model with pesticide resistance development.Assume that the pest population satisfy the Logistic growth and are divided into susceptible pests to pesticide and resistant pests.We introduce pesticide function with residual effects,and the pest control model with pesticide resistance under the influence of pesticide function is established.The threshold condition of pest extinction is obtained by theoretical analysis.Further,numerical simulations show that the period of spraying pesticides affects the development of pest resistance.The shorter the period,the faster the pest resistance develops,and also we find that the threshold valueR₀（h,_NT）will be less than 1 in the beginning of spraying pesticide,which suggests that pesticides are very effective on controlling the pest populations.However,with the increase of spraying times,the resistance of pests will develop fast,and eventually the pest population will break out.Then,how to take measures to control the pest population is the next question to be discussed.On the one hand,if we take the threshold value as the criterion for the switching of pesticides,the optimal switching time of the pesticides is determined according to its expression;On the other hand,if we take the pesticide efficiency as the criterion for the switching of pesticides,when the number of pest populations for the first time increases in comparison with the previous one,the pesticides are switched to the new one.Comparing these two switching strategies for pesticides,it is not difficult to find that the switching time in the first strategy is earlier than that in the second strategy.In the third chapter,on the basis of the previous chapter,we investigate the dynamics of two population integrated pest management model with resistance development under the influence of pesticide function taking the same frequency of chemical control and biological control.The threshold condition of pest extinction is given.The results show that the integrated pest management model is more effective than any single chemical or biological control.Actually,in the beginning of pest control,single chemical control can control the pest population,and does not need to release natural enemies.However,once the pesticide resistance of the pest develops to a certain extent,the pest population will increase rapidly.In order to control the pests,we give the specific tactics for the release of natural enemies.Finally,according to the sensitivity analysis of the threshold valueR₀¹（h,_NT）to the parameters,it shows thatR₀¹（h,_NT）is positive correlation related to₃m,₄m,?₄ and negative correlation related to?,_NT and?₃.Since the absolute value of PRCC of?,_NT,₄m,?₄ is over 0.4,it shows that these parameters have great influences on the thresholdR₀¹（h,_NT）and play key roles in the pest control.