Nonlinear Delay Dynamic Model Of Forest Diseases And Insect Pests

Recently, research on plant diseases and insect pests which is common concerned has become one of the hottest issues at home and abroad.Especially, A lot of important theories and methods of modern mathematics and system control are applied to the forest protection study research which have made important progress.According to the quantitative descriptions of the actual development communication of some forest pests and diseases, we establish time-delay forest diseases and insect pests dynamic models by using those theories and methods, we systematically analyzed the Spreading law of the time-delay effect of diseases and pests,those results can provide theoretical support and basis to the comprehensive administration of forest diseases and insect pestsIn chapter two, we mainly discuss the model of forest insect pests with nonmonotonic incidence rate. Firstly, we prove the existence of disease-free equilibrium point and endemic equilibrium point, and the basic reproductive number denoted byR0is derived. WhenR0<1, by using the Lyapunov functional, we proved the disease-free equilibrium point is globally asymptotically stable; then, When Ro=1, the global attractively of disease-free equilibrium point is demon-started from Lyapunov-LaSalle invariance principle. Secondly, considering the proper Lyapunov functional, further to prove the local asymptotically stability of endemic equilibrium point. Finally, The correctness of the conclusion is verified by selecting the appropriate values for numerical simulation with Matlab.In chapter three, we mainly discuss a time-delayed epidemic model with a nonlinear incidence. Firstly, According to the characteristics of transmission of forest diseases and insect pests, we Set up the time-delay differential equation model which is more in line with the actual situation,and proved the existence of disease-free equilibrium point and endemic equilibrium point; then, we proved the global stability of disease-free equilibrium point and endemic equilibrium point by using the method of time-delay stability theory. Theoretical analysis shows that Small delay does not affect the stability of the positive equilibrium point under the special conditions. Finally, studying the numerical simulations with Matlab to evidence the conclusion of the theory.In chapter four, we mainly discuss the stability and time-varying transmission rates of the time-delayed epidemic model with a sublinear infection rate. Firstly, we proved the stability of disease-free equilibrium point and endemic equilibrium point when basic reproductive Ro is changed; secondly, Time-varying transmission of the time-delay systems is discussed, when the number of infected trees and the prevention and control of trees is known, the time-varying transmission rates are discussed respectively, and the expression of time-varying transmission rates is given at this time.