Study On Two Population Model And Properties Of Plant Diseases And Insect Pests

At present,when vigorously advocating the concept of green environmental protection development,the study of plant pest prevention and control becomes more and more important,especially the mathematical analysis of plant pests and diseases can provide important theoretical basis for our prevention and control management.In this paper,the theory and method of stability of differential equation and functional differential equation are used to study the model and dynamic behavior of single and two species of plant diseases and insect pests,providing theoretical basis for plant diseases and insect pests control.The first part studies the structure model of plant diseases and insect pests with bilinear incidence.A class of SEIR model with bilinear incidence rate is established for plant population.The equilibrium points of pest-free and pest-disease are calculated.The stability of pest-free and pest-free equilibrium points is discussed based on LaSalle invariant set principle and Routh-Huritz decision theorem.Sufficient conditions for local asymptotic stability of the equilibrium points are given.The second part studies plant disease and insect pest models with saturated incidence.Considering the saturation factor in the non-linear part of the model and adding a saturation incidence rate,the basic regeneration number of the system is calculated and the disease-free equilibrium point and the pest-disease equilibrium point of the system are obtained by calculating.Secondly,the first approximation method of stability is used to prove the local asymptotic stability of disease-free equilibrium,and the conclusion is verified by numerical simulation with matlab.Comparing with the numerical simulation results of the first part,the differences of the characteristics between the plant disease and insect pest models with saturated incidence and those without saturated incidence were analyzed.The third part studies plant disease and insect pest models of plant and pest.Assuming that plant growth conforms to logistic growth,a model consisting of susceptible plants,infected plants,healthy pests and infected pests is established.Firstly,the basic regeneration number of the system is obtained.By judging the existence of the system equilibrium point,the existence of the system pest equilibrium point is given.Then the equilibrium points of the models under different conditions are obtained.The stability analysis of equilibrium point is carried out by using Hurwitz theorem,and the conditions for local stability of equilibrium point are obtained.Finally,the exact value of the equilibrium point of the model is obtained by the parameter values satisfying the conditions,and the meaningful and existing equilibrium points are simulated by MATLAB software.The conclusion of the theorem is analyzed and verified,and the reference basis for the actual prevention and control of pests and diseases is provided through comparative analysis.