Research On Pest Management Model With Birth Pulse And Pesticide Function

Spraying pesticide is the most commonly used and convenient way on control pest strategies.How to efficiently use pesticide and minimize the damage of the pesticide to crops has been the problems we want to solve all the time.In this paper,pest populations are divided into two stages of immature and mature,it is assumed that mature population reproduce at fixed time every year,thus the increase of immature population is completed instantaneously,so this phenomenon can be simulated by the birth pulse model.In this paper,the three different pesticide functions are introduced,and we establish the pest control model with birth pulse and stage-structured under two different birth functions:Beverton-Holt function and Ricker function.The dynamics of such model is analyzed systematically.In the first chapter,biological background of this paper,model formulation and preliminaries which are needed in the process of the model analysis are given.Considering that the pesticide effect on pests will weaken over time,we give three different kinds of pesticide function.In the second and third chapters,piecewise function and negative exponential function is used to simulate the effect of the pesticide.The stability of trivial equilibrium and positive equilibrium of the model are analyzed,and we give the threshold conditions of pest eradication and permanence of the system.If the birth rate of the pest population0?27?b?27?b₀?0?27?p?27?p₀?,pest eradication periodic solution is locally asymptotically stable;ifb₀?27?b?27?b_c?p₀?27?p?27?p_c?,the model has a locally asymptotically stable positive periodic solution;ifb?29?b_c?p?29?p_c?,by numerical simulations,the dynamics of the system is very complex.By analyzing the sensitivity of the parameters,we obtain the key factors of the pest eradication or permanence of the system.In the fourth chapter,we use the pollutant discharge model to simulate the pesticide spraying process,then the pesticide function tends to a globally asymptotically stable periodic solution.Thus the dynamics are analyzed by using the limit system of the model.The stability of trivial equilibrium and positive equilibrium of the model is analyzed,and the threshold conditions of pest eradication and permanence of the system are given.We obtain the optimal frequency of spraying pesticide by numerical simulations.The important parameters related to the pest eradication or permanence of the system are given by analyzing the sensitivity of the parameters.