Effect Of Spatial Factors And Control Strategies Within Each Generation On Pest Management

In agricultural production,pest management has attracted great attentions for the farmers.Spraying pesticide is one of its main management tactics,and how to evaluate its effectiveness and analyze the key factors are of great concern to the agricultural management department.Note that mathematical model is useful to evaluate its effectiveness and help to find the key factors influencing the pest control.In pest management,the control strategies usually are implemented within each generation of the pest growth.The question is how to use difference equation models to describe the pest population growth with control measures which are applied within each generation for the pests with non-overlapping generations?Moreover,pest dispersal is also a key factor affecting pest management,another question is how to introduce spatial factors into pest management models?and then how to analyze the pesticide efficacy,the timing of pesticide application,the space factor which could result in paradoxical effects during the pest control?In order to answer those questions,the second chapter of this thesis first assumes that the growth stage of the pest population within each generation follows the Logistic equation,and assumes that pesticides are sprayed once within each generation.By some theoretical analyses,we have developed a new discrete model,which could depict the control measures applied within discrete generation,a so-called extended Beverton-Holt model.Furthermore,taking the spatial factors into account,an integrodifference equation model has been proposed as follows:For the above model,we first choose the exponential distribution function as the dispersal kernel,obtain the critical wave speed and the travelling wave solution of the model,then simulate the shape of the travelling wave solution.When the dispersal kernel is the bilateral exponential distribution function and the parameters satisfy certain conditions,by some theoretical analyses,we have proven that the wave converges to the positive equilibrium at +?.Next,we analyze the effect of parameters on the critical wave speed and the travelling wave solution by simulation.In order to investigate the effects of dynamic complexity on pest control and spread,the third chapter of this thesis first establish a pest management model with dynamic complexity,then analyze the effects of the pesticide efficacy and timing of pesticide application on the positive equilibrium,get a threshold killing rate q*:the density of the pest population could be enhanced if a low dose of pesticide is applied under the condition q<q*.In order to investigate the effects of dynamic complexity on pest dispersal,we develop a pest dispersal model with dynamic complexity in section 3.2.Given the exponential distribution function as the dispersal kernel,we obtain the critical wave speed and analyze the effect of parameters on the critical wave speed.When the dispersal kernel is the bilateral exponential distribution function and the parameters satisfy certain conditions,the wave speed is larger than the critical wave speed,we prove that the wave converges to the positive equilibrium at +?.Finally,we analyze the effect of parameters on the travelling wave solution by simulation.The main results of this thesis are as follows:without considering the influence of dynamic complexity on pest dispersal,the larger the survival rate is,the faster the critical wave speed c*is,while the timing factor ? does not affect the c*.When the travelling wave solution exists,the larger survival rate and the earlier timing of pesticide application will cause the increase of the population density.In order to investigate the effects of dynamic complexity on pest control and spread,the larger the survival rate is,the faster the critical wave speed c*is,while the timing factor? does not affect the c*.When the survival rate is larger,the model will produce chaotic phenomena.When the timing of pesticide application and the survival rate is in the appropriate range,population density and dispersal will appear differences between odd and even generations.The main results confirm that the earlier the pesticide application and the smaller survival rate,the more easily do paradoxical effects occur,and then bring greater challenges to pest control.